Theory and Decision

, Volume 80, Issue 4, pp 501–521 | Cite as

The emergence of reciprocally beneficial cooperation



We offer a new and robust model of the emergence and persistence of cooperation when interactions are anonymous, the population is well mixed, and evolution selects strategies according to material payoffs. The model has a Prisoner’s Dilemma structure, but with an outside option of non-participation. The payoff to mutual cooperation is stochastic; with positive probability, it exceeds that from cheating against a cooperator. Under mild conditions, mutually beneficial cooperation occurs in equilibrium. This is possible because the non-participation option holds down the equilibrium frequency of cheating. Dynamic properties of the model are investigated theoretically and through simulations based on replicator dynamics.


Cooperation Voluntary participation Random payoffs 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Economics and StatisticsUniversity of Napoli Federico IINaplesItaly
  2. 2.School of Economics, Centre for Behavioural and Experimental Social ScienceUniversity of East AngliaNorwichUK

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