Journal of Global Optimization
On Equitable Resource Allocation Problems: a Lexicographic Minimax Approach
Operations Research
Generative relations for evolutionary equilibria detection
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Evolutionary detection of aumann equilibrium
Proceedings of the 12th annual conference on Genetic and evolutionary computation
DEMO: differential evolution for multiobjective optimization
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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The most popular solution concept in game theory, Nash equilibrium, has some limitations when applied to real life problems. Nash equilibrium rarely assures maximal payoff. A possibility is to consider Pareto equilibrium, inspired from the standard solution concept in multi-criteria optimization, but the obtained equilibria often consists of a large set of solutions that is too hard to process. Our aim is to find an equilibrium concept that provides a small set of efficient solutions, equitable for all players. The Lorenz dominance relation is investigated in this respect. A crowding based differential evolution method is proposed for detecting the Lorenz-optimal solutions. Based on the Lorenz dominance relation, the Lorenz equilibrium for non-cooperative games is proposed. The Lorenz equilibrium consists of those Pareto-optimal solutions that are the most balanced and equitable solutions for all players. We propose to use Lorenz equilibrium for selecting one Nash equilibrium for games having several Nash equilibria.