Rushes in Large Timing Games
Axel Anderson, Lones Smith, Andreas Park
Econometrica · 2017 · Volume 85 · Issue 3
Abstract
We develop a continuum player timing game that subsumes standard wars of attrition and pre-emption games, and introduces a new rushes phenomenon. Payoffs are continuous and single-peaked functions of the stopping time and stopping quantile. We show that if payoffs are hump-shaped in the quantile, then a sudden “rush” of players stops in any Nash or subgame perfect equilibrium. Fearrelaxes the first mover advantage in pre-emption games, asking that the least quantile beat the average;greedrelaxes the last mover advantage in wars of attrition, asking just that the last quantile payoff exceed the average. With greed, play is inefficiently late: an accelerating war of attrition starting at optimal time, followed by a rush. With fear, play is inefficiently early: a slowing pre-emption game, ending at the optimal time, preceded by a rush. The theory predicts the length, duration, and intensity of stopping, and the size and timing of rushes, and offers insights for many common timing games.
Keywords
Timing games, war of attrition, pre-emption game, tipping, bubbles, sorority rushes, bank runs, population games
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