Co-evolution of strategies for multi-objective games under postponed objective preferences

Abstract

The vast majority of studies that are related to game theory are on Single Objective Games (SOG), also known as single payoff games. Multi-Objective Games (MOGs), which are also termed as multi payoff, multi criteria or vector payoff games, have received lesser attention. Yet, in many practical problems, generally each player cope with multiple objectives that might be contradicting. In such problems, a vector of objective functions must be considered. The common approach to deal with MOGs is to assume that the preferences of the players are known. In such a case a utility function is used, which transforms the MOG into a surrogate SOG., This paper deals with non-cooperative MOGs in a non-traditional way. The zero-sum MOG, which is considered here, involves two players that postponed their objective preferences, allowing them to decide on their preferences after tradeoffs are revealed. To solve such problems we propose a co-evolutionary algorithm based on a worst-case domination relation among sets. The suggested algorithm is tested on a simple differential game (tug-of-war). The obtained results serve to illustrate the approach and demonstrate the applicability of the proposed co-evolutionary algorithm.