Language: 日本語 English

repeated Prisoner’s Dilemma

Takako Fujiwara-Greve and Yosuke Yasuda
Sat, 2009-06-20

In many repeated interactions, repetition is not guaranteed but instead
must be agreed upon. We formulate a model of voluntary repetition by introducing
outside options to a repeated Prisoner’s Dilemma and investigate how the structure
of outside options affects the sustainability of mutual cooperation. When the outside
option is deterministic and greater than the value of mutual defection, the lower bound
of the discount factors that sustain repeated cooperation is greater than the one for
ordinary repeated Prisoner’s Dilemma, making cooperation more difficult. However,
stochastic outside options with the same mean may reduce the lower bound of discount
factors as compared to the deterministic case. This is possible when the stochasticity
of the options increases the value of the cooperation phase more than the value of the
punishment phase. Necessary and sufficient conditions for this positive effect are given
under various option structures.