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Complete null agent for games with externalities
عامل پوچ کامل برای بازی با اثرات جانبی-2019
Game theory provides valuable tools to examine expert multi-agent systems. In a cooperative game, col- laboration among agents leads to better outcomes. The most important solution for such games is the Shapley value, that coincides with the expected marginal contribution assuming equiprobability. This as- sumption is not plausible when externalities are present in an expert system. Generalizing the concept of marginal contributions, we propose a new family of Shapley values for situations with externalities. The properties of the Shapley value offer a rationale for its application. This family of values is charac- terized by extensions of Shapley’s axioms: efficiency, additivity, symmetry, and the null player property. The first three axioms have widely accepted generalizations to the framework of games with externali- ties. However, different concepts of null players have been proposed in the literature and we contribute to this debate with a new one. The null player property that we use is weaker than the others. Finally, we present one particular value of the family, new in the literature, and characterize it by two additional properties.
Keywords: Game theory | Multi-agent systems | Externalities | Partition function | Marginal contribution