Axioms for the outcomes of negotiation in matrix games

Suppose that we are given the payoff matrix for a game G of perfect information but with no side-payments. We seek to study the likely results if rational players negotiate a settlement involving only pure strategies. Axioms are presented for the set X(G) of payoff vectors that might actually occur under these idealized circumstances. We also present a formal negotiation process analogous to the rules in the Theory of Moves that realizes such a set X(G). The process shows that the axioms are consistent and therefore provide a possible indication of what should be simultaneously attainable by negotiation. Such a result could also provide a guide to arbitration. Among these axioms are Pareto-optimality of the payoff vectors in X(G) and natural properties with respect to nontriviality, lower bounds, symmetry, strong dominance, floors, and default reduction. Examples show that X(G) can be readily calculated, by hand in the case of 2 by 2 matrices, or on the computer in more complicated cases. The procedures work for any finite number of players.  2000 Elsevier Science B.V. All rights reserved.