pB 1 Similarly for s 0 B p 1 \u02c6 q pB p 1 \u02c6q pB 1 p \u02c6 q pB 1 p \u02c6 q pB p 1 \u02c6 q pB

Pb 1 similarly for s 0 b p 1 ˆ q pb p 1 ˆq pb 1 p

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4. Consider the following decision theoretic problem.Playerifirst choosesa{0,1}andthen receives a signals(a)about an underlying state of natureω{0,1}.Theex anteprobability thatω=1 is denoted bypand known toi. After observings(a),ichoosesx{0,1}. The signals(a)is distributed as follows:Pr[s(a)=ω]=0.75ifa=1 andω=10.55ifa=1 andω=00.55ifa=0 andω=1Qifa=0 andω=0whereQis an exogenous parameter known by playeri. Playeri’s payoff isu(a,ω,x)=-(ω-x)2.(a)[5pts]Suppose thatp=0.95 andQ=1. What is the optimal strategy for playeri?(Your answer should describe bothaandx). 4
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  • Spring '11
  • JohnPaddy
  • Game Theory, PBE, player, subgame perfect Nash, perfect Nash equilibrium

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