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"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.
Games can be a single round or repetitive. The approach a player takes in making their moves constitutes their strategy. Rules govern the outcome for the moves taken by the players, and outcomes produce payoffs for the players; rules and resulting payoffs can be expressed as decision trees or in a payoff matrix. Classical theory requires the ...
Normal form or payoff matrix of a 2-player, 2-strategy game ... game theory is used to model the decision-making process of players, such as investors, project ...
Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied. [19] One result of stochastic theory is that there exists a stationary vector v for the matrix v such that =.
Consider the decision to be made by the 20th and final competitor, of whether to choose in or out.He knows that if he chooses in, Player A receives a higher payoff from choosing to cooperate than aggressive, and being the last period of the game, there are no longer any future competitors whom Player A needs to intimidate from the market.
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).
This rule does not apply to the case where mixed (stochastic) strategies are of interest. The rule goes as follows: if the first payoff number, in the payoff pair of the cell, is the maximum of the column of the cell and if the second number is the maximum of the row of the cell – then the cell represents a Nash equilibrium.
The process repeats for each player until the initial node is reached. For example, Player 2 would choose "Joker" for the first subgame in the next iteration because a payoff of 11 ending in (9, 11) is greater than "Terminator" with a payoff of 6 at (6, 6).