國外博弈論課件lecture(2)-在線瀏覽
2024-12-05 12:47本頁面
【正文】 e 7 15 Expected payoffs: example ? Mixed strategies: p1=( 3/4, 0, 188。 p2=( 0, 1/3, 2/3 ). ? Player 1: ? EU1(T, p2)=3?(1/3)+1?(2/3)=5/3, EU1(M, p2)=0?(1/3)+2?(2/3)=4/3 EU1(B, p2)=5?(1/3)+0?(2/3)=5/3. v1(p1, p2) = 5/3 ? Player 2: ? EU2(L, p1)=2?(3/4)+4?(1/4)=5/2, EU2(C, p1)=3?(3/4)+3?(1/4)=5/2, EU2(R, p1)=1?(3/4)+7?(1/4)=5/2. v1(p1, p2) = 5/2 Player 2 L (0) C (1/3) R (2/3) Player 1 T (3/4) 0 , 2 3 , 3 1 , 1 M (0) 4 , 0 0 , 4 2 , 3 B (1/4) 3 , 4 5 , 1 0 , 7 May 28, 2021 73347 Game TheoryLecture 7 16 Mixed strategy equilibrium ? Mixed strategy equilibrium ? A probability distribution for each player ? The distributions are mutual best responses to one another in the sense of expected payoffs May 28, 2021 73347 Game TheoryLecture 7 17 Mixed strategy equilibrium: 2player each with two pure strategies ? Mixed strategy Nash equilibrium: ? A pair of mixed strategies ((r*, 1r*), (q*, 1q*)) is a Nash equilibrium if (r*,1r*) is a best response to (q*, 1q*), and (q*, 1q*) is a best response to (r*,1r*). That is, v1((r*, 1r*), (q*, 1q*)) ? v1((r, 1r), (q*, 1q*)), for all 0? r ?1 v2((r*, 1r*), (q*, 1q*)) ? v2((r*, 1r*), (q, 1q)), for all 0? q ?1 Player 2 s21 ( q ) s22 ( 1 q ) Player 1 s11 ( r ) u1(s11, s21), u2(s11, s21) u1(s11, s22), u2(s11, s22) s12 (1 r ) u1(s12, s21), u2(s12, s21) u1(s12, s22), u2(s12, s22) May 28, 2021 73347 Game TheoryLecture 7 18 Find mixed strategy equilibrium in 2player each with two pure strategies ? Find the best response correspondence for player 1, given player 2’s mixed strategy ? Find the best response correspondence for player 2, given player 1’s mixed strategy ? Use the best response correspondences to determine mixed strategy Nash equilibria. May 28, 2021 73347 Game TheoryLecture 7 19 Employee Monitoring ? Employees can work hard or shirk ? Salary: $100K unless caught shirking ? Cost of effort: $50K ? Managers can monitor or not ? Value of employee
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