Monday, November 7, 12:00, A 0.23

Author: Matthijs van Veelen (University of Amsterdam)

In and out of equilibrium: evolution of strategies in repeated games with discounting and population structure

Repeated games tend to have large sets of equilibria. We also know that in the repeated prisoners dilemma there is a profusion of neutrally stable strategies, but no strategy that is evolutionarily stable. But how stable is neutrally stable? We show that there is always a stepping stone path away from equilibrium: there is always a neutral mutant that can enter a population and create an actual selective advantage for a second mutant. Such stepping stone paths out of equilibrium generally exist both in the direction of more and in the direction of less cooperation.

While the central theorems show that such paths out of equilibrium exist, they could still be rare compared to the size of the strategy space. Simulations however suggest that they are not too rare to be found by a reasonable mutation process, and that typical simulation paths take the population from equilibrium to equilibrium through series of indirect invasions.