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Effect of punishment strictness on the evolution of cooperation.
Mayuko Nakamaru
Department of Value and Decision Science, Tokyo Institute of Technology
Abstract
Whether or not costly punishment promotes the evolution of cooperation has been investigated not
only in evolutionary biology but also in other research fields such as mathematical sciences and social
sciences. The previous theoretical studies assume that each player chooses either cooperation or
defection and either punishment or non-punishment; one reason is to make a simple mathematical
model. In reality, different players have different cooperation level and decide how to punish others
according to their cooperation level. For example, some players punish opponents strictly if their
cooperation level is lower than the threshold and they do not, otherwise. Some players impose gradual
punishment proportional to the opponent's cooperation level on the opponent. The former is called
strict punishment and the latter is called graduate punishment. We investigate which punishment
promotes the evolution of cooperation level in the complete mixing population or in the lattice
structured population, by means of adaptive dynamics and computer simulations. The results are (1)
strict punishment promotes the evolution of cooperation level and both coevolve in the lattice
structured population, and (2) graduate punishment promotes the evolution of cooperation level and
both coevolve in the complete mixing population under the condition that punishment helps
cooperators invade the population occupied by defectors.
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