The role of luck in political and economic competition: noisy all-pay auctions

We study all-pay auctions with noise both theoretically and experimentally. First we show theoretically that all-pay auctions with noise (or “luck”) can be surprisingly like standard all-pay auctions with complete information in several important respects. Equilibria in both formats feature the same expected expenditures and payoffs. One difference, however, is that without noise predictions are in mixed strategies, while with noise predictions are in pure strategies. We next report the results of an experiment on our model and find qualitative support for the predicted equivalence of expected expenditures. Our experimental results on the noisy version of the model are particularly interesting, as subjects’ behavior appears to be more closely in line with the model’s theoretical equilibrium predictions than the treatment without noise in terms of reduced variance.