387hw6 - W ⊂ R 2 We say a,u is admissable with respect to...

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Economics 387. Banking and Financial Intermediation. Spring 2002. Department of Economics, University of Texas Instructor: Dean Corbae, BRB 3.118, (o) 512-475-8530 Homework #6 - Due 4/17/02 Consider the repeated 2 player prisoner±s dilemma game with stage game payo f matrix: player 2 Actions C D player 1 C (2,2) (-1,3) D (3,-1) (0,0) Compute the set of equilibrium payo f s V by applying the algorithm (Theorem 5) provided in Abreu, Pearce, and Stachetti (1990). Use the set valued operator B ( W )= { w W :( a,u ) is admissable with respect to W and w = E ( a ; u ) } where a S = { C,D C,D } and u : S
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Unformatted text preview: W ⊂ R 2 . We say ( a,u ) is admissable with respect to W if (i) u ∈ W and (ii) E i ( a ; u ) ≥ E i (( α i ,a − i ); u ) for all α i ∈ { C,D } and i = 1 , 2 , where E i ( a ; u ) := (1 − δ ) π i ( a ) + δu i , i = 1 , 2 . Start with W = { ( − 1 , 3) , (0 , 0) , (2 , 2) , (3 , − 1) } and iterate W n = B ( W n − 1 ) until k W n − W n − 1 k is arbitrarily small where k•k is the sup norm. Your pro-gram should use Theorem 3 (i.e. you can use the extreme points of W ). Compute it once with δ = 3 4 and once with δ = 1 4 . 1...
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