(Symmetric two-player strategic game with ordinal preferences) A two-player strategic game with…

(Symmetric two-player strategic game with ordinal preferences) A two-player strategic game with ordinal preferences is symmetric if the players’ sets of actions are the same and the players’ preferences are represented by payoff functions u1 and u2 for which u1(a1, a2) = u2(a2, a1) for every action pair (a1, a2). A two-player game in which each player has two actions is symmetric if the players’ preferences are represented by payoff functions that take the form shown in Figure 50.1, where w, x, y, and z are arbitrary numbers. Several of the two-player games we have considered are symmetric, including the Prisoner’s Dilemma, the two-player Stag Hunt (given again in Figure 50.2), and the game in Exercise 36.2. BoS (Figure 16.1) and Matching Pennies (Figure 17.1) are not symmetric.

 

 

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