企業(yè)管理中的競爭問題(ppt)(編輯修改稿)
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【文章內(nèi)容簡介】 sh 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 Strategies （ 混合策略） ? A mixed strategy is a profile that specifies the probability of each pure strategy that is to be played. ? Nash Theorem: ? For any game with finite number of pure strategies, there always exists a Nash Equilibrium in mixed strategy form. 23 Nash Equilibrium (納什均衡 ) ? Mixed Strategies （ 混合策略） : Examples ? Coordination Game ? Jones plays (Large, Small) according to (p, 1p) ? Smith’s expected payoffs are: ? “Large”: 2p+(1)(1p) = US(L |(p, 1p)) ? “ Small” : (1)p+1(1p) = US(S |(p, 1p)) ? Smith should be “indifferent” between the two choices ? US(L |(p, 1p)) = US(S |(p, 1p)) ? p = 2/5 ? Hence Jones’ optimal mixed strategy must be (, ) ? Exercise: find the optimal mixed strategy for Smith. ? Matching the Pennies ? Find the Nash equilibrium in mixed strategies 24 正常經(jīng)濟情況 舊 廠 低價 高價 進入市場 100, 50 100,100 新廠 不進入 0,50 0,300 25 經(jīng)濟萎縮期 舊廠 低價 高價 進入市場 160, 110 40,40 新廠 不進入 0, 10 0,240 26 Nash Equilibr
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