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The best-known example of a 2-player anti-coordination game is the game of Chicken (also known as Hawk-Dove game). Using the payoff matrix in Figure 1, a game is an anti-coordination game if B > A and C > D for row-player 1 (with lowercase analogues b > d and c > a for column-player 2). {Down, Left} and {Up, Right} are the two pure Nash equilibria.
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 describing the payoffs of player 1 and matrix describing the payoffs of player 2.
A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a ...
However, many of the commonly studied 2x2 games are at least ordinally symmetric. The standard representations of chicken, the Prisoner's Dilemma, and the Stag hunt are all symmetric games. Formally, in order for a 2x2 game to be symmetric, its payoff matrix must conform to the schema pictured to the right.
"A best response to a coplayer’s strategy is a strategy that yields the highest payoff against that particular strategy". [9] A matrix is used to present the payoff of both players in the game. For example, the best response of player one is the highest payoff for player one’s move, and vice versa.
Suppose a zero-sum game has a payoff matrix M where element M i,j is the payoff obtained when the minimizing player chooses pure strategy i and the maximizing player chooses pure strategy j (i.e. the player trying to minimize the payoff chooses the row and the player trying to maximize the payoff chooses the column).
Payoff matrix: Template documentation. Usage. This template allows simple construction of 2-player, 2-strategy payoff matrices in game theory and other articles. ...
The game of chicken, also known as the hawk-dove game or snowdrift game, [1] 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 neither yields), individuals try to avoid it out of pride, not wanting to look like "chickens".