Expectations, Drift, and Volatility in Evolutionary Games

This paper proposes an evolutionary model of learning in simple coordination games where expectations are the driving force of the process. As time proceeds, agents adjust their expectations through some (possibly different) updating rules, whose only requirement is that of consistency with long stationary evidence. Sporadically, expectations are also subject to arbitrary perturbation. The main point of the paper is that, due to the possibility of random drift on expectations, the evolutionary process will be subject to high volatility across equilibria. Specifically, every Nash equilibrium (even if risk- or payoff-dominated) will have significant positive weight in the long-run invariant distribution.