Abstract
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.
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