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【正文】 inant strategy implies that all other choices are in fact the dominated strategies. ? But it is possible that there are dominated strategies, while there is no dominant strategy 15 B L C R U 3, 0 0, 5 0, 4 M 1, 1 3, 3 2, 4 A D 2, 4 4, 1 1, 8 Application: Iterative Eliminations ? Example 16 Nash Equilibrium (納什均衡 ) ? Even though using a dominant strategy or a dominated strategy is a powerful simple way of “solving” a game, this kind of game is usually an exception, instead of a norm. ? We must have a generic method of finding the solution(s) of a game. ? Solution Concepts ? Nash Equilibrium is the very first solution concept for noncooperative games. 17 Nash Equilibrium (納什均衡 ) ? Essence of Nash Equilibrium ? A Nash Equilibrium is defined as a set of strategies such that non of the participants in the game can improve their payoff, given the strategies of the other participants. ? No one has a strictly incentive to deviate from the strategies in a Nash Equilibrium. 18 Nash Equilibrium (納什均衡 ) ? Example ? Consider the following game. Is there any dominant or dominated strategy? Pl aye r 2 L C R U 5, 3 0, 4 3, 5 M 4, 0 5, 5 4, 0 Pl aye r1 D 3, 5 0, 4 5, 3 19 Nash Equilibrium (納什均衡 ) ? Problem of Nash Equilibrium: ? Multiple solutions! ? Examples: ? Battle of Sex ? Coordination Game 男 (The Man) 歌劇 拳擊 女 (The Lady) 歌劇 2， 1 0， 0 拳擊 0， 0 1， 2 Jones Large Small Smith Large 2, 2 1, 1 Small 1， 1 1, 1 20 Nash Equilibrium (納什均衡 ) ? Problem of Nash Equilibrium: ? Insensitive to extreme payoffs (risks) ? Example: Dangerous Coordination Game Jones Large Small Smith Large 2, 2 1000, 1 Small 1， 1 1, 1 In Practice, it is almost sure that Smith wants to “play safe” and never try “l(fā)arge”! 21 Nash Equilibrium (納什均衡 ) ? Problem of Nash Equilibrium: ? Nonexistence of pure strategy Nash Equilibrium ? Example: Match the Pennies ? No dominant strategy, no dominated strategy no pure strategy Nash equilibrium as well! B Head Tail A Head 1, 1 1, 1 Tail 1， 1 1, 1 22 Nash Equilibrium (納什均衡 ) ? Mixed Strategie
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