PS5_Sol.pdf - HE3002 Game Theory(Sem 1 AY2019\/20 Problem Set 5 Solution(for tutorial on 22 Oct 2019 1(Market for \u201cLemons\u201d(a Suppose that the seller

# PS5_Sol.pdf - HE3002 Game Theory(Sem 1 AY2019/20 Problem...

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HE3002: Game Theory (Sem 1, AY2019/20) Problem Set 5 Solution (for tutorial on 22 Oct 2019) 1. (Market for “Lemons”.) (a) Suppose that the seller plays ( p 15 , p 5 ) . The buyer’s best response is to play ( A | p 15 , R | p 5 ) . However, seller L will then prefer to play p 15 instead of p 5 because he will get 15 instead of 0 . Therefore, seller L will deviate. (Not PBE.) Suppose that the seller plays ( p 5 , p 15 ) . The buyer’s best response is to play ( R | p 15 , A | p 5 ) . However, seller L will prefer to play p 5 instead of p 15 since he will get 5 instead of 0 . Therefore, seller L will deviate. (Not PBE.) Therefore, there is no PBE involving the seller playing a separating strategy. (b) First, consider the seller playing ( p 15 , p 15 ) . Upon observing p 15 , the buyer assigns probability π and 1 - π to the car being H and L respectively. He will choose A over R if and only if 5 π - 15(1 - π ) 0 ⇐⇒ π 3 4 Off the equilibrium path (i.e., when buyer observes p 5 ), let him assign probability μ 5 and 1 - μ 5 to the car being H and L respectively. He will choose A over R if and only if

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