Flocking in the depths of strategic iterated reasoning

Must it be the case that increasingly deep levels of strategic iterated reasoning by humans give increasingly close approximations of normative economic rationality? And if not, what might they do instead? We argue that human higher-level reasoning processes may support non-equilibrium, non-convergent "flocking" behavior. Flocking in the physical world is the sustained convergence of both the positions and velocities of the members of a group. We make the metaphor to flocking in our experiments by introducing decision environments in which participants' choices and reasoning processes function as their positions and velocities, respectively. With this definition, we demonstrate flocking in multiple group experiments over three unrelated economic games. The first game is the classic Beauty Pageant, the second is called the Mod Game, and we introduce the Runway Game. Though they three bear no formal resemblance to each other, subjects play them the same: as eliciting iterated reasoning in a way that causes individuals to converge to a "normed" depth of iterated reasoning. Our analyses and modeling suggest that flocking emerges from the way that players integrate feedback to adjust their depths of reasoning each round — an unexpected interaction between "higher"and "lower"-level reasoning processes. We offer new opportunities for cognitive science in behavioral game theory by speculating on the role that mental models play in helping participants represent these games as games of iterated reasoning.