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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. [1] Player 1 is often called the "row player" and player 2 the "column player". If player 1 has possible actions and player 2 has possible actions, then each ...
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.
The structure of the optional prisoner's dilemma can be generalized from the standard prisoner's dilemma game setting. In this way, suppose that the two players are represented by the colors, red and blue, and that each player chooses to "Cooperate", "Defect" or "Abstain". [3] The payoff matrix for the game is shown below:
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 ...
In a Prisoner's Dilemma game between two players, player one and player two can choose the utilities that are the best response to maximise their outcomes. "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 ...
Player 1's payoff: Bid Accepted is , Bid Rejected is 0; Player 2's payoff: Bid Accepted is p, Bid Rejected is v; Side point: cut-off strategy. Player 2's strategy: Accept all bids above a certain cut-off P ∗, and Reject and bid below P ∗, is known as a cut-off strategy, where P ∗ is called the cut-off.
For a zero-sum 2-player game the payoff of player A doesn’t have to be displayed since it is the negative of the payoff of player B. [9] An example of a simultaneous zero-sum 2-player game: Rock–paper–scissors is being played by two friends, A and B for $10. The first cell stands for a payoff of 0 for both players.
If player 1 plays D, player 2 will play U' to maximise their payoff and so player 1 will only receive 1. However, if player 1 plays U, player 2 maximises their payoff by playing D' and player 1 receives 2. Player 1 prefers 2 to 1 and so will play U and player 2 will play D' . This is the subgame perfect equilibrium.