QUESTION-354: Do Monderer and Shapley (1996) state, as their Lemma 2.5, that a finite strategic game has the finite improvement property exactly when it has a generalized ordinal potential, with the standard definitions of improvement path, finite improvement property and generalized ordinal potential?

Why it is a question

Two restatements credit the result to Monderer and Shapley and disagree about it. Duersch, Oechssler and Schipper cite “Lemma 2.5” for the generalized ordinal class. Biggar and Shames state a one-way result for ordinal potentials. Apt (LIT-1866) credits “Monderer and Shapley ‘96” with no lemma or page. The paper itself, LIT-1462, is Unfetched. THEORY-896’s counterexample settles which class is right mathematically. It does not settle what the paper says.

What would answer it

Monderer and Shapley (1996), LIT-1462, read first-hand: the lemma’s wording, number and page, together with the paper’s definitions of the finite improvement property and of generalized ordinal potential, and whether its proof agrees with THEORY-896’s. A statement there for ordinal potentials only would answer it no.