Uncorrelated asymmetry

In game theory an uncorrelated asymmetry is an arbitrary asymmetry in a game which is otherwise symmetrical. The name 'uncorrelated asymmetry' is due to John Maynard Smith who called payoff relevant asymmetries in games with similar roles for each player 'correlated asymmetries' (note that any game with correlated asymmetries must also have uncorrelated asymmetries).

The explanation of an uncorrelated asymmetry usually makes reference to "informational asymmetry". Which may confuse some readers, since, games which may have uncorrelated asymmetries are still games of complete information . What differs between the same game with and without an uncorrelated asymmetry is whether the players know which role they have been assigned. If players in a symmetric game know whether they are Player 1, Player 2, etc. (or row vs. column player in a bimatrix game) then an uncorrelated asymmetry exists. If the players do not know which player they are then no uncorrelated asymmetry exists. The information asymmetry is that one player believes he is player 1 and the other believes he is player 2. Therefore, "informational asymmetry" does not refer to knowledge in the sense of an information set in an extensive form game.

The concept of uncorrelated asymmetries is important in determining which Nash equilibria are evolutionarily stable strategies in discoordination games such as the game of chicken. In these games the mixing Nash is the ESS if there is no uncorrelated asymmetry, and the pure conditional Nash equilibria are ESSes when there is an uncorrelated asymmetry.

The usual applied example of an uncorrelated asymmetry is territory ownership in the hawk-dove game. Even if the two players ("owner" and "intruder") have the same payoffs (i.e., the game is payoff symmetric), the territory owner will play Hawk, and the intruder Dove, in what is known as the 'Bourgeois strategy' (the reverse is also an ESS known as the 'anti-bourgeois strategy', but makes little biological sense).

References

Maynard Smith, J (1982) Evolution and the Theory of Games Cambridge University Press. ISBN 0-521-28884-3

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian-Nash Perfect Bayesian Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Screening game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Kenneth Arrow Robert Aumann Kenneth Binmore Samuel Bowles Melvin Dresher Merrill M. Flood Drew Fudenberg Donald B. Gillies John Harsanyi Leonid Hurwicz David K. Levine Daniel Kahneman David M. Kreps Harold W. Kuhn Eric Maskin Jean-François Mertens Paul Milgrom Oskar Morgenstern Hervé Moulin Roger Myerson John Nash John von Neumann Ariel Rubinstein Thomas Schelling Reinhard Selten Herbert Simon Lloyd Shapley John Maynard Smith Jean Tirole Albert W. Tucker Amos Tversky William Vickrey Robert B. Wilson Peyton Young

See also	Tragedy of the commons Tyranny of small decisions All-pay auction List of games in game theory Confrontation analysis List of game theorists Combinatorial game theory Alpha–beta pruning Bertrand paradox Bounded rationality No-win situation Coopetition

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Uncorrelated asymmetry

References

See also