Abstract
In this paper we present two formulations of an equilibrium notion for large games in which each player cannot observe precisely the moves of the other players in the game. In the context of large anonymous games where the moves of the other players are summarized by a probability measure on the action space, imperfect observability is formulated as a map from the space of such measures to the space of probability measures on this space. In the context of large non-anonymous games where the moves of the other players are summarized by a measurable function from the space of players to the action space, imperfect observability is formulated as a conditional expectation of such a function with respect to a σ-subalgebra of the measure space of players. We report results both on the existence and upper hemicontinuity of equilibrium.
A preliminary version of this paper was presented at the Midwest Mathematical Economics Conference in Spring 1990, at the Ohio State University Conference on Game Theory, and at the International Conference on Game Theory and Economic Applications held at ISI, New Delhi in December 1990. We thank especially Alejandro Manelli, John Hillas and David Schmeidler for their stimulating comments.
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Chakrabarti, S.K., Khan, M.A. (1991). Equilibria of Large Games with Imperfect Observability. In: Positive Operators, Riesz Spaces, and Economics. Studies in Economic Theory, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58199-1_3
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DOI: https://doi.org/10.1007/978-3-642-58199-1_3
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