| Routes to Cooperation and Herding Effects in the Prisoner's Dilemma Game (2009) | |||||||||
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| Game theory formalizes interactions between living beings in biology, sociology, and economics, or even between physical particles [D. Helbing, T. Vicsek, New J. of Phys. 1, 13.1 (1999)] and quantifies the outcomes by payoffs. The prisoner's dilemma describes situations in which it is profitable if everybody cooperates as compared to defection (free-riding) by everybody, but where cooperation is risky and defection is tempting. The expected outcome is defection. Introducing a suitable two-parameter representation of the game-dynamical replicator equation, shows that the five rules for the evolution of cooperation [M. A. Nowak, Science 314, 1560 (2006)] can be subsumed into two routes to cooperation. It also reveals the existence of additional routes. The transitions to cooperation are classified into transitions of zeroth, first, and second order, corresponding to cases of equilibrium displacement, selection, and creation. Second-order transitions can result from herding effects, which make the payoffs dependent on the internal dynamics in the population. The resulting multi-stability can induce unexpected transitions to cooperation.. Comment: For related work see http://www.soms.ethz.ch/ | |||||||||
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