A COUPLE OF COLLECTIVE UTILITY AND MINIMUM PAYOFF PARITY LOSS RULES FOR REFINING NASH EQUILIBRIA IN BIMATRIX GAMES WITH ASYMMETRIC PAYOFFS
Journal Title: Вісник Кременчуцького національного університету імені Михайла Остроградського - Year 2018, Vol 1, Issue 108
Abstract
Purpose. For furthering the known approaches to the Nash equilibria refinement, an approach should be suggested that could exploit more than just one technique of operating over payoffs in bimatrix games. The payoffs must be asymmetric as refining Nash equilibria with symmetric payoffs without additional information is impossible. For creat-ing the new approach, initial denotations, a convention on payoff matrices, a convention on the players’ rationalism, and a refinement mathematical problem are to be stated. Methodology. Values of entries in payoff matrices have identical measurement units. Without loss of generality, we also presume the payoff matrices to be nonnegative. A number of efficient Nash equilibria is presumed to be greater than 1. At least a pair of players’ payoffs in an efficient Nash equilib-rium must have diverse payoffs. At least a pair of players’ payoffs in an efficient Nash equilibrium must be different from other pairs/pair. The players are assumed to be not ultimately avaricious implying that some concessions/retreats are admissible. Players may lose more without retreats but the retreat must be made by a single player. A minimal re-treat must be chosen. An efficient Nash equilibrium corresponding to the minimal retreat is then focused on and called a metaequilibrium. Findings. A two-criteria problem for the metaequilibrium is stated, wherein the collective utility is maximized and the payoff parity loss is minimized. This problem is solved via scalarization with weighing the criteria. Originality. A couple of collective utility and minimum payoff parity loss rules is used as for refining Nash equilibria, as well as for ranking efficient Nash equilibria. Practical value. The metaequilibrium prevents the players from spring-ing off equilibria themselves. Its applications are basically in law, economics, bioecological processes, where interac-tion events need the equilibria. References 18, figures 4.
Authors and Affiliations
V. Romanuke
Keywords
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