Equilibrium analysis underpins most of modern economic theory. Individuals are assumed to coordinate to equilibria where their actions and beliefs are mutually consistent. This assumption has profound consequences in terms of policy, from the idea of laissez-faire to the characterization of the business cycle as an essentially exogenous phenomenon. If major economic downturns such as the 2008 crisis are rather caused by endogenous forces, this opens up the possibility for early-warning signals and targeted interventions. So, when is the equilibrium assumption reasonable?
This project starts answering this question in the context of game theory, which is a transparent framework to study interdependent choices. The players are often assumed to coordinate on a Nash Equilibrium (NE). One seemingly convincing justification is learning: the participants of the game learn the NE. We show that this is not necessarily the case: both in simple and complicated games the learning dynamics may be complex, even chaotic. The players react too quickly to the moves of their opponent, so that their beliefs keep changing and fail to become coordinated. Strategic interactions might be governed by adaptation to an ever-changing environment, rather than by static and rational decision making, questioning the validity of equilibrium reasoning. For the learning algorithms investigated so far, we find that as the number of moves increases and the number of players gets larger, chaos tends to dominate. We also find interesting dependence on the degree of competition in the games and other parameters.
External collaborator: Tobias Galla