Reaction function of punishment and the evolution of cooperation level

Mayuko Nakamaru
(Tokyo Institute of Technology)

Ulf Dieckmann
(IIASA)

06/11/06, 13:30 at Room 3631 (6th floor of building 3 of the Faculty of Sciences)


Punishment is one of important factors for the evolution of cooperation, and the coevolution of cooperation and punishment has been discussed using the discrete type strategies such as a cooperator who punishes a defector, a pure cooperator who do not punish a defector, a pure defector, and a defector who also punishes a defector in non-spatial and spatial structured populations. Here we investigate the evolution of reaction norm of punishment, which defines who is a defector or a cooperator, assuming the continuous traits of cooperation and punishment in order to see if a defector who never punishes others could evolve to be a cooperator who punishes others defines as a defector. The adaptive dynamics does not show that cooperation is promoted by punishment in the complete mixing population. The lattice-structured population, on the other hand, can promote the evolution of the cooperation level, which is predictable. Then punishment also promotes the cooperation level in the lattice-structured population, especially when the cooperation cost function is decelerating. We also observe that either the implemental error or the perception error never affects the evolutionary dynamics, but large and high mutations do. When the reaction norm of punishment has a strict threshold that defines a defector, the evolved cooperation level can be high. These results can hold when we investigate the coevoluion of cooperation and the reaction norm of punishment.


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