Solving zero-sum multi-objective games with a-priori secondary criteria

Solving non-cooperative zero-sum multi-objective Games (zsMOGs), under undecided objective preferences results, for each of the players, in a Set of Rationalizable Strategies (SRS) to choose from. First, this paper deals with finding for each of the players a preferred subset of such rationalizable strategies based on a-priori incorporation of partial preferences of the decision-makers using secondary criteria. The obtained subset is termed the Set of Preferred Strategies (SPS). Here, a novel archive-based co-evolutionary algorithm is suggested to search for the SPS for each of the players. An academic example is suggested to demonstrate and validate the algorithm. It concerns a zsMOG that involves two adversarial planar manipulators. Based on a theorem that is proven here, a theoretic reference SRS is found for each of the players. This reference SRS is applied to find a reference SPS, which is used for validating the algorithm. Next, a comparison study is performed between the proposed archive-based co-evolutionary algorithm and an elite-based version of this algorithm. The results clearly show that the archive-based algorithm is superior to the elite-based version, yielding results that correspond well to the theoretic sets.