Rationality Postulates for Bargaining Solutions in Cooperative and in Non-Cooperative Games

The von Neumann-Morgenstern theory yields a determinate solution (a unique payoff vector) only for the two-person zero-sum game and some other special cases. But if we adopt a small number of additional rationality postulates we obtain determinate solutions for all known classes of games. The rationality postulates needed include the expected-utility maximization postulate; postulates involving payoff-dominance concepts; and postulates imposing certain consistency requirements on the expectations that rational players can entertain about each other's strategies. For some games the solution can be defined essentially in terms of payoff-dominance concepts. But more generally the solutions depend on the analysis of bargaining among the players.