Before revision: πi(ai, bj) represents the payoffs player i receives Player i's kindness to player j is given by: ƒi(ai, bj) = [πj(bj, ai) - πje(bj)]/[πjh(bj) - πjmin(bj)] πje(bj)= [πjh(bj)+ πjl(bj)]/2, where πjh(bj)is player j's highest payoff and πjl(bj) is player j's lowest payoff among points that are Pareto efficient πjmin(bj) is the worst possible payoff in the matrix for player j Player i's belief about how kind player j is being to him is given by: ƒj(bj, ci) = [πi(ci, bj) - πie( cj )]/[πjh( cj ) - πimin(ci)] πimin(ci) is player i's worst possible payoff πie(ci)= [πih(ci)+ πil(ci)]/2, where πih(ci)is player j's highest payoff and πil(ci) is player i's lowest payoff among points that are Pareto efficient The two functions above can now specify player's preferences.
After revision: πi(ai, bj) represents the payoffs player i receives Player i's kindness to player j is given by: ƒi(ai, bj) = [πj(bj, ai) - πje(bj)]/[πjh(bj) - πjmin(bj)] πje(bj)= [πjh(bj)+ πjl(bj)]/2, where πjh(bj)is player j's highest payoff and πjl(bj) is player j's lowest payoff among points that are Pareto efficient πjmin(bj) is the worst possible payoff in the matrix for player j Player i's belief about how kind player j is being to him is given by: ƒj(bj, ci) = [πi(ci, bj) - πie( ci )]/[πjh( ci ) - πimin(ci)] πimin(ci) is player i's worst possible payoff πie(ci)= [πih(ci)+ πil(ci)]/2, where πih(ci)is player j's highest payoff and πil(ci) is player i's lowest payoff among points that are Pareto efficient The two functions above can now specify player's preferences.