Journal ArticleDOI
Pure strategy equilibria in games with countable actions
Haomiao Yu,Zhixiang Zhang +1 more
TLDR
In this paper, the Radner-Rosenthal theorem with finite action spaces was extended to the case that the action space is countable and complete, and the existence of a pure strategy equilibrium for a game with a continuum of players of finite types was shown.About:
This article is published in Journal of Mathematical Economics.The article was published on 2007-02-01. It has received 20 citations till now. The article focuses on the topics: Countable set & Correlated equilibrium.read more
Citations
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Journal ArticleDOI
Large Games with a Bio-Social Typology
TL;DR: This work addresses dissonance arising from the use of a Lebesgue interval for playerʼs names by showing a saturated probability space as being a necessary and sufficient name-space for the existence and upper hemi-continuity of pure-strategy Nash equilibria in large games with traits.
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Location of Nash equilibria: A Riemannian geometrical approach
TL;DR: In this article, the existence and location of Nash equilibrium points are studied for a large class of a finite family of payoff functions whose domains are not necessarily convex in the usual sense; the geometric idea is to embed these non-convex domains into suitable Riemannian manifolds regaining certain geodesic convexity properties of them.
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On games with incomplete information and the Dvoretsky–Wald–Wolfowitz theorem with countable partitions☆
TL;DR: In this article, it was shown that the results of Milgrom-Weber [Milgrom, P.R., Weber, R.J., 1985] are valid for action sets with a countably infinite number of elements.
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An Agent-Based Pythagorean Fuzzy Approach for Demand Analysis with Incomplete Information
Ulas Baran Baloglu,Yakup Demir +1 more
TL;DR: A Bayesian game is described with a large number of finite players, and this is followed by a Pythagorean fuzzy‐based decision mechanism to construct an agent‐based system that efficiently reduces the peak amounts in a smart grid by analyzing the demand.
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Rationalizability in large games
TL;DR: The authors characterizes both point-rationalizability and rationalizability in large games when societal responses are formulated as distributions or averages of individual actions, and shows that the sets of point rationalizable and rationalizable responses are convex, compact and equivalent to those outcomes that survive iterative elimination of never best responses, under point-beliefs and probabilistic beliefs, respectively.
References
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Book
Infinite Dimensional Analysis: A Hitchhiker's Guide
TL;DR: In this paper, Riesz spaces are used to represent the topology of the space of sequences of sequences and correspondences of correspondences in Markov transitions, where the correspondences correspond to Markov transition.
Book
Private information and pure-strategy equilibria
Roy Radner,Robert Rosenthal +1 more
TL;DR: It is proved that in games with a finite number of players and a finite amount of moves, if each player observes a private information random variable which has an atomless distribution and is independent of the observations and payoffs of all other players, then the game possesses a pure-strategy equilibrium.
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Relations among certain ranges of vector measures
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Elimination of Randomization in Certain Statistical Decision Procedures and Zero-Sum Two-Person Games
TL;DR: In this paper, it was shown that randomization is unnecessary in the sense that every randomized decision function can be replaced by an equivalent nonrandomized decision function, in the case when the decision space is compact.
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On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players
TL;DR: In this paper, the existence of pure strategy Nash equilibria in nonatomic games was shown by means of counterexamples and the stringent conditions on the cardinality of action sets cannot be relaxed, and thus resolve questions which have remained open since Schmeidler's 1973 paper.