Hierarchies of Beliefs for Many Player Games

Venkata Tanay Kasyap Kondiparthy
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Venkata Tanay Kasyap Kondiparthy: Warwick University

Warwick-Monash Economics Student Papers from Warwick Monash Economics Student Papers

Abstract: Mertens and Zamir (1985) first provided the universal type space construction for finite player games of incomplete information with a compact state space. Brandenburger and Dekel (1993) complemented it for a Polish state space. This paper extends the construction of Brandenburger and Dekel (1993) to games with infinitely many players for Harsanyi’s notion of a type. The extension is formulated by randomly drawing a countably infinite set of actual players from a continuum of potential players, represented by their labels in [0,1]. The random distribution of the countably infinite set of actual players almost surely converges to Lebesgue due to the Glivenko–Cantelli theorem. A coherent type is shown to induce beliefs over other player’s types and common knowledge of coherency closes the model of beliefs. Implications of dropping the Polish space assumption are discussed and an informal extension to measurable spaces is provided for future work. The formalisation provided here allows Harsanyi’s notion of type to be applied in classes of games with many players such as Morris and Shin (2001)

Keywords: Higher Order Beliefs; Universal Type Space; Many Player Games JEL classifications: C70; D83 (search for similar items in EconPapers)
Date: 2024
New Economics Papers: this item is included in nep-gth and nep-mic
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