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【正文】 ) 0 = 6r ? Player 2 is indifferent between playing L and R ? EU2(L, (r, 1–r)) = EU2(R, (r, 1–r)) 2 2r = 6r 8r = 2 This gives us r = 188。 ? ( (1/4, 3/4), (2/3, 1/3) ) is a mixed strategy Nash equilibrium. Player 2 L ( q ) R ( 1–q ) Player 1 T ( r ) 6 , 0 0 , 6 B ( 1–r ) 3 , 2 6 , 0 May 30, 2021 73347 Game TheoryLecture 9 17 Example 3:Market entry game ? Two firms, Firm 1 and Firm 2, must decide whether to put one of their restaurants in a shopping mall simultaneously. ? Each has two strategies: Enter, Not Enter ? If either firm plays “Not Enter”, it earns 0 profit ? If one plays “Enter” and the other plays “Not Enter” then the firm plays “Enter” earns $500K ? If both plays “Enter” then both lose $100K because the demand is limited May 30, 2021 73347 Game TheoryLecture 9 18 Example 3:Market entry game ? How many Nash equilibria can you find? ? Two pure strategy Nash equilibrium (Not Enter, Enter) and (Enter, Not Enter) ? One mixed strategy Nash equilibrium ((5/6, 1/6), (5/6, 1/6)) That is r=5/6 and q=5/6 Firm 2 Enter ( q ) Not Enter ( 1–q ) Firm 1 Enter ( r ) 100 , 100 500 , 0 Not Enter ( 1–r ) 0 , 500 0 , 0 May 30, 2021 73347 Game TheoryLecture 9 19 Example 4 ? How many Nash equilibria can you find? ? Two pure strategy Nash equilibrium (B, L) and (T, R) ? One mixed strategy Nash equilibrium ((2/3, 1/3), (1/2, 1/2)) That is r=2/3 and q=1/2 Player 2 L ( q ) R ( 1–q ) Player 1 T ( r ) 1 , 1 1 , 2 B ( 1–r ) 2 , 3 0 , 1 May 30, 2021 73347 Game TheoryLecture 9 20 Summary ? Mixed strategies ? Mixed Nash equilibrium ? Find mixed Nash equilibrium ? Next time ? 2player game each with a finite number of strategies ? Reading lists ? Chapter of Gibbons and Cha of Osborne
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