The strategic environment effect in beauty contest games

Recent experimental studies have shown that observed outcomes deviate significantly more from the Nash equilibrium when actions are strategic complements than when they are strategic substitutes. This “strategic environment effect” offers promising insights into the aggregate consequences of interactions among heterogeneous boundedly rational agents, but its macroeconomic implications have been questioned because the underlying experiments involve a small number of agents. We studied beauty contest games with a unique interior Nash equilibrium to determine the critical group size for triggering the strategic environment effect, and we use both theory and experiments to shed light on its effectiveness. Based on cognitive hierarchy and level-K models, we show theoretically that the effect is operative for interactions among three or more agents. Our experimental results show a statistically significant strategic environment effect for groups of five or more agents, establishing its robustness against the increase in the population size.