When Aspiring and Rational Agents Strive to Coordinate

The paper studies a game of common interest played infinitely many times between two players, one being aspiration driven while the other being a myopic optimizer. It is shown that the only two long run stationary outcomes are the two static equilibrium points. Robustness of long run behaviour is studied to show that whenever the optimizer is allowed to make small mistakes, players are able to coordinate on the Pareto dominant equilibrium point most of the time in the long run if the speed of evolution of aspirations is sufficiently fast. However, when only the aspiring player is allowed to make small mistakes, achieving coordination is inevitable and independent of the speed at which aspirations evolve.