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2024-10-16 14:00 本頁(yè)面
【正文】 ? ( (1/2, 1/2), (1/2, 1/2) ) is a mixed strategy Nash equilibrium. Sheila H ( q ) T ( 1–q ) Bruce H ( r ) 1 , 4 4 , 1 T ( 1–r ) 4 , 1 1 , 4 May 30, 2021 73347 Game TheoryLecture 9 15 Example 2 ? Player 1’s expected payoff of playing T ? EU1(T, (q, 1–q)) = q 6 + (1–q) 0 = 6q ? Player 1’s expected payoff of playing B ? EU1(B, (q, 1–q)) = q 3 + (1–q) 6 = 63q ? Player 1 is indifferent between playing T and B ? EU1(T, (q, 1–q)) = EU1(B, (q, 1–q)) 6q = 63q 9q = 6 This give us q = 2/3 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 16 Example 2 ? Player 2’s expected payoff of playing L ? EU2(L, (r, 1–r)) = r 0+(1–r) 2 =2 2r ? Player 2’s expected payoff of playing R ? EU2(R, (r, 1–r)) = r 6+(1–r) 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) ? On
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