Problem 1 consider the following 3-player game. Alice chooses the row from {U, D}, Bob chooses the column from {L, R}, a

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Problem 1 Consider The Following 3 Player Game Alice Chooses The Row From U D Bob Chooses The Column From L R A 1 (91.49 KiB) Viewed 27 times

Problem 1 consider the following 3-player game. Alice chooses the row from {U, D}, Bob chooses the column from {L, R}, and Colin chooses the matrix from {0,6,7,8}. CY Bob L R Alice U 7, 7, 12 7,7,0 7,7,0 7,7,0 D B Bob L R Alice U 7,7,7,7,0 7,7,0 7,7,2 D 7 Bob L R Alice U 7, 7,0 7,7,0 D 7,7,0 7,7,12 8 Bob L R Alice U 7,7,5 7,7,5 D7,7,57,7,5 1. Suppose that Colin's beliefs are restricted to being uncorrelated i.e., Alice plays U and D with some probability and Bob plays L and R with some probability, and Colin's perceived probability of any element of S_Colin is just the product of these probabilities. Find a value for 2 E R such that strategy B (i.e. choosing matrix B) is never a best response, and yet it is not strictly dominated. Prove that r is as desired. 2. Show that, for your choice of x above, if we allow for correlated beliefs, then strategy B is a best response to some beliefs.