5 A Strange Correspondence Consider the correspondence 0 : [0, 1] = [0, 1] whose graph is shown below. : a. Is this correspondence upper hemi-continuous? b. Does this correspondence have a fixed point? Relate your answer to the Kakutani fixed-point theorem. 2 c. Consider a two-player normal-form game where S1 = {U, D}, S2 = {L, R}. Let BR2 : [0, 1] = [0, 1] be such that BR2() := {y: the mixed strategy 02 with 02(L) = y best responds to Pl's strategy 01(U)= I} Are there payoff functions ui, uz in the game so that BR2 is the same correspondence as o? = 5 A Strange Correspondence Consider the correspondence 0 : [0, 1] = [0, 1] whose graph is shown below. : a. Is this correspondence upper hemi-continuous? b. Does this correspondence have a fixed point? Relate your answer to the Kakutani fixed-point theorem. 2 c. Consider a two-player normal-form game where S1 = {U, D}, S2 = {L, R}. Let BR2 : [0, 1] = [0, 1] be such that BR2() := {y: the mixed strategy 02 with 02(L) = y best responds to Pl's strategy 01(U)= I} Are there payoff functions ui, uz in the game so that BR2 is the same correspondence as o? =