Cyclical behavior in large location games

Location games capture important economic phenomena ranging from preemption to choice of bank leverage. We explore a parametric family of location games with many players, each facing a conflict between maximizing a fundamental payoff component and a relative (or quantile dependent) component. Using simulations and human subject experiments we show that, behaviorally, the stationary Nash equilibria in such games are terrible predictions of behavior and payoffs when players can freely adjust their locations. Instead, large cycles consistently emerge, in which behavior slowly grows bolder over time. This corresponds to progressively earlier timing in pre-emption games or to increasingly later timing in wars of attrition. When locations are maximally bold, namely at the end of the domain of Nash play, behavior quickly reverts to the peak fundamental and a new cycle begins.