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Chapter 56 Values of games with infinitely many players
Neyman, Abraham - In: Handbook of game theory with economic applications : …, (pp. 2121-2167). 2002
This chapter studies the theory of value of games with infinitely many players.Games with infinitely many players are …-handed influence. The interactions are modeled as cooperative games with a continuum of players. In general, the continuum consists of … framework for mathematical analysis, and approximates the results for large finite games well. Also, it enables a unified view …
Persistent link: https://www.econbiz.de/10014024489
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The Language of Game Theory:Putting Epistemics into the Mathematics of Games
Brandenburger, Adam - World Scientific Publishing Co. Pte. Ltd.
Theorem on Beliefs in Games <i>(Adam Brandenburger and H Jerome Keisler)</i></li> <li>Hierarchies of Beliefs and Common …>(Adam Brandenburger and Eddie Dekel)</i></li> <li>Intrinsic Correlation in Games <i>(Adam Brandenburger and Amanda Friedenberg …>Lexicographic Probabilities and Choice Under Uncertainty <i>(Lawrence Blume, Adam Brandenburger, and Eddie Dekel)</i></li> <li>Admissibility in …
Persistent link: https://www.econbiz.de/10011010976
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Epistemic Conditions for Nash Equilibrium
Aumann, Robert; Brandenburger, Adam - In: The Language of Game Theory:Putting Epistemics into the …
Sufficient conditions for Nash equilibrium in an n-person game are given in terms of what the players know and believe — about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the...
Persistent link: https://www.econbiz.de/10011206381
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Admissibility in Games
Brandenburger, Adam; Friedenberg, Amanda; Keisler, H. Jerome - In: The Language of Game Theory:Putting Epistemics into the …
Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement — that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide...
Persistent link: https://www.econbiz.de/10011206393
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Hierarchies of Beliefs and Common Knowledge
Brandenburger, Adam; Dekel, Eddie - In: The Language of Game Theory:Putting Epistemics into the …
Game-theoretic analysis often leads to consideration of an infinite hierarchy of beliefs for each player. Harsanyi suggested that such a hierarchy of beliefs could be summarized in a single entity, called the player's type. This chapter provides an elementary construction, complementary to the...
Persistent link: https://www.econbiz.de/10011206453
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Self-Admissible Sets
Brandenburger, Adam; Friedenberg, Amanda - In: The Language of Game Theory:Putting Epistemics into the …
behavior of SAS's in some games of interest — Centipede, the Finitely Repeated Prisoner's Dilemma, and Chain Store. We then … establish some general properties of SAS's, including a characterization in perfect-information games. …
Persistent link: https://www.econbiz.de/10011206587
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Lexicographic Probabilities and Choice Under Uncertainty
Blume, Lawrence; Brandenburger, Adam; Dekel, Eddie - In: The Language of Game Theory:Putting Epistemics into the …
Two properties of preferences and representations for choice under uncertainty which play an important role in decision … event and which corresponds to the individual's preferences. The conventional Bayesian theory of choice under uncertainty …
Persistent link: https://www.econbiz.de/10011206642
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Rationalizability and Correlated Equilibria
Brandenburger, Adam; Dekel, Eddie - In: The Language of Game Theory:Putting Epistemics into the …
We discuss the unity between the two standard approaches to noncooperative solution concepts for games. The decision …
Persistent link: https://www.econbiz.de/10011206697
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Intrinsic Correlation in Games
Brandenburger, Adam; Friedenberg, Amanda - In: The Language of Game Theory:Putting Epistemics into the …
Correlations arise naturally in noncooperative games, e.g., in the equivalence between undominated and optimal … strategies in games with more than two players. But the noncooperative assumption is that players do not coordinate their … strategy choices, so where do these correlations come from? The epistemic view of games gives an answer. Under this view, the …
Persistent link: https://www.econbiz.de/10011206775
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An Impossibility Theorem on Beliefs in Games
Brandenburger, Adam; Keisler, H. Jerome - In: The Language of Game Theory:Putting Epistemics into the …
A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin …
Persistent link: https://www.econbiz.de/10011206790