Repeated Games with Incomplete Information

By Jérôme Renault. Encyclopedia of Complexity and Systems Science, 2009

590 citations recorded by the source corpus.

Repeated game with incomplete information A situation where several players repeat the same stage game, the players having different knowledge of the stage game which is repeated. Strategy of a player A rule, or program, describing the action taken by the player in any possible situation which may happen, depending on the information available to this player in that situation. Strategy profile A vector containing a strategy for each player. Lack of information on one side Particular case where all the players but one perfectly know the stage game which is repeated. Zero-sum games 2-player games where the players have opposite payoffs. Value Solution (or price) of a zero-sum game, in the sense of the fair amount that player 1 should give to player 2 to be entitled to play the game. Equilibrium Strategy profile where each player’s strategy is in best reply against the strategy of the other players. Completely revealing strategy Strategy of a player which eventually reveals to the other players everything known by this player on the selected state. Non revealing strategy Strategy of a player which reveals nothing on the selected state. The simplex of probabilities over a finite set For a finite set S, we denote by (S) the set of probabilities over S, and we identify (S) to fp D (ps )s2S 2 RS ;8s 2 S ps 0 and P s2S ps D 1g. Given s in S, the Dirac measure on s will be denoted by is. For p D (ps )s2S and q D (qs )s2S in RS , we will use, unless otherwise specified, kp qk D P s2S jps qs j.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/0f16cfc8a943cb123e6fc998e806d46e4fb9a3cd

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Citations in the corpus

Information Design: A Unified Perspective (2019, background): “This concavification argument (building on Aumann and Maschler (1995)) is the focus of both Kamenica and Gentzkow (2011) and the large and important literature inspired by their work. The many players case is significantly harder than the single player case, as it is no longer the set of probability”
Sixteen common misconceptions about the evolution of cooperation in humans (2011, background): “…dates back to Hume (1739) and had already been analysed in detail in the economics literature before Trivers rediscovered it (reviewed by Aumann, 1981; Aumann & Maschler, 1995; Binmore, 1994, 1998, 2005b, 2007; Fudenberg & Maskin, 1986; Kandori, 1992; Luce & Raiffa, 1957; Mailah & Samuelson, 2006).”
Bayesian Persuasion (2024, background): “Since consumers are risk-neutral, each will buy the product if and only if Eµ [ω] ≥ p where µ is their posterior belief about the quality of the product.”