 On the space of players in idealized limit gamesLei Qiao and Haomiao Yu Journal of Economic Theory, 2014, vol. 153, issue C, 177-190 Abstract: This paper demonstrates the class of atomless spaces that accurately models the space of players in a large game which represents an idealized limit of a sequence of finite-player games. Through two examples, we show that arbitrary atomless probability spaces, in particular, the Lebesgue unit interval, may not be appropriate to model the space of players of an idealized limit. This inappropriateness hinges on the fact there is a convergent sequence of exact pure-strategy Nash equilibria in the sequence of finite-player games, while the idealized limit game of the sequence does not have any equilibrium. Instead, a saturated probability space is shown to be not only sufficient but also necessary, to model the space of players in any proper idealized limit. This complements the study of large games with a bio-social typology in Khan et al. [10] as such a connection between finite-limiting and idealized continuum-limit games was not able to be obtained in their framework. Keywords: Large games; Games with traits; Idealized limit; Saturated probability space; Pure-strategy Nash equilibrium; Weak closed-graph property (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:153:y:2014:i:c:p:177-190 DOI: 10.1016/j.jet.2014.06.009 Access Statistics for this article Journal of Economic Theory is currently edited by A. Lizzeri and K. Shell More articles in Journal of Economic Theory from Elsevier |
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