Joint work with James Sanders, Tobias Galla, Doyne Farmer.
How do players coordinate on specific profiles of strategies in non-cooperative games, and why should they coordinate on an equilibrium profile? Coordination is central to economics, and game theory provides a transparent framework to understand this issue. Here we focus on the simplest setting, that is generic 2-player, 2-strategy games, and we consider Experience-Weighted Attraction learning as a way to achieve coordination. We show that if the players are irrational and/or do not have enough incentives to focus on a specific strategy, they simply randomize between their possible moves. In the opposite case, we find striking behavioural differences according to the classes of games one is considering: (i) dominance solvable games (e.g. Prisoner Dilemma) show convergence all the time; (ii) coordination/anticoordination games (e.g. Stag-Hunt or Chicken) display convergence to multiple NE; (iii) discoordination games (e.g. Matching Pennies) commonly yield limit cycles or low-dimensional chaos, and thus a dynamic failure of coordination.
In a first part of the talk, I will review some of the literature on learning in games, showing that it is fairly well known that the learning dynamics may fail to converge to an equilibrium, either reaching a different fixed point, or endlessly cycling between the profiles of strategies. In the second part, I will present our approach and defend its novelty. First, we prove that the existence of a cycle in beliefs, coupled with a quick enough learning, is a sufficient condition for non-converging dynamics, and we impose no further restrictions on the payoff matrix. Second, we find explicit boundaries for the parameters where instability settles in. Third, from a methodological point of view, we use a different approach than most of the literature.
Any feedback is greatly appreciated.