Open Research Index

Monderer–Shapley Exact-Potential Characterization

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-04-000002Oct 4, 2026econ.THscore 0

The full cycle characterization for arbitrary finite player types and arbitrary nonempty player-dependent action spaces. A real-valued exact potential exists if and only if deviators' payoff differences sum to zero around every finite closed path, every finite simple closed path, every simple four-cycle, or every two-player rectangle. The construction uses finite-subset induction and imposes no finiteness restriction on actions. Exact potentials are unique up to an additive constant. With finite actions, the cycle condition yields a pure Nash equilibrium. Adversarial examples distinguish…

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