The Impossibility of Cooperation in Prisoner’s Dilemma Games under Local Interaction and Imitation

This paper analyzes a repeated game of prisoner’s dilemma, in which players meet all of their neighbors once, then imitate the neighbors or themselves whoever have the highest total payoffs, and finally make mistakes with small probability at each time period. All the limit states, including cooperation, no-cooperation, and coexistence of both in unperturbed dynamics are first derived. It is then shown that non-cooperation is the unique stochastically stable state of perturbed dynamics. Moreover, the convergence rate to the stochastically stable state is provided. These results imply that cooperation is never a long-run equilibrium under certain local-interaction and imitation dynamics.