國外博弈論課件lecture(2)-資料下載頁
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【正文】 output: $200K ? Profit if employee doesn’t work: $0 ? Cost of monitoring: $10K May 28, 2021 73347 Game TheoryLecture 7 20 ? Employee’s best response B1(q): ? Shirk (r=0) if q ? Work (r=1) if q ? Any mixed strategy (0?r?1) if q= Employee Monitoring Manager Monitor ( q ) Not Monitor (1q) Employee Work ( r ) 50 , 90 50 , 100 Shirk (1r ) 0 , 10 100 , 100 50 100(1q) Expected payoffs Expected payoffs 100r10 200r100 May 28, 2021 73347 Game TheoryLecture 7 21 ? Manager’s best response B2(r): ? Monitor (q=1) if r ? Not Monitor (q=0) if r ? Any mixed strategy (0?q?1) if r= Employee Monitoring Manager Monitor ( q ) Not Monitor (1q) Employee Work ( r ) 50 , 90 50 , 100 Shirk (1r ) 0 , 10 100 , 100 50 100(1q) Expected payoffs Expected payoffs 100r10 200r100 May 28, 2021 73347 Game TheoryLecture 7 22 1 q r 1 ? Employee’s best response B1(q): ? Shirk (r=0) if q ? Work (r=1) if q ? Any mixed strategy (0?r?1) if q= ? Manager’s best response B2(r): ? Monitor (q=1) if r ? Not Monitor (q=0) if r ? Any mixed strategy (0?q?1) if r= Employee Monitoring Mixed strategy Nash equilibrium ((,),(,)) May 28, 2021 73347 Game TheoryLecture 7 23 2player each with two strategies ? Theorem 1 (property of mixed Nash equilibrium) ? A pair of mixed strategies ((r*, 1r*), (q*, 1q*)) is a Nash equilibrium if and only if v1((r*, 1r*), (q*, 1q*)) ? EU1(s11, (q*, 1q*)) v1((r*, 1r*), (q*, 1q*)) ? EU1(s12, (q*, 1q*)) v2((r*, 1r*), (q*, 1q*)) ? EU2(s21, (r*, 1r*)) v2((r*, 1r*), (q*, 1q*)) ? EU2(s22, (r*, 1r*)) 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 24 Summary ? Mixed strategies ? Mixed strategy Nash equilibrium ? Next time ? Mixed strategy Nash equilibrium ? Use indifference to find MNE ? Reading lists ? Chapter of Gibbon
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