We examine behavior of subjects in simultaneous and sequential multi-battle contests, where each individual battle is modeled as an all-pay auction with complete information. In simultaneous best-of-three contests, subjects are predicted to make positive bids in all three battles, but we find that subjects often make positive bids in only two battles. In sequential contests, theory predicts sizable bids in the first battle and no bids in the subsequent battles. Contrary to this prediction, subjects significantly underbid in the first battle and overbid in subsequent battles. Consequently, instead of always ending in the second battle, contests often proceeds to the third battle. Finally, although the aggregate bid in simultaneous contests is similar to that in sequential contests, in both settings, subjects make higher aggregate bids than predicted. The observed behavior of subjects can be rationalized by a combination of multi-dimensional iterative reasoning and a non-monetary utility of winning.
Mago, S.D., & Sheremeta, R.M. (2016). Multi-battle contests: An experimental study. ESI Working Paper 16-25. Retrieved from http://digitalcommons.chapman.edu/esi_working_papers/203/