Greed, Fear, and Rushes

We develop a tractable continuum player timing game that subsumes wars of attrition and pre-emption games, in which greed and fear relax the last and first mover advantages. Payoffs are continuous and single-peaked functions of the stopping time and quantile. Time captures the payoff-relevant fundamental, as payoffs "ripen'', peak at a "harvest time'', and then "rot''. The nonmonotone quantile response rationalizes sudden mass movements in economics, and explains when it is inefficiently early or late. With greed, the harvest time precedes an accelerating war of attrition ending in a rush; with fear, a rush precedes a slowing pre-emption game ending at the harvest time.The theory simultaneously predicts the length, duration, and intensity of gradual play, and the size and timing of rushes, and offers insights for an array of timing games. For instance, matching rushes and bank runs happen before fundamentals indicate, and asset sales rushes occur after. Moreover, (a) "unraveling'' in matching markets depends on early matching stigma and market thinness; (b) asset sales rushes reflect liquidity and relative compensation; (c)a higher reserve ratio shrinks the bank run, but otherwise increases the withdrawal rate