Reflective evolution under strategic uncertainty. (English) Zbl 1411.91085

Dragicevic, Arnaud Z.

Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 2, Article ID 1950018, 14 p. (2019).

Summary: We consider population dynamics of agents who can both play the cooperative strategy and the competition strategy but ignore whether the game to come will be cooperative or noncooperative. For that purpose, we propose an evolutionary model, built upon replicator(-mutator) dynamics under strategic uncertainty, and study the impact of update decay. In replicator-mutator dynamics, we find that the strategy replication under certain mutation in an unstructured population is equivalent to a negative strategy replication in a structured population. Likewise, in replicator-mutator dynamics with decay, the strategy replication under certain mutation in a structured population is equivalent to a negative replication issued from an unstructured population. Our theoretical statements are supported by numerical simulations performed on bifurcation diagrams.

MSC:

91A22	Evolutionary games
92D25	Population dynamics (general)
91A06	\(n\)-person games, \(n>2\)

Keywords:

bioeconomics; evolutionary game theory; structured population; strategic uncertainty

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