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Evolutionary dynamics for multicriteria games generated by p-norm-based pairwise proportional imitation

Multicriteria evolutionary games model interactions among many players who make decisions on the basis of multiple criteria. In single-criterion games, imitative behaviors of the players are described by revision protocols. The pairwise proportional imitation is one of the revision protocols. The evolutionary dynamics derived from the protocol is well-known as replicator dynamics. In multicriteria games, however, there are few studies on the evolutionary dynamics. In this paper, we consider the evolutionary dynamics in multicriteria games. We extend the pairwise proportional imitation to the multicriteria games and derive the evolutionary dynamics. We also show the relationships between the stability of equilibrium points of the proposed dynamics, and the equilibrium and evolutionary stability concepts of multicriteria games.