A_Course_in_Game_Theory_-_Martin_J._Osborne 28

A_Course_in_Game_Theory_-_Martin_J._Osborne 28 - Page 13...

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Page 13 Figure 13.1 A convenient representation of a two-player strategic game in which each player has two actions. Under a wide range of circumstances the preference relation of player i in a strategic game can be represented by a payoff function (also called a utility function ), in the sense that whenever . We refer to values of such a function as payoffs (or utilities). Frequently we specify a player's preference relation by giving a payoff function that represents it. In such a case we denote the game by rather than . A finite strategic game in which there are two players can be described conveniently in a table like that in Figure 13.1. One player's actions are identified with the rows and the other player's with the columns. The two numbers in the box formed by row r and column c are the players' payoffs when the row player chooses r and the column player chooses c , the first component being the payoff of the row player. Thus in the game in Figure 13.1 the set of actions of the row player is {
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