Games with multiple payoffs

Abstract

The traditional theories of decision making and games are based on an assumption that prevents their broader practical utilization:a single dimensional payoff. In reality, any alternative is likely to imply more than one payoff, e.g. not only costs but also time, price, quality, safety, maintainability, productivity, etc. Similarly, the Theory of Games faces difficulties as we attempt to apply it to the conflict situations of the social and business environment. The assumption that a single dimensional payoff, like money, points or chips, is a realistic consequence of individual moves or strategies, is difficult to sustain. In this short paper, concepts of nondominated solutions and a decomposition of parametric spaces are used to formulate and resolvedecision problems with vector payoffs. Both Games against Nature and Two-Person, Zero-Sum frameworks are considered. A concept of compromise solutions is introduced to help the decision maker with further reduction of the nondominated set. Some numerical examples are given.