“What you think I think you think I think” causes cycles and flocking in multi-player Rock-Paper-Scissors

Recent provocative 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, economists have counter-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. Iterated reasoning is difficult to model and to test, but extant research supports economists’ defense of equilibrium theory.

We report stable periodic behavior in human groups playing a multi-player version of Paper-Rock-Scissors. The game rewarded subjects for thinking exactly one step ahead of others in their group. Groups that played this game exhibited cycles that are inconsistent with any fixed-point equilibrium concept. These cycles are also significantly more profitable than the random play that game theory calls rational. The efficient complexity of behavior in this game challenges the preconception that coordination mechanisms must converge on equilibria to be promising for social applications.

Furthermore, these cycles are driven by a “hopping” behavior that can only be explained by iterated reasoning. Iterated reasoning, which was expected to eliminate cycles, seems to be driving them. If iterated reasoning is complicit in complex dynamics, then cycles and chaos may in fact be driving fluctuations in financial markets and other real-world economic systems. This research represents the power of cognitive science, collective behavior, and dynamical systems to push the frontiers of economic behavior.