Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Game theory — strategic interaction and its equilibria — evolutionary stability, repeated games, bargaining, coordination, signalling and conventions — in biology, economics and philosophy (ADR-019).
54 of 2004 LIT documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| LIT-067 v2 | A Social Equilibrium Existence Theorem | Debreu (1952), DOI-10.1073/pnas.38.10.886. Debreu proves existence of an equilibrium for an “abstract economy” (generalized game), in which each agent’s feasible set A_ι(ā_ι) depends on the others’ actions. The conditions: each action set 𝔄_ι is a contractible polyhedron; A_ι has a closed graph with non-empty compact values; f_ι is continuous on the graph into the extended reals; the value function φ_ι(ā_ι) = max f_ι is continuous; and each best-response set M_ā_ι is contractible. The proof applies the Eilenberg–Montgomery/Begle fixed-point theorem to the product best-response map. A Remark replaces the joint continuity of φ_ι with continuity (lower hemicontinuity) of A_ι plus a compact graph. A Corollary gives a saddle-point theorem that contains Kakutani’s and von Neumann’s. | Active — read in full 2026-09-25 (NOTE-037); the original existence theorem for generalized (constrained) games, underlying Arrow–Debreu (1954). Short, fully self-contained, and still the canonical citation. Later results (Shafer–Sonnenschein 1975; the generalized-Nash literature) weaken its hypotheses but do not supersede it as the source. |
| LIT-473 v2 | Convention: A Philosophical Study | Lewis (1969), DOI-10.1002/9780470693711 (the 2002 Blackwell reissue). The founding analysis of convention as a self-perpetuating solution to a recurring coordination problem with more than one equilibrium, sustained by a system of mutual expectations rather than by agreement, with conventions of language and communication as the main application. Unread: filed from catalogue records and chapter titles; the content summary is as Hindriks & Guala and the SEP entry state it. | Unavailable — filed 2026-10-02 from catalogue records and the chapter list, not read: no lawful full text was reachable. The Harvard 1969 edition is lending-only at the Internet Archive (access-restricted, printdisabled), and the Wiley-Blackwell reissue of 2002 is paywalled. What the book argues is known here only through readings that state it (Hindriks & Guala, LIT-481; the SEP entry, LIT-487), and is labelled as theirs. It stays Unavailable until a copy is supplied. |
| LIT-481 | Institutions, rules, and equilibria: a unified theory | Hindriks & Guala (2015, online 2014), DOI-10.1017/S1744137414000496. Institutions are rules in equilibrium: correlated equilibria of coordination games with several equilibria, which the players represent to themselves as rules. Searle’s constitutive rules (“X counts as Y in C”) are obtained from a regulative rule by splitting it with a new term, a base rule (X is Y) and a status rule (if Y then Z). The new term is conservative and eliminable, so the constitutive-rules account reduces to the rules-in-equilibrium account, and Lewis’s theory of theoretical terms says the term refers if the rules are true. Shown on one toy institution (first-occupancy property); general reduction asserted. | Active — read in full 2026-10-02 (NOTE-395), with the authors’ reply to their six commentators in the same issue; worth reading as the shortest statement of the rules-in-equilibrium theory of institutions and of the claim that Searle’s constitutive rules are regulative rules with a name added. The equilibrium half is a clear synthesis of Lewis, Aumann, Aoki and Greif. The reduction of constitutive rules is shown on one toy institution and asserted in general, and it leans on a reading of “collective acceptance” loose enough to make it hard to fail. |
| LIT-493 v2 | The Grammar of Society: The Nature and Dynamics of Social Norms | Bicchieri (2006; print December 2005), DOI-10.1017/CBO9780511616037. Per its publisher, an integrated account, drawing on social psychology, experimental economics and evolutionary game theory, of how social norms such as fairness, cooperation and reciprocity emerge, why and when people follow them, when they attend to the relevant norm, why inefficient norms survive, and how psychological dispositions can lead to fairness norms like ours. Unread: filed from the description and contents only. | Unavailable — filed 2026-10-02 from the publisher’s description and table of contents, not read: no lawful full text was reachable. Cambridge Core is paywalled. The author’s own copy of chapter 1 on her University of Pennsylvania pages and the publisher’s excerpt at assets.cambridge.org both failed (HTTP 403; connection reset), and the Internet Archive has no copy. It is the standard equilibrium-and-expectations account of social norms; what its definition of a norm says was not seen. It stays Unavailable until a copy is supplied. |
| LIT-498 | The Evolution of Cooperation | Axelrod & Hamilton (1981), DOI-10.1126/science.7466396. In an iterated Prisoner’s Dilemma with probability w of meeting again, TIT FOR TAT won two computer tournaments (14 and 62 entries) and an ecological simulation, and no strategy can do better against it when w ≥ max((T−R)/(T−P), (T−R)/(R−S)). ALL D is always stable; reciprocity can still enter through kinship or a cluster, after which a nice stable strategy resists clusters. Applications range from cleaner fish to disease and nondisjunction. | Active — read in full 2026-10-02 (NOTE-411); worth reading as the formal statement of how reciprocity can start, spread and hold: tit-for-tat is robust in Axelrod’s tournaments, cannot be bettered by any mutant when the continuation probability w is high enough, and can enter an all-defect population through kinship or clustering. “Evolutionarily stable” is stronger than what is proved: the proof shows no strategy does better than TIT FOR TAT, and always-cooperate does as well, which Boyd & Lorberbaum (1987) later turned into a proof that no pure strategy is evolutionarily stable in the repeated game. It grounds the exchange domain of morality-as-cooperation; it is not about morality. |
| LIT-501 | Five Rules for the Evolution of Cooperation | Nowak (2006), DOI-10.1126/science.1133755. Five mechanisms let natural selection favour cooperators who pay c to give b: kin selection (r > c/b), direct reciprocity (w > c/b), indirect reciprocity (q > c/b), network reciprocity (b/c > k) and group selection (b/c > 1 + n/m). Each is cast as a 2×2 game, from which conditions for cooperators to be evolutionarily stable, risk-dominant or advantageous follow. Punishment is said not to be a mechanism. Cooperation is proposed as a third principle of evolution. | Active — read in full 2026-10-02 (NOTE-409), main text only; the online supplement with the derivations was not read. Worth reading as the standard short map of mechanisms for the evolution of cooperation (kin selection, direct, indirect and network reciprocity, group selection), each reduced to a benefit-to-cost threshold from a 2×2 game. Every mechanism is modelled with the donation game, so it covers altruism only: mutualism, coordination and conflict resolution, four of morality-as-cooperation’s seven domains, are outside it. Its one sentence on morality credits indirect reciprocity with “the evolution of morality”, citing Alexander (1987). |
| LIT-503 | Morality as Cooperation: A Problem-Centred Approach | Curry (2016), DOI-10.1007/978-3-319-19671-8_2. Morality is “a collection of biological and cultural solutions to the problems of cooperation and conflict recurrent in human social life”. Nonzero-sum game theory yields seven problems (kin, coordination, exchange, hawkish and dovish contest displays, division, possession) and hence seven moral domains, illustrated but not tested. The chapter predicts that non-cooperative behaviour is morally neutral everywhere, and that MFT’s purity domain has no connection to cooperation. | Proposed — read in full 2026-10-02 (NOTE-408); the founding statement of morality-as-cooperation and the place its predictions are stated most sharply, including the one its own tests have not run: that behaviour unrelated to cooperation will be morally neutral, and that no culture’s morality will be about “aesthetics or nutrition” (p. 40). It reports no data. The seven domains are derived from game theory and then illustrated with quotations from philosophers and ethnographers, so the chapter shows the taxonomy is coherent, not that it is the right one. It would be settled by the test LIT-047 lacks: blind coding of all moralized content in one sample, asking whether non-cooperative domains are moralized. |
| LIT-505 | The Logic of Animal Conflict | Maynard Smith & Price (1973), DOI-10.1038/246015a0. Why do animals with dangerous weapons fight conventionally? A simulation of five strategies (Mouse, Hawk, Bully, Retaliator, Prober-Retaliator) shows Hawk is not an evolutionarily stable strategy while Retaliator nearly is, so “limited war” can be favoured by individual selection. In a pure war of attrition no fixed persistence is stable; the ESS is an exponential mixture. There is no Hawk–Dove game and no ownership asymmetry here. | Active — read in full 2026-10-02 (NOTE-404); worth reading as the paper that introduced the evolutionarily stable strategy and showed that “limited war” in animal contests can be favoured by individual selection. It is not the source of the Hawk–Dove game or of owner–intruder conventions, though morality-as-cooperation cites it for both: its strategies are Mouse, Hawk, Bully, Retaliator and Prober-Retaliator, its contestants are symmetric, and its “Retaliator is an ESS” ties with Mouse, so it fails the paper’s own second ESS condition. What it does ground for MAC’s contest domains is restraint backed by retaliation, and, informally, retreat before a visibly superior opponent and honest signals of formidability. |
| LIT-583 v2 | Breakdown of Will | Ainslie (2001), Cambridge University Press. The book-length statement of picoeconomics: hyperbolic discounting makes a person a population of bargaining interests, and will is the recursive bundling of choices into precedents. Unread: registered from the publisher’s description and the précis, LIT-586, which stands in for it. | Unavailable — registered 2026-10-03 from the publisher’s description and from the outline of the book given in its précis, not read. Not open access: Unpaywall reports no open copy, and no author deposit of the book was found (the author’s site, picoeconomics.org, carries the précis and articles, not the book). The owner suggested the précis instead, and it is read and filed as LIT-586 (NOTE-443), which follows the book’s three sections and twelve chapters. The book is kept as the citation others reach for. A human with library access could read chapters 5-8 (the bargaining model and its evidence) against the précis. |
| LIT-586 | Précis of Breakdown of Will | Ainslie (2005), Behavioral and Brain Sciences 28(5), the précis of Breakdown of Will (2001). People and other animals discount delayed rewards hyperbolically, so preferences reverse as a smaller, sooner reward comes near, and a person becomes a population of reward-seeking “interests” that must forestall one another. Willpower is the bundling of future choices by treating the present one as a precedent: an intertemporal repeated prisoner’s dilemma, not an organ or a top-down ego. The same recursion predicts the will’s costs: legalism, circumscribed “lapse districts”, motivated blindness to lapses, and rules that favour countable goals over subtle ones. | Active — read in full 2026-10-03 (NOTE-443), as the substitute for the 2001 book (LIT-583), which the owner suggested and which the précis follows chapter by chapter. Worth reading as the shortest complete statement of picoeconomics in Ainslie’s own words. Hyperbolic discounting makes preference reverse as a smaller, sooner reward draws near, so a person behaves like a population of “interests” that bargain across time. Will is not a faculty above them but a recursive self-prediction: treating each choice as a precedent “bundles” future rewards, an intertemporal repeated prisoner’s dilemma in which “credibility is power”. The same mechanism predicts the will’s side effects: legalism, “lapse districts”, motivated misperception and compulsive over-control. |
| LIT-700 | Three kinds of collective attitudes | List (2014), Erkenntnis 79(S9):1601–1622. Collective attitudes come in three kinds. Aggregate attitudes summarise members’ attitudes by a rule or a market, supervene proposition-wise and need not be rational. Common attitudes are held by all members with common awareness, matter for coordination, and inherit consistency from their unanimity. Corporate attitudes belong to a group agent, guide its action, supervene holistically on members’ contributions and must be rational. The kinds are almost logically independent, and fears and hopes divide the same way as beliefs and desires. | Active — read in full 2026-10-04 (NOTE-554); worth reading as the disambiguation the collective-attitudes literature needs: aggregate attitudes (summaries, supervening proposition by proposition), common attitudes (unanimous and commonly known, supervening on a slightly enriched base) and corporate attitudes (a group agent’s, supervening holistically and not straightforwardly reducible). The three are almost logically independent. A review by its own description, with no new theorem; its value for this record is that it names fears and hopes among the attitudes the split applies to, which gives the collective-emotion debate a vocabulary. |
| LIT-719 | Beyond Markets and States: Polycentric Governance of Complex Economic Systems | Ostrom (2009), Nobel lecture; AER 2010. Polycentric arrangements of many formally independent decision centres can perform better than a single hierarchy. Long-surviving common-pool resource institutions share eight design principles, among them monitoring by users or those accountable to them, graduated sanctions, local conflict resolution and nested layers. Communication and self-chosen sanctions raise cooperation in experiments. Fit to local conditions matters more than the type of regime. | Active — read 2026-10-05 (NOTE-563): the Nobel Prize lecture in full, from the Nobel Foundation’s PDF. Worth reading as Ostrom’s own summary of fifty years of work: polycentricity defined, the eight design principles of long-surviving common-pool resource institutions in their updated form, the experiments on communication and self-chosen sanctions, the field evidence on local monitoring, and the warning against single policy prescriptions. A retrospective lecture, not a report of new results. |
| LIT-737 v2 | Governing the Commons: The Evolution of Institutions for Collective Action | Ostrom (1990), Cambridge University Press: from case studies of long-enduring and failed common-pool resource institutions, argues that resource users can and do govern commons themselves, without either privatisation or state control, and proposes design principles shared by the institutions that lasted. Unread: the principles are read in Ostrom’s Nobel lecture LIT-719. | Unavailable — registered 2026-10-05 from Crossref, not read: no lawful full text could be reached (Cambridge Core is closed). Its design principles are read first-hand in Ostrom’s Nobel lecture (LIT-719), §4E, in the updated wording of Cox, Arnold & Villamayor-Tomás that she adopts there. Filed because an essay the owner is writing cites “Ostrom’s work on differentiated and polycentric governance”. It stays Unavailable until a copy is supplied, not on merit. |
| LIT-809 v2 | That’s what she (could have) said: How alternative utterances affect language use | Bergen, Goodman & Levy (2012), Proceedings of the 34th Annual Meeting of the Cognitive Science Society, 120–125. Recursive speaker–listener reasoning yields specificity implicatures, but cannot derive Horn’s principle from costs alone; adding uncertainty over the lexicon does, in one-shot signalling games, without equilibrium refinements. Two online games with novel symbols find both implicatures drawn without prior conventions. | Active — read 2026-10-09 (NOTE-613); worth reading as the paper in which the RSA recursion is made to derive Horn’s division of pragmatic labour (costlier forms for less likely meanings) in one-shot signalling games with no prior conventions: the basic recursion cannot break the symmetry between equally meaningless costly and cheap signals, but a listener and speaker uncertain about the lexicon, marginalizing over every lexicon that could assign the signals meanings, converge on the efficient mapping without an equilibrium-selection rule. Two small Mechanical Turk games (40 and 140 participants) show people drawing specificity and Horn implicatures among novel symbols in five rounds, with no first-round difference. Source, with LIT-821 and LIT-816, of THEORY-172. |
| LIT-843 | Combining contextuality and causality: a game semantics approach | Abramsky, Barbosa & Searle (2024), ARXIV-2307.04786, Phil. Trans. R. Soc. A 382:20230002. Adds an enabling relation to a measurement scenario and reads contextuality as a game: the Experimenter chooses measurements, Nature chooses outcomes, and Nature’s deterministic strategies replace the event sheaf. Recovers flat contextuality and Gogioso–Pinzani causal Bell scenarios, and expresses adaptive MBQC by Experimenter strategies. The strategy presheaf is not a sheaf: compatible deterministic strategies can fail to glue or glue non-uniquely. | Active — read in full 2026-10-09 (NOTE-646); worth reading as the version of sheaf-theoretic contextuality in which measurements are performed in a causal order and the choice of the next one may depend on earlier outcomes. A causal measurement scenario adds an enabling relation (Kahn and Plotkin’s information matrices renamed); Nature’s deterministic strategies over it replace the event sheaf, and the Abramsky–Brandenburger definitions of empirical model and contextuality then go through unchanged. Flat scenarios and Gogioso and Pinzani’s Bell scenarios with a causal order come out as special cases, and Experimenter strategies express adaptive measurement, as in the Anders–Browne GHZ OR-gate. Its sharpest point is that the strategy presheaf is not a sheaf: deterministic, compatible local strategies can fail to glue (Example 7.2) or glue non-uniquely (Example 7.3). A short paper; several results are deferred to an extended version. |
| LIT-966 v2 | Cooperative Dilemmas in Rational Debate | Handfield et al. (2025). Two debaters in a Betz-style logical space choose fixed argument strategies, with payoff w·v − d (true beliefs against changes of mind). At low and moderate truth weights the game is a cooperative dilemma: a prisoner’s dilemma, stag hunt or, most often, a snowdrift in which one debater argues boldly and the other free-rides. At low weight both exit. At high weight in short debates mutual boldness is the unique, truth-optimal equilibrium. In a narrow band of mixed equilibria, raising the truth weight slightly lowers collective accuracy. All exact results are for n = 3 propositions. | Active — read 2026-10-14 (NOTE-795) in full; worth reading as a clean game-theoretic statement of epistemic free-riding in debate. Two deductive reasoners who value true beliefs but pay for each change of mind face a cooperative dilemma at low and moderate truth weights: typically one argues boldly and the other free-rides, and at low weights both exit. Read it knowing that it models two people and three propositions, that its outcome is collective accuracy and not a shared belief, and that the drop in accuracy as truth motivation rises is small and confined to a narrow band of mixed equilibria. Filed for QUESTION-047; THEORY-290 holds what it shows. |
| LIT-1021 v2 | Bayesian Persuasion | Kamenica & Gentzkow (2011), Am. Econ. Rev. 101(6): 2590–2615. With a common prior and a signal the receiver observes and the sender commits to, any distribution of posteriors that averages to the prior can be induced. The sender’s best value is the concave closure of its value over posteriors, at the prior. A Bayesian judge who knows the investigation was designed to convict convicts 60 percent of defendants when 70 percent are innocent. At the optimum the receiver is certain when she takes the sender’s worst action and indifferent otherwise. Blackwell is not cited and manipulation is not analysed. | Active — read in full 2026-10-13 (NOTE-717) from the published AER PDF posted on Gentzkow’s Stanford faculty page (web.stanford.edu/~gentzkow/research/BayesianPersuasion.pdf); the online Appendix was not read. Registered at the owner’s request from the survey of the Mathematics of Meaning corpus, for QUESTION-070 and QUESTION-071. Worth reading for the result that an overt, committed choice of experiment moves a fully informed Bayesian receiver, and for the optimum’s signature: certainty when she takes the sender’s worst action, indifference otherwise. It does not analyse manipulation and does not cite Blackwell. |
| LIT-1214 v3 | Some constraints and tradeoffs in the design of network communications | Akkoyunlu, Ekanadham & Huber (1975). A design paper on interprocess communication in networks of sequential processes. Complete status of a transaction is impossible in an arbitrary distributed facility and, with time-outs, even in a reliable one; an intermediate process can be made invisible only if the system withholds status it knows. Its appendix proves, as a story of gangsters and a messenger who may be mugged, that no finite exchange over a lossy channel brings two parties to know they agree the message got through: later called the coordinated attack or two generals problem. | Active — read 2026-10-29 (NOTE-1410) in full, from a scan of the SOSP ‘75 pages on the TU Wien Distributed Systems Group’s course page (https://dsg.tuwien.ac.at/linksites/teaching/courses/AdvancedDistributedSystems/download/1975_Akkoyunlu,%20Ekanadham,%20Huber_Some%20constraints%20and%20tradeoffs%20in%20the%20design%20of%20network%20communications.pdf); worth reading as the earliest statement the record holds, with a proof, that no finite exchange over a lossy channel brings two parties to know they agree a message got through: the coordinated attack problem in substance, three years before Gray (1978). Read it knowing that the result is a one-page appendix to a design paper on interprocess communication, told as gangsters and a messenger, that its goal is mutual knowledge of delivery rather than coordinated action, and that its fuller proof is deferred to an unpublished working paper. |
| LIT-1313 v2 | Information Design: A Unified Perspective | Bergemann & Morris (2019). Given a game with uncertain payoffs, information design asks how far the provision of information alone can influence players’ behaviour; under a literal reading there is a designer who commits to an information structure, under a metaphorical one the analyst characterizes play across all information structures, and the two readings unify communication in games, Bayesian persuasion and robust prediction. What an omniscient designer can attain is exactly the set of Bayes correlated equilibria, given by linear obedience constraints. | Active — read 2026-10-21 (NOTE-1034) in full, from Cowles Foundation Discussion Paper 2075R3 (March 2018, the accepted manuscript); worth reading as the general frame for designing what others know: what an omniscient designer can bring about is exactly the Bayes correlated equilibria, a polytope given by linear obedience constraints (THEORY-844), read literally as a designer’s reach and metaphorically as a bound over all information structures, with prior information shrinking it and an incentive order that extends Blackwell’s (THEORY-853). Read it knowing that it is a survey whose central results are proved in the authors’ other papers, that its players are Bayesian with a common prior, and that its two-firm example with strategic substitutes states an optimal rule that is infeasible under the parameters it assumes (the copy read; the JEL text was not compared). |
| LIT-1318 v3 | When Is Society Susceptible to Manipulation? | Mostagir, Ozdaglar & Siderius (2022). In a social-learning model a principal manipulates agents’ beliefs by using the same forces that produce the wisdom of the crowd; characterizes the social norms and network structures susceptible to such manipulation, the conditions under which a network is impervious to it, and a new centrality measure. | Unfetched — filed 2026-10-21; on 2026-10-21 a lawful full text was sought and none was reached, so no NOTE is filed. Open copies exist, so this failed on access, not availability. The authors’ working paper is in the University of Michigan’s Deep Blue repository (handle 2027.42/154046, files reputation-v11Submit.pdf and manipulation-final.pdf, by web search), but every Deep Blue URL tried (handle page, item page, bitstream and REST API) returned a Cloudflare browser check to this client, and WebFetch got HTTP 403. A copy on James Siderius’s MIT LIDS site (siderius.lids.mit.edu/wp-content/uploads/sites/36/2021/09/manipulation.pdf, by web search) failed DNS resolution from this client, and Mohamed Mostagir’s Michigan page (public.websites.umich.edu/~mosta) returned 403; mostagir.engin.umich.edu was refused by the proxy. CORE holds Deep Blue’s copy (core.ac.uk/download/287611458.pdf), which returned 403 to curl and to WebFetch, and CORE’s API withholds the full text from public users. SSRN (doi:10.2139/ssrn.3474643, which Unpaywall lists as the only open location) returned 403. Unpaywall and OpenAlex list the Management Science article as closed, Semantic Scholar had no record of its DOI, and arXiv has no copy. A copy the owner supplies would let it be read. |
| LIT-1326 v2 | Algorithmic monoculture and social welfare | Kleinberg & Raghavan (2021). In a model of two firms hiring from one pool by noisy rankings, if both use the same algorithm, even one more accurate than their private rankings, the quality of decisions can fall without any shocks: under two conditions on the ranking model, for every private accuracy there is a more accurate shared algorithm that is strictly dominant for both firms and lowers both firms’ utility and social welfare, a Braess paradox. The Mallows model always meets the conditions; Plackett–Luce never does. | Active — read 2026-10-21 (NOTE-1033), from arXiv:2101.05853v2: the main text and Appendices A, B and E in full, Appendices C, D and F in statement; worth reading for the exact conditions under which a shared, more accurate screening algorithm is dominant for every firm and still lowers welfare without any shock (THEORY-835), and for the identity that makes independence valuable to a second mover. Read it knowing that the model has two firms hiring one candidate each, that the conditions hold for Mallows rankings always, for Gaussian and Laplacian random utility models with three candidates, and never for Plackett–Luce, and that the losses measured are small (about 4% in one instance). |
| LIT-1375 v3 | Diplomacy and domestic politics: the logic of two-level games | Putnam (1988). Models international negotiation as two games played at once: a chief negotiator bargains with foreign counterparts while any agreement must be ratified at home, so a deal is possible only where the domestic win-sets overlap. A win-set’s size depends on domestic preferences and coalitions, ratification institutions and the negotiators’ strategies; a small one is both a bargaining advantage and a risk of involuntary defection, and domestic division can make agreement easier. | Active — read 2026-10-30 (NOTE-1436) in full, from the JSTOR scan posted on a course page of the Athens University of Economics and Business (eclass.aueb.gr, course DEOS290), read through the OCR text of another download of the same scan at gwern.net/doc/politics/1988-putnam.pdf, the course copy having no text layer; worth reading as the standard statement of two-level games: a negotiator bargains abroad over a deal that must be ratified at home, so the overlap of domestic win-sets decides whether a deal is possible, and their size who gains. Read it knowing that it is a framework illustrated by cases, chiefly the 1978 Bonn summit, with no formal solution, and that it treats one negotiation at a time. |
| LIT-1389 v4 | Willpower and Personal Rules | Bénabou and Tirole (2004). Models personal rules as self-reputation: an agent with imperfect recall of its own past motives reads its own lapses and successes as evidence about its willpower, so a single lapse can become a damaging precedent and rules can be self-enforcing or brittle. | Unfetched — no lawful copy reached, 2026-10-22; failed on access. Lawful copies exist and could not be fetched: Roland Bénabou’s Princeton page hosts the paper (rbenabou.scholar.princeton.edu/document/34) behind a Cloudflare check that refused every request, and the CEPR working-paper version (DP3143) is on SSRN and the CEPR site, both of which returned 403. Unpaywall and OpenAlex list only the SSRN copy; the RePEc listings of the Princeton and CEPR working papers carry no file; the Toulouse repository pages returned 404 or 500; the Internet Archive’s Wayback Machine was blocked by this client’s network policy. The owner can fetch the Princeton copy in a browser. Registered from the owner’s exchange of 2026-10-22, “Graph Learning Applications”. No NOTE is filed. Tried again once on 2026-10-30: the Princeton address answered HTTP 403 with a Cloudflare challenge (cf-mitigated: challenge), which was not retried. Free copy: rbenabou.scholar.princeton.edu/document/34. |
| LIT-1418 v2 | Economic Interdependence and War: A Theory of Trade Expectations | Copeland (1996). Proposes trade-expectations theory to reconcile liberal and realist views of interdependence: what matters is not the present level of trade but a state’s expectations of future trade. A highly dependent state that expects trade to continue has reason for peace; one that expects to be cut off has reason to fight while it still can, so high interdependence with negative expectations makes war likelier. Standardly cited with historical cases from the great-power wars. | Unavailable — filed 2026-10-23, not read. A lawful full text was sought on 2026-10-29 and not reached. OpenAlex reports it closed: MIT Press, JSTOR (doi:10.2307/2539041) and Project MUSE offer it behind subscriptions. A web search found no author-posted copy; the later book (Princeton, 2014) is not this work. It stays Unavailable until a copy is supplied. No NOTE is filed. |
| LIT-1442 | Flows and Decompositions of Games: Harmonic and Potential Games | Candogan, Menache, Ozdaglar & Parrilo (2011), Mathematics of Operations Research 36:474–503. The space of finite games is a direct sum P ⊕ H ⊕ N of potential, harmonic and nonstrategic subspaces (Theorem 4.1), pulled back from the Helmholtz decomposition of the game graph’s flow of unilateral payoff differences. Potential games are P ⊕ N (Theorem 5.1). Harmonic games, such as rock–paper–scissors, generically have no pure equilibrium, and the closest potential game is given in closed form under a weighted l2 norm (Theorem 6.2). | Active — read 2026-10-23 (NOTE-1116): in full, from arXiv 1005.2405v2 (45 pp.). Every finite game in strategic form splits uniquely into a potential, a harmonic and a nonstrategic component. The split pulls back the Helmholtz decomposition of the flow of unilateral payoff differences on the game graph. Potential games are exactly the games with no harmonic component. Harmonic games generically have no pure equilibrium. The nearest potential game, in a weighted l2 norm, is given in closed form. It is the paper behind the record’s measure of a potential’s share of a negotiation, and it shows that the share is cardinal. |
| LIT-1462 v3 | Potential Games | Monderer & Shapley (1996), Games and Economic Behavior 14:124–143. The paper defines exact, weighted, ordinal and generalized ordinal potentials for games in strategic form, and it is reported (Lemma 2.5, per Duersch et al.) to show that a finite game has the finite improvement property exactly when it has a generalized ordinal potential. Unread: no lawful copy was reached by this client. | Unfetched — registered 2026-10-23 from Crossref, not read: a lawful copy exists but this client could not fetch it, so this failed on access, not availability. OpenAlex lists the paper as closed, with no repository copy. The publisher (ScienceDirect) is paywalled. Two course-page copies were found: Frieze’s INFONET reading list at CMU, www.math.cmu.edu/~af1p/Teaching/INFONET/Papers/EconomicModels/PotGam.pdf, and a Bowdoin course page, tildesites.bowdoin.edu/~mirfan/files/3210/Monderer_Shapley_1996_Potential%20Games.pdf. Both failed TLS certificate verification from this client on 2026-10-23 and again on 2026-10-30 (curl error 60: the chain each serves ends at emSign Root CA - G1, which this client does not trust; verification was not overridden). A second fetcher got HTTP 503 from both on 2026-10-23. An author upload on ResearchGate (Monderer’s) was not tried, and Unpaywall was skipped because it requires an email address. Its central lemma, that a finite game has the finite improvement property exactly when it has a generalized ordinal potential, is held only as later papers restate it: Duersch, Oechssler and Schipper (arXiv 1003.4274) attribute it to Lemma 2.5, and Candogan et al. (LIT-1442) restate its equilibrium results. The record’s own proof of the finite case is in THEORY-896, which this paper bears on. Filed because the record is renaming “ascendancy” to “potential” in this paper’s sense. It stays Unfetched until a copy is supplied, not on merit; either course copy, fetched by hand, would clear it. Free copies: www.math.cmu.edu/~af1p/Teaching/INFONET/Papers/EconomicModels/PotGam.pdf; tildesites.bowdoin.edu/~mirfan/files/3210/Monderer_Shapley_1996_Potential%20Games.pdf. |
| LIT-1475 v3 | Cooperation under the Security Dilemma | Jervis (1978). Anarchy and the security dilemma, in which what increases one state’s security decreases another’s, make common interests hard to realize. Modelled as a Prisoner’s Dilemma, cooperation is likelier when the costs of being exploited and gains from exploiting are low, gains from mutual cooperation and costs of mutual defection are high, and each side expects the other to cooperate. The dilemma eases when defence has the advantage and defensive postures are distinguishable from offensive ones, giving four security worlds shaped by geography and technology. | Unavailable — filed 2026-10-24 from the owner’s exchange of 2026-10-23/24, shared at https://chatgpt.com/share/6adc1ece-bb28-83e9-a8f6-cadf0f8b7113, where it is cited at turn U16; a reading was attempted on 2026-10-24 and failed on availability. The article is closed: Unpaywall, OpenAlex and Semantic Scholar list no open copy and no repository full text, and JSTOR and Cambridge Core offer it only by subscription or purchase. Web copies exist only as JSTOR downloads reposted on course and personal pages (sfu.ca, a USP course site), which are not lawful public copies and were not used. It stays Unavailable until a copy is supplied. No NOTE is filed. |
| LIT-1484 | The Hive Mind is a Single Reinforcement Learning Agent | Soma, Bouteiller, Hamann and Beltrame show that in an infinite, well-mixed population, imitation of success has the expected update of a single Cross Learning bandit agent, and the weighted voter model of the honey-bee waggle dance the expected update of “Maynard-Cross Learning”, π_a ← π_a + (r_k / v^π)(1[a = k] − π_a), which is the Maynard-Smith replicator dynamic. Each member is one parallel action sample of the population’s policy, and the members themselves do not learn. Simulations, qualitative by the authors’ account, show the result surviving moderate swarm and neighbourhood sizes, and finite populations losing options for good. | Active — read in full 2026-10-24 (NOTE-1132) from arXiv v6 (21 July 2026, CC BY 4.0); worth reading as a proved aggregation result: in an infinite, well-mixed population, two imitation rules with no individual learning have the expected update of a single bandit-learning agent. Imitation of success gives Cross Learning (the Taylor replicator dynamic), the honey-bee weighted voter model gives what the authors call Maynard-Cross Learning (the Maynard-Smith replicator dynamic). The macro-agent is a stateless bandit policy over the members’ types. The biological model is deliberately partial, the simulations qualitative, and pure imitation has no way back once a type is lost or the environment changes. |
| LIT-1501 | A selection-mutation model for Q-learning in multi-agent systems | Tuyls, Verbeeck & Lenaerts (2003). Derives the continuous-time dynamics of Boltzmann Q-learning in two-player stateless matrix games, as later restated by Kaisers & Tuyls: ẋ_i = x_i α(τ⁻¹[(Ay)_i − x·Ay] − log x_i + Σ_k x_k log x_k), a replicator (selection) term plus an entropy (mutation) term, linking exploration in reinforcement learning to mutation in evolutionary game theory. Summary drawn from the abstract and from Kaisers & Tuyls 2010, not from the paper. | Unavailable — filed 2026-10-24 for the owner’s question how the record stands on multi-agent reinforcement learning; a reading was attempted the same day and failed on access. The ACM Digital Library (doi:10.1145/860575.860687) answered every request from this client with a Cloudflare challenge (403). Unpaywall and OpenAlex list no open copy. The repository records OpenAlex names hold no file this client could reach: the VUB repository (biblio.vub.ac.be) page is a script-only catalogue entry, ULB’s DI-fusion record shows no attached full text, the Hasselt document server returned 503 and a search result describes its record as “No Fulltext”, and CiteSeerX reset the connection. Web searches found no author copy. The model the paper derives is read instead through Kaisers & Tuyls 2010 (LIT-1511, NOTE-1140), which restates its equation and shows that it describes frequency-adjusted, not plain, Q-learning. It stays Unavailable until a copy is supplied. No NOTE is filed. |
| LIT-1503 | QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning | Rashid et al. represent a team’s joint action-value Q_tot as a mixing of per-agent values Q_a(τ^a, u^a) constrained by ∂Q_tot/∂Q_a ≥ 0, with non-negative mixing weights produced from the global state by hypernetworks. Monotonicity makes the joint argmax the profile of individual argmaxes, so execution is decentralised and maximisation is linear in the number of agents. It represents more than a sum (VDN), learning the optimal policy of a two-step game VDN misses, and beat VDN and independent Q-learning on six StarCraft II maps; it cannot represent joint values in which an agent’s best action depends on the others’. | Active — read in full 2026-10-24 (NOTE-1154) from arXiv v2 (6 June 2018, the ICML camera-ready, arXiv non-exclusive licence); worth reading for one structural condition: if the joint action-value is non-decreasing in each agent’s own value, the profile of individually greedy actions is a greedy joint action, so a collective can act on a common value while each member consults only its own. The condition is sufficient, not necessary, and it cannot represent a joint value in which one agent’s best action depends on what the others do at the same step. Its evidence is a two-step matrix game and StarCraft II win rates on six small maps. |
| LIT-1504 | Real World Games Look Like Spinning Tops | Czarnecki, Gidel, Tracey, Tuyls, Omidshafiei, Balduzzi & Jaderberg (NeurIPS 2020). Games in which players can signal n bits before the outcome is settled contain every win–loss pattern on 2ⁿ strategies, so cycles of length 2ⁿ (Go: at least 2¹⁰⁰⁰). Nash clustering orders a game’s strategies into clusters weakly ordered by population performance. Empirical games sampled from small board games and the AlphaStar league show cluster size peaking at middling strength, the “spinning top”, and population-based training converges once the population is large enough. | Active — read in full 2026-10-24 (NOTE-1146) from arXiv v2 (17 June 2020); worth reading for one clean theorem, one general lemma and a hypothesis with evidence. The theorem: where players can signal n bits before the result is settled, every pattern of wins and losses among 2ⁿ strategies, a cycle through all of them included, is realized. The lemma: Nash clusters are weakly ordered by population performance, and beating a population that contains a whole cluster lifts a strategy above it. The hypothesis, that real games are shaped like a spinning top, with cycles thickest at middling strength, rests on sampled empirical games. The abstract says it is proved and the body says it is not. The random-game theorem’s proof is defective, and the fixed-memory fictitious play result needs a replacement rule it does not state. |
| LIT-1505 | Learning Through Reinforcement and Replicator Dynamics | Börgers & Sarin (1997; working paper 1993). For two players each running Cross’s version of Bush–Mosteller learning with payoffs in (0, 1), the expected change of each player’s mixed strategy equals the discrete replicator step of a two-population biological model, and in the continuous-time limit the learning process converges in probability to the continuous (Taylor) replicator dynamic at every finite time. Asymptotically it does not: the discrete process is absorbed in a pure strategy profile with probability one for every learning speed. With negative payoffs the limit adds a probability-matching term to a replicator term in “benefits”. | Active — read in full 2026-10-24 (NOTE-1149) from the authors’ working paper of October 1995, as held in Levine’s Working Paper Archive; worth reading as the proved source of “Cross learning is the replicator dynamic”: a single Bush–Mosteller learner with positive payoffs moves in expectation exactly as a population under the discrete replicator dynamic, and in the continuous-time limit follows the continuous replicator dynamic on any finite horizon. Two limits matter as much as the result. Asymptotically the discrete learner is absorbed in a pure strategy profile with probability one at every learning speed, even in matching pennies where the replicator dynamic cycles; and with negative payoffs a second force, probability matching, enters beside the replicator term. |
| LIT-1506 | Optimal Reward Functions in Distributed Reinforcement Learning | Wolpert & Tumer: members of a multi-agent system each run a reinforcement learner, and the designer must give each a private utility such that their learning maximises a world utility G. A private utility is factored when it ranks a member’s own alternatives, others fixed, as G does; the Wonderful Life Utility G(ζ) − G(CL(ζ)), with the member’s effect set clamped, is factored and has higher learnability than G. A sketched approximation sets the clamp to the expected action rather than zero; in a 60-agent bar problem, clamping to the average action learned best across attendance levels, clamping to absence close behind, and G itself worst. | Active — read in full 2026-10-24 (NOTE-1153) from the NASA Technical Reports Server copy (document 20010066523, a 7-page scanned report marked public use permitted), not the version in the Intelligent Agent Technology proceedings; worth reading as the most compact statement the record holds of difference rewards. A member’s private utility is factored when it ranks the member’s own alternatives as the world utility does, the others held fixed; the Wonderful Life Utility, world utility minus its value with the member’s effect set clamped, is factored and learns faster than the world utility itself. Clamping to the average action did better than clamping to the member’s absence. The optimal clamp is only sketched (“too long to go through here”) and the experiment is one bar problem. |
| LIT-1508 | Re-evaluating Evaluation | Balduzzi, Tuyls, Pérolat & Graepel (NeurIPS 2018). Evaluation data are antisymmetric matrices: Elo is their row mean in logit space, exact only when the log-odds are curl-free, and inflatable by copies; the Schur decomposition gives a multidimensional Elo for cyclic interactions. Nash averaging scores agents (and tasks) against the maximum-entropy Nash equilibrium of a zero-sum meta-game, which ignores exact copies when that equilibrium is unique. Applied to Atari, human ties with the best agents. | Active — read in full 2026-10-24 (NOTE-1155) from arXiv v2 (30 October 2018, the authors’ “NIPS 2018, final version”); worth reading as the source of the Hodge and Schur reading of evaluation data and of Nash averaging. Elo is the row mean of the log-odds matrix, exact only when the log-odds have no cyclic part, and copies of an agent move it. Nash averaging scores each agent against the maximum-entropy Nash team of the meta-game. Its invariance to copies is proved only for the Nash set (Lemma 1): when the meta-game has more than one equilibrium, copying an agent moves the maximum-entropy selection and the Nash averages with it, which the reading checked by script. The Atari re-evaluation used an LP solution, not the maximum-entropy one. |
| LIT-1509 | Open-ended Learning in Symmetric Zero-sum Games | Balduzzi, Garnelo, Bachrach, Czarnecki, Pérolat, Jaderberg & Graepel (ICML 2019). Every symmetric zero-sum game between parametrized agents splits into a transitive part and a cyclic part relative to a measure on agents. In cyclic games individual performance is meaningless, so the paper measures populations, by the value of the game between them and by the convex hull of their evaluation rows (the gamescape). Response to the Nash mixture enlarges the gamescape, and response to the rectified Nash, which trains each supported agent on what it beats, grows it in Blotto-type games where self-play does not. | Active — read in full 2026-10-24 (NOTE-1143) from arXiv v2 (13 May 2019, the authors’ “ICML 2019, final version”); worth reading for one invariant and one reframing. The invariant: the value of the zero-sum game between two populations, which does not depend on the choice of Nash, ignores members that are behavioural mixtures of others, and cannot be positive for a population inside another’s hull. The reframing: in a cyclic game an individual agent’s performance means nothing, so progress is the growth of a population’s gamescape. Its functional Hodge decomposition is right but is stated with a degenerate inner product, and it depends on a measure over agents. Experiments are two small resource-allocation games. |
| LIT-1510 | QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning | Son, Kim, Kang, Hostallero & Yi define Individual-Global-Max (IGM): a joint action-value is factorised by per-agent values when the joint argmax is the profile of individual argmaxes. Additivity (VDN) and monotonicity (QMIX) are sufficient for it; QTRAN instead trains the sum of individual values plus a state value to equal the joint value at the greedy profile and to bound it elsewhere (Theorem 1), a condition also necessary up to positive rescaling. On 310 random 3×3 matrix games it learned the optimum in all, VDN and QMIX failed in 177; it also did better on Gaussian squeeze and a penalised predator-prey task. | Active — read in full 2026-10-24 (NOTE-1141) from arXiv v1 (14 May 2019, the ICML version with its supplement, arXiv non-exclusive licence); worth reading for the Individual-Global-Max condition, that the agents’ individually greedy actions form a greedy joint action, and for showing it strictly weaker than additive or monotonic factorisation. The authors’ own supplement notes that every single-state matrix game satisfies it, so IGM has bite only where each agent sees part of the state; it is a condition on whether members acting on local information can jointly reach the collective optimum, not a condition for a common currency. Evidence is matrix games, Gaussian squeeze and a predator-prey variant. |
| LIT-1511 | Frequency adjusted multi-agent Q-learning | Kaisers & Tuyls (AAMAS 2010). The replicator-plus-entropy model of Boltzmann Q-learning derived by Tuyls et al. (2003, 2005), ẋ_i = x_i α(τ⁻¹[(Ay)_i − x·Ay] − log x_i + Σ_k x_k log x_k), assumes that every Q-value changes at rate α. In Q-learning only the chosen action’s value is updated, so E[Q̇_i] carries a factor x_i, and trajectories in the prisoners’ dilemma, battle of the sexes and matching pennies deviate from the model, depending on initialization. Frequency Adjusted Q-learning scales each update by min(β/x_i, 1) and follows the model wherever x_i ≥ β. | Active — read in full 2026-10-24 (NOTE-1140) from the AAMAS 2010 proceedings PDF on the IFAAMAS site; read in place of Tuyls, Verbeeck & Lenaerts 2003 (LIT-1501), whose model it restates and corrects. Worth reading as the correction to “Q-learning is replicator dynamics plus mutation”: the selection–mutation equation describes Q-learning with Boltzmann exploration only if every action’s estimate is updated at the same rate. In Q-learning the chosen action is updated more often, so the expected change of Q_i carries a factor x_i, and the learning traces depart from the model, depending on how the Q-values are initialized. Frequency Adjusted Q-learning divides the step by x_i and matches the model. Evidence is three 2×2 games, plotted, with no quantitative measure of fit. |
| LIT-1512 | Mean Field Multi-Agent Reinforcement Learning | Yang, Luo, Li, Zhou, Zhang & Wang (2018). Factorizing each agent’s Q-function into pairwise terms and expanding about the neighbours’ mean action reduces many-agent interaction to an agent against the average of its neighbours. Mean field Q-learning and actor-critic follow; MF-Q is proved to converge to the Nash Q-value under strong assumptions. With 500 and 1000 agents in Gaussian Squeeze the mean field methods learn where four baselines fail; MF-Q reproduces the order parameter of a 20 × 20 Ising model against MCMC; and it wins a 64-versus-64 battle game. | Active — read in full 2026-10-24 (NOTE-1148) from arXiv v5 (15 December 2020), the ICML 2018 paper with appendices; worth reading as the standard way multi-agent RL reaches hundreds of agents: each agent’s Q-function takes its own action and the mean action of its neighbours, so many-body interaction becomes a two-body one between an agent and the average of the rest. Mean field Q-learning is proved to converge to a Nash Q-value under strong assumptions, every stage game met in training having a global optimum or a saddle point among them, and learns where four baselines fail with 500 and 1000 agents. The approximation needs agents that are homogeneous and interchangeable within a neighbourhood; the bound on its error is loose and the cancellation of errors argued, not proved; and the contraction step needs a high Boltzmann temperature while the convergence assumptions need it to go to zero. |
| LIT-1513 | Multi-agent Reinforcement Learning in Sequential Social Dilemmas | Leibo, Zambaldi, Lanctot, Marecki & Graepel (2017). Defines a sequential social dilemma as a Markov game whose cooperative and defecting policies, played against each other, give payoffs satisfying the social dilemma inequalities. Independent deep Q-learners in a fruit-Gathering game learn aggression when apples are scarce or a tagged rival is out long; in Wolfpack they hunt together when the joint-capture bonus and radius are high. Both games embed Prisoner’s Dilemmas, but network size raises defection in Gathering and lowers it in Wolfpack, which no matrix game captures. | Active — read in full 2026-10-24 (NOTE-1151) from arXiv v1, the AAMAS 2017 paper; worth reading as the paper that moved social dilemmas from matrix games to learned policies in Markov games. Two two-player games, Gathering (apples, and a beam that removes the rival for a while) and Wolfpack (lone or joint capture of prey), both yield Prisoner’s Dilemma payoff matrices when the learned policies are played off, yet respond in opposite directions to agent capacity: a larger network makes Gathering agents more aggressive and Wolfpack agents more cooperative, because aggression is the harder policy to implement in one and cooperation in the other. Agents learn aggression where apples are scarce. It is a descriptive simulation with independent learners, no figures of spread, and no protective institution or depletable commons. |
| LIT-1515 | Optimal Payoff Functions for Members of Collectives | Wolpert & Tumer (2001). Members of a collective each maximise a private payoff utility; the design question is which payoffs make the members’ success yield a high provided world utility. Against the “team game”, which gives each member the world utility, the paper uses “a novel mathematical framework” to review the class of payoffs that are easy to maximise and aligned with the world utility, the Aristocrat Utility and a new variant of the Wonderful Life Utility, and reports experiments in which they beat earlier COIN utilities, the team game and “perhaps the most natural version” of endogenizing externalities (abstract, RePEc). | Unavailable — filed 2026-10-24 for difference rewards (the Wonderful Life Utility); a reading was attempted the same day and failed on access to a lawful copy. The version of record is closed at World Scientific; Unpaywall and OpenAlex report it closed with no repository copy. The second author’s publications page at Oregon State (web.engr.oregonstate.edu/~ktumer), which lists the paper, failed certificate verification through this client’s proxy and returned 503 to a second fetcher. CiteSeerX, which OpenAlex lists, reset every connection. It is not on arXiv (both authors’ arXiv listings checked) or NASA NTRS. A copy is posted on a third party’s course-library server (jmvidal.cse.sc.edu), not by the authors or their institution; it was not used. The closest lawful text, the authors’ NASA report of the same programme with a near-identical abstract, is filed and read as LIT-1506. It stays Unavailable until a copy is supplied or the author’s page can be reached. No NOTE is filed. |
| LIT-1516 | α-Rank: Multi-Agent Evaluation by Evolution | Omidshafiei, Papadimitriou, Piliouras, Tuyls, Rowland, Lespiau, Czarnecki, Lanctot, Pérolat & Munos (Scientific Reports 2019). Agents in a K-player meta-game are ranked by the stationary distribution of a Markov chain on pure profiles whose transitions are fixation probabilities of Fermi imitation with rare mutation. Unique at every finite ranking intensity α; as α → ∞ the transitions become those of Markov-Conley chains, the sink components of the better-response graph, which the paper ties to the chain components of the replicator flow. Applied to AlphaGo, AlphaZero, MuJoCo soccer and poker meta-games. | Active — read in full 2026-10-24 (NOTE-1156) from arXiv v4 (4 October 2019); worth reading as the evolutionary alternative to Nash for ranking agents when wins cycle. It ranks strategy profiles by the stationary distribution of a finite-population, rare-mutation imitation chain, unique at every finite ranking intensity α. As α grows its transitions become those of Markov chains on the sink strongly connected components of the better-response graph. The paper calls these sinks Markov-Conley chains and ties them to the chain components of the replicator flow. The large-α limit of the stationary distribution, and so the selection among several sinks, is not characterized. In the symmetric single-population model a copied strategy changes the ranking (checked by script), so it does not share Nash averaging’s resistance to padding. |
| LIT-1517 | Counterfactual Multi-Agent Policy Gradients | Foerster, Farquhar, Afouras, Nardelli & Whiteson train decentralised actors with one centralised critic Q(s, τ, u) and credit agent a with A^a = Q(s, τ, u) − Σ_{u′a} π^a(u′a | τ^a) Q(s, τ, (u^−a, u′a)): the value of the joint action against the critic’s average over a’s own alternatives under a’s policy, the others’ actions fixed. The baseline does not depend on a’s action, so it does not change the expected gradient (Lemma 1). On decentralised StarCraft micromanagement with a narrow field of view, it beat independent and central-V/QV critics on four maps. | Active — read in full 2026-10-24 (NOTE-1152) from arXiv v3 (11 December 2024, arXiv non-exclusive licence), the corrected version; worth reading as the standard statement of counterfactual credit in cooperative multi-agent learning: each agent’s action is scored against the critic’s average over that agent’s own alternatives, the others’ actions held fixed, and that baseline provably leaves the expected gradient unchanged. The counterfactual values are the learned critic’s estimates, which exist only for actions the agents sometimes take, so the method credits agents that all act on every step and does not recover the value of one that is never heeded. Results are StarCraft win rates on four small maps. |
| LIT-1518 | Eliciting Informative Feedback: The Peer-Prediction Method | Miller, Resnick & Zeckhauser (2005). A center with no independent information scores each rater by applying a strictly proper scoring rule to the distribution of a reference rater’s report that her own report implies, given a common prior and signal model. Truthful reporting is a strict Nash equilibrium; scaling the scores induces costly effort and can outweigh bribes; three or more raters allow budget balance. Uninformative equilibria also exist, and collusion, risk aversion, unmodelled private signals and trust in the center are named limits. | Active — read in full 2026-10-24 (NOTE-1139) from the authors’ final pre-publication draft of 26 January 2005, on Paul Resnick’s University of Michigan page; worth reading as the founding scoring rule for evaluators when there is no ground truth. Each rater reports a signal, the center turns it into a posterior over a reference rater’s report, and the rater is paid a strictly proper scoring rule on that posterior against what the reference rater actually reported. Truth-telling is then a strict Nash equilibrium (Proposition 1), and scaling the payments buys effort. It is not the only equilibrium: everyone always reporting h, or always l, is an equilibrium too, and collusion is named as a limit the paper does not settle. The mechanism needs a common prior and a signal model the center knows. |
| LIT-1519 | Learning with Opponent-Learning Awareness | Foerster et al. replace an agent’s objective V¹(θ¹, θ²) with its value after the opponent’s anticipated naive gradient step, V¹(θ¹, θ² + Δθ²), and differentiate through Δθ² = η∇θ²V², adding (∇θ²V¹)ᵀ∇θ¹∇θ²V² · δη to the naive gradient. In the memory-one iterated prisoner’s dilemma, two exact-gradient LOLA learners played tit-for-tat-like policies in 81% of runs (return −1.06 against −1.98 for naive learners); in iterated matching pennies they settled at the mixed Nash equilibrium. A policy-gradient version cooperated in the Coin Game, and with opponent modelling did so less reliably. | Active — read in full 2026-10-24 (NOTE-1150) from arXiv v4 (19 September 2018, the AAMAS 2018 text, arXiv non-exclusive licence); worth reading as the first learning rule that models another learner’s update and climbs its own return through it: a LOLA agent adds to its gradient the effect of its own parameters on the opponent’s next naive step. Two exact-gradient LOLA learners reached tit-for-tat-like reciprocity in the iterated prisoner’s dilemma where naive learners defected. Shaping is one step deep, assumes access to the opponent’s parameters (or a behavioural clone of them), and is shown only in two-player games; its numbers have one internal inconsistency (see the NOTE). |
| LIT-1520 | Coupled replicator equations for the dynamics of learning in multiagent systems | Sato & Crutchfield (2002; PRE 2003). Two agents choose by softmax over reward memories Q_i that decay at rate α. In the limit where learning is slow relative to play, each agent’s choice distribution follows ẋ_i/x_i = β[(Ay)_i − x·Ay] + α Σ_j x_j log(x_j/x_i): a coupled replicator dynamic plus an entropy-like term towards uniform play. With α = 0 it is the conservative two-population replicator equation; with α > 0 it is dissipative. In rock–scissors–paper, simulations show quasiperiodic tori and Hamiltonian chaos without decay, and limit cycles, intermittency and chaotic attractors with it. | Active — read in full 2026-10-24 (NOTE-1144) from arXiv:nlin/0204057v2 (18 August 2002); worth reading as a four-page derivation of the learning dynamics of softmax reinforcement learners with forgetting: two such agents follow coupled replicator equations plus a term α_X Σ_j x_j log(x_j/x_i), set by the rate at which reward memories decay, that pushes each agent towards uniform play. Without forgetting the system is conservative, Hamiltonian in zero-sum games, and in rock–scissors–paper it is chaotic for nonzero tie rewards; with forgetting it is dissipative, with limit cycles and chaotic attractors. The memory update is not Watkins’s Q-learning: every action’s memory is updated with its average reward at the same rate. |
| LIT-1521 | A Simple Adaptive Procedure Leading to Correlated Equilibrium | Hart & Mas-Colell (Econometrica 2000; handout 1996). Regret matching: each period a player who last played j switches to k with probability R_t(j, k)/μ, the positive part of its average gain had it played k whenever it played j, and otherwise repeats j. If all players do so, the empirical distribution of play converges almost surely to the set of correlated equilibria. The proof runs through Blackwell’s approachability theorem; regrets vanish exactly when the empirical distribution approaches the correlated-equilibrium set. Inertia, a positive probability of repeating, is needed for the result. | Active — read in full 2026-10-24 (NOTE-1142) from the published article as posted on Sergiu Hart’s homepage; worth reading as the theorem that correlated equilibrium is reachable by simple adaptive play: if every player switches from its last action to each alternative with probability proportional to its positive regret for not having made that switch in the past, the empirical joint distribution of play converges almost surely to the set of correlated equilibria. No device, no forecasts and no best replies are needed; the common history is the correlating device. The limits matter: convergence is to the set, not to a point; correlated equilibria that are interior and not pure Nash cannot be the limit of the empirical distribution; and the players must observe one another’s past play. |
| LIT-1524 v2 | Cleaning up the neighborhood: A full classification for adversarial partial monitoring | Lattimore & Szepesvári (2018; ALT 2019). Completes the classification of finite adversarial partial-monitoring games by minimax regret to all games, including the degenerate ones (with actions optimal only on a lower-dimensional part of the simplex) that Bartók et al. (2014) left open: 0 with no pair of neighbouring actions, Θ̃(√n) when locally observable, Θ(n^2/3) when globally but not locally observable, and Ω(n) otherwise. A new NeighborhoodWatch2 attains √n with high probability by redistributing mass onto degenerate actions in proportion to the neighbours they lie between. It corrects a slip in Bartók et al.’s T^2/3 lower-bound proof and, in the preprint’s words, an exchanged expectation and maximum in the earlier localisation argument. A second algorithm, RelExp3, gives point-locally observable games an asymptotic √n bound free of arbitrarily large game constants, with a matching linear dependence on the number of feedback symbols. | Active — read 2026-10-25 (NOTE-1162) in full, from the arXiv preprint v1 of 23 May 2018 (arxiv.org/pdf/1805.09247v1, 24 pp.); the ALT 2019 version (PMLR 98:529–556) was fetched and its theorem statements, footnote and contribution list compared, not read in full. Worth reading for the completed classification of finite adversarial partial-monitoring games, degenerate and duplicate actions included (THEORY-963); for how actions that are optimal only on a boundary enter it, through the neighbourhood set and not as neighbours, and for its correction of the lower-bound proof of Bartók et al. (2014) (THEORY-961); for NeighborhoodWatch2, a simpler algorithm with a high-probability √n bound; and for RelExp3 on point-locally observable games (THEORY-950). Read it knowing that the arXiv text says Foster and Rakhlin and Bartók et al. “inadvertently exchanged an expectation and maximum” in their localisation argument and the published text no longer says so, though both abstracts say “correct errors in previous analyses”; that it proves only the two pieces of the classification that were missing or flawed and cites the rest; that its constants are game-dependent and can be large; and that a few small typos survive in the arXiv text. |
| LIT-1526 v2 | Online Learning and Blackwell Approachability with Partial Monitoring: Optimal Convergence Rates | Kwon & Perchet (2017). Blackwell approachability generalizes regret minimization (multi-criteria optimization, online optimization of a convex loss, online linear optimization under a cumulative constraint). Under partial monitoring the decision maker does not see outcomes but a random signal correlated with the decision–outcome pair, or with the outcome only. The paper gives the first approachability algorithms for polytope target sets with convergence rate O(T^-1/2) when the signal does not depend on the decision and O(T^-1/3) for general signals, and shows that these rates cannot be improved without further assumptions on the objectives or the signals (abstract). | Active — read 2026-10-25 (NOTE-1159) in full, from the PMLR copy and its supplementary material; worth reading for the reduction of approachability under partial monitoring to full-information approachability in a lifted space of flags, for the optimal worst-case rates, O(T^-1/3) for general signals and O(T^-1/2) when the signal does not depend on the decision (THEORY-947), and for the exploration floor that decision-dependent signals require (THEORY-957). Read it knowing that approachability is assumed rather than decided, that the guarantees concern the average payoff and so let violations be compensated over time, that optimality is worst case over games, that the constants grow with a simplicial subdivision, and that the proof for outcome-dependent signals is omitted. |
| LIT-1528 v3 | Partial Monitoring—Classification, Regret Bounds, and Algorithms | Bartók, Foster, Pál, Rakhlin & Szepesvári (2014). In a partial-monitoring game the learner picks an action, the environment an outcome, and the learner suffers a loss and receives a feedback signal, both fixed functions of action and outcome. For every game with finitely many actions and outcomes (against adversarial opponents, every non-degenerate one) the minimax regret is zero or scales as T^1/2, T^2/3 or T, up to constants and logarithmic factors; computationally efficient algorithms attain it within a logarithmic factor, with individual bounds on expected regret for i.i.d. outcomes (abstract). | Active — read 2026-10-25 (NOTE-1164) in full, from the authors’ preprint of March 2013 on Alexander Rakhlin’s MIT page; worth reading for the complete classification of finite partial-monitoring games by minimax regret (0, Θ̃(√T), Θ(T^2/3), Θ(T); THEORY-964), for the linear-algebra conditions, global and local observability, that decide the class (THEORY-962), and for the algorithms CBP and NeighborhoodWatch. Read it knowing that the adversarial classification covers non-degenerate games only, that Lattimore and Szepesvári (2019, LIT-1524) completed it to degenerate games, corrected the kernel in its T^2/3 lower-bound proof, and, in their preprint, an exchanged expectation and maximum in NeighborhoodWatch’s localisation (THEORY-963, THEORY-961), that the classification concerns the best policy in a fixed, known game, and that the copy read is the preprint, not the journal text. |
| LIT-1603 v2 | The Evolution of Cooperation | Sachs, Mueller, Wilcox & Bull (2004). A tripartite framework for how cooperation within and between species evolves and is maintained: directed reciprocation, shared genes (kin selection) and byproduct benefits, each subdivided. Plant–rhizobium and squid–Vibrio symbioses are fitted to it, and natural systems often combine models. | Unavailable — filed 2026-10-27, not read. Registered in the second pass on the exchange of 2026-10-27, “Repository coverage assessment”, at the owner’s request to find what it mentioned and did not cite (second curation entry of 2026-10-27). No NOTE is filed, and it stays Unavailable until it is read, not on merit. A lawful full text was looked for on 2026-10-27 and none was found: OpenAlex lists it as closed with no open location, Unpaywall reports it closed with no open locations, and Europe PMC has no free copy. |
| LIT-1698 | Team Reasoning and Intentional Cooperation for Mutual Benefit | Sugden (2015). Social preferences cannot represent trust: on Rabin-style intention-based preferences, the common-knowledge practice of trust in the Trust Game is not an equilibrium. Team reasoning can, but not Bacharach’s version, which maximizes a team utility, trades members’ interests off against each other and needs no assurance that others reason as a team. Sugden’s Schema of Cooperative Team Reasoning aims at each member’s benefit over a maximin benchmark, follows existing practices and binds only given reciprocal reason to believe the others endorse it. So a market exchange that serves each party’s interest can still be intended as mutual benefit, neither self-interest nor sacrifice. | Active — read in full 2026-10-29 (NOTE-1288) from the published version, open under CC BY-NC-ND at the Journal of Social Ontology; worth reading as Sugden’s own later statement of team reasoning, read in place of his 2003 paper (LIT-1782, Unavailable), and for its claim that team reasoning cannot be reduced to self-interest or to social preferences by redefining payoffs, which bears on the owner’s thesis (CLAIM-491). |
| LIT-1782 | The Logic of Team Reasoning | Sugden (2003). A logic of team reasoning, in which agents ask “what should we do?” and act on their part of the best joint plan, conditional on assurance that others reason likewise; it explains coordination (the Hi-Lo game) that individual best-reply reasoning cannot. | Unavailable — filed 2026-10-29; reading attempted the same day, no lawful copy reached. OpenAlex lists no open copy and an exact-title web search found none posted by an author or publisher; PhilArchive has a record (SUGTLO) that answered HTTP 403, so whether it holds a file is unknown; UEA’s repository and RePEc for the 2005 reprint in Teamwork offer no download. No NOTE is filed. It stays Unavailable until a copy is supplied (ADR-041). Read in its place, and not a substitute for reading it: Sugden 2015 (LIT-1698). |
| LIT-1785 | Activating the legacy motive mitigates intergenerational discounting in the climate game | A laboratory climate game: 180 people in 30 groups of six, each with 0, 4 into a climate account. If the group reaches 45 endowment is saved; if not, it is lost with 90% probability. When the saved endowments were paid to the players the next day, 9 of 10 groups reached the target. When they went instead to planting trees for future generations, 2 of 10 did. When players in the tree-planting game also read three short messages meant to activate the legacy motive (death awareness, the powerlessness of future generations, and paying forward a past generation’s sacrifice), 7 of 10 did, and group investment rose from 105.20. All three messages raised investment over the matched rounds of the plain tree-planting game. Legacy induction made fair shares, not extra giving, the norm. There were no manipulation checks and no control message. The authors say people invest in legacies “for largely—although not entirely—selfish reasons”. | Active — read in full 2026-10-29 (NOTE-1279), in place of LIT-1760, which could not be reached; worth reading as a conceptual extension of the 2012 mortality-and-legacy result to group cooperation, and as the record’s nearest substitute for Wade-Benzoni et al. 2012 (LIT-1760). Read it knowing that its legacy induction bundles three mechanisms, one of them identification with past and future generations, so it cannot say which did the work. |
| LIT-1866 | Potential Games | Apt (2013), lecture slides, CWI. Best-response dynamics; exact, ordinal and generalized ordinal potentials after Monderer and Shapley (1996); the finite improvement property (every improvement path is finite); the theorem, credited to Monderer and Shapley, that a finite game has a generalized ordinal potential if and only if it has the FIP, proved one way and sketched the other by counting the improvement sequences that end at each profile; a game with the FIP and no ordinal potential; Rosenthal’s theorem that congestion games are potential games; the Braess paradox; and price-of-stability bounds. | Active — read 2026-10-30 (NOTE-1427) in full, all 47 slides, from the author’s course page at CWI (homepages.cwi.nl/~apt/stra13/potential13-sli.pdf). Worth reading as a clear secondary statement of the potential-game definitions and of Monderer and Shapley’s theorem that a finite game has a generalized ordinal potential exactly when it has the finite improvement property, with a two-by-two game that has the property but no ordinal potential. Read it knowing that it is lecture slides: the theorem is attributed to “Monderer and Shapley ‘96” with no lemma number or page, and the converse is a sketch. |