Interactive strategy sets in multiple payoff games

In game theory, it is usually assumed that each player has only one payoff function and the strategy set of the game is composed of the topological product of individual players' strategy sets. In real business and system design or control problems, however, players' strategy sets may be interactive and each player may have more than one payoff function. This paper investigates the more general situation of multiple payoff and multiple person games in a normal form. In this paper, each player has several payoff functions which are dominated by certain convex cones, and the feasible strategy set of each player may be interactive with those of the other players. This new model is applied to a classical example without requiring variational and quasi-variational inequalities, or point-to-set mappings.