{"id":"palomar/PALOMAR-2026-10-04-000002","url":"https://github.com/Arthur742Ramos/monderer-shapley-potential-lean/tree/bce2e989bc8243f938a34ac0f027b57063c71380","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-04-000002-v1.json","repo":"https://github.com/Arthur742Ramos/monderer-shapley-potential-lean","tags":["econ.TH","cs.GT","msc:91A10","msc:68V20","potential-games","game-theory","nash-equilibrium","formal-verification"],"score":0,"title":"Monderer–Shapley Exact-Potential Characterization","trust":"high","domain":"econ.TH","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"econ.TH","summary":"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…","category":"research","comments":0,"disputed":false,"division":"econ","mentions":0,"verified":true,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":true,"formalizes":[{"title":"Potential Games","identifier":"https://doi.org/10.1006/game.1996.0044","relationship":"formalizes"}]}