Source
Wolpert & Tumer, LIT-1506, read in NOTE-1153 from the NASA Technical Reports Server copy (document 20010066523): the definition of factored, the Theorem and Eq. 1, and the WLU (p. 3); the clamp derivation (p. 4); the bar-problem results and Figure 1 (pp. 5–6).
What was actually shown
- Factored. γ_η(C(ζ₀)) ≥ γ_η(C(ζ′₀)) ⇔ G(C(ζ₀)) ≥ G(C(ζ′₀)) for initial states differing only for η.
- The characterisation (stated). Factored at every ζ iff γ_η = Φ_η(ζ outside η’s effect set, G(ζ)) with ∂Φ_η/∂G > 0; the proof is in the authors’ earlier work. The “if” half is immediate: with the first argument fixed, which a change in η’s state cannot alter, Φ_η increasing in G orders η’s alternatives as G does. Checked when filed.
- The WLU is factored. G(ζ) − G(CL(ζ)): the subtracted term depends only on components outside η’s effect set, so the WLU is Φ_η with Φ_η(x, g) = g − G(CL(·)). Checked when filed.
- The experiment. 60 agents, attendance sets of 1 to 6 of 7 nights, 20 runs. The average-action clamp performed well at every level; the zero clamp nearly as well, slipping as nights increased; the all-ones clamp poorly for few nights; G worst throughout (Figure 1a).
What this does not say
- That the WLU answers “what if the agent had not acted”. Others’ behaviour is held as it was; it needs no model of their response.
- That the optimal clamp is derived. The derivation is “too long to go through here”.
- Anything beyond one congestion game with simple Boltzmann learners, where each agent’s effect set is taken to be its own actions.
- What the Advances in Complex Systems paper adds, a new framework and the Aristocrat Utility, which was not read.