F. A Caveat: Absolute versus Relative Payoffs Many caveats need to be kept in mind when actually determining what kind of game is at ssue. In all the cases above, the pay-off matrices presented only absolute payoffs, with the assumption that the players were using these absolute payoffs in determining their strategy. In the world of international law, this might not be valid assumption. Players, might, for example, be using relative pay-offs in determining strategies. Consider the pay-off in Table 1, a pure common interest game, which would lead to a stable Nash equilibrium which was Pareto optimal, if the players were using the absolute pay-off matrix. ' A reciprocity constraint was superfluous. However, if the players were concerned with relative pay-offs, the game would be transformed into a negative sum prisoner's dilemma. The pay-off matrix would take the following form See table I supra Part 1.A and accompanying discussion One can think of this as an armament game, where the cost of each weapon to a player is 1, and the benefit (or cost)of having one more weapon than the other is +2/-2
23See Table 1 supra Part 1.A and accompanying discussion. 24One can think of this as an armament game, where the cost of each weapon to a player is 1, and the benefit (or cost) of having one more weapon than the other is +2/-2. 15 F. A Caveat: Absolute versus Relative Payoffs Many caveats need to be kept in mind when actually determining what kind of game is at issue. In all the cases above, the pay-off matrices presented only absolute payoffs, with the assumption that the players were using these absolute payoffs in determining their strategy. In the world of international law, this might not be valid assumption. Players, might, for example, be using relative pay-offs in determining strategies. Consider the pay-off in Table 1, a pure common interest game, which would lead to a stable Nash equilibrium which was Pareto optimal, if the players were using the absolute pay-offmatrix.23 A reciprocityconstraint was superfluous. However, if the players were concerned with relative pay-offs, the gamewould be transformed into a negative sumprisoner’s dilemma.24 The pay-off matrix would take the following form:
0,0|-2,1-4 Figure(8): Relative Payoff Game Now, imposing a reciprocity constraint would result in an improvement in welfare by forcing both players to play strategy I, with payoff (0, 0). This is the outcome the players would have reached, without needing a reciprocity constraint, if they were considering absolute payoffs alone SThus. there is a credible commitment that ends the armament race
25Thus, there is a credible commitment that ends the armament race. 16 Figure (8): Relative Payoff Game Now, imposing a reciprocity constraint would result in an improvement in welfare by forcing both players to play strategy I, with payoff (0, 0).25 This is the outcome the players would have reached, without needing a reciprocity constraint, if they were considering absolute payoffs alone