Costly waiting in dynamic contests: Theory and experiment

We extend the war of attrition by studying three-period dynamic contest games. In our game, players can either fight against their opponents at the last period or can fight at any period. Waiting is costly. We focus on the role of waiting costs and show that the value of waiting costs is a key factor in determining the type of equilibrium in such dynamic contests. Specifically, when players are allowed to fight only at the last period, as waiting costs increase, contests end earlier, battles are less likely to occur, and the weaker player in a pair is more likely to flee. When allowing players to fight at any time, the pure-strategy Bayesian equilibrium does not exist under sufficiently high waiting costs. A lab experiment verifies most key features of our model in scenarios where players are allowed to fight only at the last period. However, unlike theoretical predictions, we find that as waiting costs increase, the duration of contests and the frequency of battles fail to drop as significantly as theory predicted. In the case where players are allowed to fight at any period, we observe a substantial increase in the frequency of battles, accompanied by a dramatic reduction in the duration of contests compared to the format where players are limited to fighting during the last period. We find evidence of suboptimal behavior among players in both contest formats.