On balanced games with infinitely many players: Revisiting Schmeidler's result

Bartl, David ORCID: https://orcid.org/0000-0003-1313-035X and Pintér, Miklós (2023) On balanced games with infinitely many players: Revisiting Schmeidler's result. Operations Research Letters, 51 (2). pp. 153-158. DOI 10.1016/j.orl.2023.01.011

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Official URL: https://doi.org/10.1016/j.orl.2023.01.011

Abstract

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 generalizes Schmeidler (1967) “On Balanced Games with Infinitely Many Players”, where the game is assumed to be non-negative. We also generalize Schmeidler's (1967) result to the case of restricted cooperation too.

Item Type:

Article

Uncontrolled Keywords:

TU games with infinitely many players, Core, Balancedness, TU games with restricted cooperation, Signed TU games, Bounded additive set functions

Divisions:

Institute of Operations and Decision Sciences

Subjects:

Mathematics, Econometrics

Funders:

Hungarian Scientific Research Fund

Projects:

K 133882, K 119930