Your money or your time? Experimental evidence on overbidding in all-pay auctions

Competition for a prize frequently takes the form of dedicating time toward winning a contest. Those who spend the most time become more likely to obtain the prize. We model this competition as an all-pay auction under incomplete information, and report an experiment in which expenditures and rewards are in terms of time. In the experiment, subjects must stay in the laboratory doing nothing for an initially prespecified length of time. However, they can bid, in terms of time, to leave early. The auction has an allpay structure so that if an individual does not submit the highest bid within her group, she must stay for the additional time that she bid. We correlate behavior in this game with behavior in an isomorphic all-pay auction played with money bids. We also consider how two measures of sophistication, the Cognitive Reflection Test (CRT) score, and performance on a probability calibration task, correlate with behavior. We find strong similarities in overall behavior between the auctions conducted with money and with time. Bidding greater than equilibrium levels is typical, and as a consequence, average earnings are negative in both auctions. Thus, the result that there is overdissipation of rent in all-pay auctions extends to competition in terms of time. Higher CRT score and more accurate probability calibration correlate with better decisions in auctions played for money but not those played for time.