In Homework 1, we saw that there is no strict dominant strategy equilibrium in an inspection game. Thus, the players must randomize and play a mixed strategy in equilibrium. Suppose the agent shirks with probability p₁ and works with probability (1P₁), while the principal inspects with probability p2 and does not inspect with probability (1p2). Find the mixed strategy equilibrium for this game. NI I (0,-k) (w,-w) W(wc, p-w – k) | (w – c, p− w) Table 1: Payoff matrix for the inspection game S
In Homework 1, we saw that there is no strict dominant strategy equilibrium in an inspection game. Thus, the players must randomize and play a mixed strategy in equilibrium. Suppose the agent shirks with probability p₁ and works with probability (1P₁), while the principal inspects with probability p2 and does not inspect with probability (1p2). Find the mixed strategy equilibrium for this game. NI I (0,-k) (w,-w) W(wc, p-w – k) | (w – c, p− w) Table 1: Payoff matrix for the inspection game S
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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Question
![In Homework 1, we saw that there is no strict dominant strategy equilibrium in an
inspection game. Thus, the players must randomize and play a mixed strategy in
equilibrium. Suppose the agent shirks with probability p₁ and works with probability
(1 - p₁), while the principal inspects with probability p2 and does not inspect with
probability (1-P2). Find the mixed strategy equilibrium for this game.
I
NI
S
(0, -k)
(w, -w)
W (w c, p-w-k)| (wc, p-w)
Table 1: Payoff matrix for the inspection game](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2891624-5653-4800-a5b8-ef2542d0501e%2Fb014f773-a86f-4efb-9009-c820d6811b15%2Fcmaxjm_processed.png&w=3840&q=75)
Transcribed Image Text:In Homework 1, we saw that there is no strict dominant strategy equilibrium in an
inspection game. Thus, the players must randomize and play a mixed strategy in
equilibrium. Suppose the agent shirks with probability p₁ and works with probability
(1 - p₁), while the principal inspects with probability p2 and does not inspect with
probability (1-P2). Find the mixed strategy equilibrium for this game.
I
NI
S
(0, -k)
(w, -w)
W (w c, p-w-k)| (wc, p-w)
Table 1: Payoff matrix for the inspection game
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