12_8 thur - Chapter 28&29 Game Theory Applications[From...

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Chapter 28&29 Game Theory& Applications [From last class: - Employee chooses ( work, shirk) with probabilities ( r, 1-r) Manager chooses (monitor, not monitor) with probabilities ( c, 1-c) - Next: finding the employee’s best response(S) for any choice of c by the manager (Recall: the probability that the manger monitors is denoted by c) - Expected payoff for employee if he works is: (50)c+(50)(1-c)=50 Expected payoff for employee if he shirks is (0)c+(100)(1-c)=100-(100)c] Expected payoff for employee if he works hard=Expected payoff for employee if he shirks - 50=100-(100)*c - c=.5 - Hence: To have the expected payoffs from the employee’s two possible strategies be equal , we must have c=.5 Pic 1. - Expected Payoff for employee if he works > = < Expected Payoff for employee if he shirks. - 50> = <100- (100)c - C > = < .50 - Hence: For c> .5 , employee’s best response is work (r=1) For c< .5 , employee’s best response is shirk (r=0) For c= .5 , each pure strategy is a best response and so is any mixed strategy ( 0≤ r ≤1) Pic2, A graph with Row’s best responses: Manger Monitor Not monitor Employee Work 50,90 50,100 Shirk 0,-10 100,-100 There isn’t always a unique best response Next: Finding the manager’s best responses for any choice of r by the employee.
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