Timing Models with Both Explosive and Timed Entry: Endogenous Herding and The Rush Hour

There is a vast collection of scenarios where people have to time a decision optimally vis-a-vis the decision of other, examples include market entry and exit, corporate restructuring, mergers and acquisitions and so on. In economics these strategic decisions are typically studied with timing games, either tailoring the question to fit a War of Attrition(having more predecessors helps), or to a pre-emption game (more predecessors hurts). In this paper we study situations where being neither first nor last or where being either first or last (but not in the middle) is optimal. Our results suggest that our model can explain behavior in a variety of applied settings: as equilibrium outcomes our model variously yields: • an initial War of Attrition ending in a pre-emptive explosion (fashion) • inaction, a War of Attrition, a pre-emptive flash (‘palm pilot’ market) • a pre-emptive entry explosion, and a War of Attrition (the Gold Rush) • inaction, a slow pre-emption game, and a War of Attrition (rush hour) The time and size of herd-like atomic entry is always endogenous, and in each case, anticipation of later timing games influences current play — from swelling the magnitude of pre-emptive explosions to truncating wars of attrition. JEL Classification: C73, D81.