Please use this identifier to cite or link to this item: https://doi.org/10.1073/pnas.93.26.15518
Title: Nonatomic games on Loeb spaces
Authors: Khan, M.A.
Sun, Y. 
Issue Date: 24-Dec-1996
Citation: Khan, M.A., Sun, Y. (1996-12-24). Nonatomic games on Loeb spaces. Proceedings of the National Academy of Sciences of the United States of America 93 (26) : 15518-15521. ScholarBank@NUS Repository. https://doi.org/10.1073/pnas.93.26.15518
Abstract: In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountable action sets, for example the unit interval, there do not exist pure-strategy Nash equilibria in such nonatomic games. In this brief announcement, we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces. We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.
Source Title: Proceedings of the National Academy of Sciences of the United States of America
URI: http://scholarbank.nus.edu.sg/handle/10635/103609
ISSN: 00278424
DOI: 10.1073/pnas.93.26.15518
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