Payoff space for C1 games

In the current Game Theory literature the study of a game in normal form consists principally in the determination of the Nash equilibria and in the analisys of their stability properties. This does not give a complete and global view of the game, since, for instance, it should be interesting to know the positions of the payoff profiles corresponding to the Nash equilibria in the payoff space of the game; but, the knowledge of these positions requires the knowledge of the entire payoff space. This need becomes inevitable when the problem to solve in the game is a bargaining one: in fact, the determination of a bargaining solution (or of compromise solutions) needs the analytical determination of the Pareto boundaries. In our paper we shall present a general method to find an explicit expression of the Pareto boundaries, via the determination of the entire topological boundary of the payoff space of the game. Resuming, the motivation of the paper resides upon the fact that a complete and deep study of a game in normal form requires the knowledge of the payoff space, or at least of its Pareto boundaries, especially when one passes to the cooperative phase of the game, because, to find bargaining solutions or other compromise solutions, the knowledge of the Pareto boundaries is necessary.