Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, game theorists have argued that iterated reasoning-our ability to think through what you think I think you think-will prevent complex dynamics and facilitate convergence to classic equilibria. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point equilibrium concept. These cycles are driven by a "hopping" behavior that can only be explained by iterated reasoning. If iterated reasoning can be complicit in complex dynamics, then game cycles and chaos may realistically be driving fluctuations in real-world social and economic systems.
Cyclic game dynamics driven by iterated reasoning
Seth Frey, Robert L. Goldstone