Cyclic game dynamics driven by iterated reasoning

TL;DR

This paper demonstrates that human groups playing a multi-player game exhibit stable cyclic behaviors driven by limited iterated reasoning, challenging the idea that such reasoning suppresses complex dynamics in social systems.

Contribution

It provides empirical evidence of stable, complex cyclic dynamics in human groups, driven by bounded iterated reasoning, in a game setting similar to Rock-Paper-Scissors.

Findings

Groups show cycles inconsistent with fixed-point solutions.

Agents learn about 0.5 additional steps of reasoning per session.

Cyclic behaviors are driven by constrained iterated reasoning.

Abstract

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, economists have argued that iterated reasoning--what you think I think you think--will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. 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 solution concept. These cycles are driven by a "hopping" behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.