2022/07/29 by David Bartl, Bartl, David, Miklós Pintér +1
Decision Sciences · Economics, Econometrics and Finance · #91A07 #91A12 #Economic Theory and Institutions #FOS: Economics and business #FOS: Mathematics #Functional Analysis (math.FA) #Game Theory and Applications #Game Theory and Voting Systems #Optimization and Control (math.OC) #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2207.14672
openalex publication_date 2022/07/29 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
We consider transferable utility cooperative games with infinitely many players and the core understood in the space of bounded additive set functions. We show that, if a game is bounded below, then its core is non-empty if and only if the game is balanced. This finding is a generalization of Schmeidler's (1967) original result ``On Balanced Games with Infinitely Many Players'', where the game is assumed to be non-negative. We furthermore demonstrate that, if a game is not bounded below, then its core might be empty even though the game is balanced; that is, our result is tight. We also generalize Schmeidler's (1967) result to the case of restricted cooperation too.