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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 ...
The movie takes this idea one step further, with the Soviet Union irrevocably committing to a catastrophic nuclear response without making the threat public. [ 158 ] The 1980s power pop band Game Theory was founded by singer/songwriter Scott Miller , who described the band's name as alluding to "the study of calculating the most appropriate ...
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 =.
"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.
There are four categories on a 2*2 matrix; horizontal is scale of payoff (or benefits), vertical is ease of implementation. By deciding where an idea falls on the pick chart four proposed project actions are provided; Possible, Implement, Challenge and Kill (thus the name PICK). Low Payoff, easy to do - Possible High Payoff, easy to do - Implement
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.
For example, in the first subgame, the choice "go to movie" offers a payoff of 9 since the decision tree terminates at the reward (9, 11), considering Player 2's previously established choice. Meanwhile, "stay home" offers a payoff of 1 since it ends at (1, 9), so Player 1 would choose "go to movie."
The first, due to Harsanyi (1973), [6] is called purification, and supposes that the mixed strategies interpretation merely reflects our lack of knowledge of the players' information and decision-making process. Apparently random choices are then seen as consequences of non-specified, payoff-irrelevant exogenous factors. [5]