The Chip Strategies Approximately Achieve Efficiency at the Optimal Rate

Abstract

For a two-player repeated favor-exchange game with private information, I compare the rates at which the chip-strategy equilibrium and the optimal perfect public equilibrium achieve the efficient payoff as the discount factor δ tends to 1. I show that (i) the convergence rate for the optimal perfect public equilibrium is no smaller than (1-δ)^(1/2); and (ii) that for the optimal chip-strategy equilibrium is no greater than (1-δ)^(1/2) , where the number of total chips grows at rate (1-δ)^(-1/2). In this sense, the chip-strategy equilibrium approximately achieves efficiency at the optimal rate (1-δ)^(1/2).