game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

an uncorrelated asymmetry is an arbitrary asymmetry in a game which is otherwise

symmetrical Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...

. The name 'uncorrelated asymmetry' is due to

John Maynard Smith John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics un ...

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 In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies ...

. 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 In game theory, a bimatrix game is a simultaneous game for two players in which each player has a finite number of possible actions. The name comes from the fact that the normal form of such a game can be described by two matrices - matrix A descri ...

) then an uncorrelated asymmetry exists. If the players do not know which player they are then no uncorrelated asymmetry exists. The

information asymmetry In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. Information asymmetry creates an imbalance of power in transactions, which ca ...

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 An extensive-form game is a specification of a game in game theory, allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, th ...

. The concept of uncorrelated asymmetries is important in determining which

Nash equilibria In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...

are

evolutionarily stable strategies An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is ''impermeable'' when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy (or set o ...

in discoordination games such as the

game of chicken The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the ideal outcome is for one player to yield (to avoid the worst outcome if ...

. 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 The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the ideal outcome is for one player to yield (to avoid the worst outcome if ...

. 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 ''Evolution and the Theory of Games'' is a book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. The book was initially published in December 1982 by Cambridge University Press. Overview In the book, John Ma ...

Cambridge University Press. {{Game theory Game theory Asymmetry

See also

References