Multi-Objective Zero-Sum Games with Postponed Objective Preferences

The Multi-Objective Game (MOG) considered here involves a lack of knowledge on the part of both players regarding the objective preferences of the opponent. In addition, each player is assumed to postpone its own objective preferences. In contrast to the commonly used utility approach, in this case we propose to apply multi-objective optimization methods that are suited for the current MOG problem. In particular, this paper applies a worst-case domination relation among the payoff vectors. Moreover, the rationality of the players under postponed objective preferences is discussed and defined. The proposed solution approach results in the rational strategies under postponed objective preferences. This allows the players to further examine their alternative strategies before objective preferences are eventually made. Hence, this paper proposes a base for future work on decision support systems for players of such MOGs.