On Balanced Games with Infinitely Many Players: Revisiting Schmeidler's Result
Optimization and Control
2022-08-01 v1 Theoretical Economics
Functional Analysis
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 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.
Keywords
Cite
@article{arxiv.2207.14672,
title = {On Balanced Games with Infinitely Many Players: Revisiting Schmeidler's Result},
author = {David Bartl and Miklós Pintér},
journal= {arXiv preprint arXiv:2207.14672},
year = {2022}
}