Community enforcement with observation costs

Takahashi (2010) [12] proves a folk theorem in an environment where a continuum of players are randomly matched in each period to play the prisoner's dilemma with a different partner. A key assumption there is that a player can observe her partner's past play without any cost, while she cannot observe the past play of her partner's past partners, the partners of her partner's past partners, and so on. However, Takahashi's [12] result is not robust to the introduction of an infinitesimal cost to acquire information about partners' past play. In this note, with the help of cheap-talk communication, I prove a folk theorem by constructing an equilibrium strategy that is robust to an infinitesimal cost.