5-1-2012Lecture NotesMidterm format: similar to homework assignmentsI. Uncertainty about PreferencesA. Nature Chooses "Type"B. Solving Gaes with TupesAid Notuncertain about whothey're playing against (0, 0)p 1-p corrupt noncorrupt Edu Limos Edu Limos (2, 2) (-2, 5) (2, 2) (-2, 1)Harsani Transformation: use nature nodes "Type": Type of preferences we're uncertain about thisNaturebelow decisions made without knowledge of uncertaintiesabove decisions made with knowledge of uncertaintiesRichNatureUncorruptPoorCorrupt PoorRichAid Not (2-4p)(0, 0)p 1-p corrupt noncorrupt Edu Limos Edu Limos (2, 2) (-2, 5) (2, 2) (-2, 1)EUr (Aid) = -2p + 2(1-p) = -2p + 2 - 2p = 2 - 4pIf 2 - 4p > 0, Rich chooses AidCase 1: p < 1/2Rollback Equilibrium: Rich Aid Uncorrupt Poor: Edu if Aid Corrupt Poor: Limos if Aid Case 2 : p > 1/2Rollback Equilibrium: Rich No Aid Uncorrupt Poor: Edu if Aid Off the Corrupt Poor: Limos if Aid Equilibrium Patheither corrupt poor has a strategy or uncorrupt poor has a strategyAll variables:Aid Not(0, 0)p 1-p corrupt noncorruptNatureUncorruptPoorCorrupt PoorRichNatureUncorruptPoorCorrupt PoorEdu Limos Edu LimosVc(E) = value to corrupt of EduVc(L) = value to corrupt of LimosVu(E) = value to uncorrupt of EduVu(L) = value to uncorrupt of EduVr(E) = value to rich of EduVr(L) = value to rich of Limosc = cost to rich of sending AidAid Not(0, 0)p 1-p corrupt noncorrupt(-c , Vc(L)) (Vr(E) - c , Vu(E)) Edu Limos Edu Limos (Vr(E) - c , Vc(E)) (-c , Vc(L)) (Vr(E) - c , Vu(E)) (-c , Vu(L))Assumptions (to minimize cases)1) Vr(L) = 02) Vc(E) < Vc(L) what it means3) Vu(E) > Vu(L) to be c or u4) Vr(E) > 0EUr(Aid) = p(-c) + (1-p)(Vr(E) - c) = -cp + (1-p)(Vr(E)) - (1-p)(c) = -c + (1-p)Vr(E)Send Aid if -c +(1-p)Vr(E) > 0c < (1-p)Vr(E)^This is the expected benefit of Aid.The cut point is in C for when the Rich sends Aid.RichNatureUncorruptPoorCorrupt