(a) Here in this game N = {1, 2}. The strategy set of player i is Si = {n| n is a positive integer , 0 n 10} The payoff of each player i is ui(si , sj ) = 0 if si < sj , 5 if si = sj , 10 if si > sj 1 Dipjyoti Majumdar (b) Also observe, 10 = u1(10, 0) > u1(0, 0) = 5 10 = u1(10, n) > u1(0, n) = 0 for all n = 1, , 9 5 = u1(10, 10) > u1(0, 10) = 0 Since the game is symmetric, a similar observation holds for player 2's payoff. Hence we see, that strategy s1 = 0, is strictly dominated by strategy s1 = 10 for player 1 and also strategy s2 = 0 is strictly dominated by strategy s2 = 10 for player 2. Given this we see, that in the next round strategy si = 1 is strictly dominated by strategy si = 10 for each player i. Proceeding in this manner we see that the only strategy that survives iterated elimination of strictly dominated strategies is s ? i = 10