Damaging conflict: All-pay auctions with negative spillovers and bimodal bidding

We investigate how the presence of a negative externality in an all-pay auction influences bidding behavior in the laboratory. In the standard risk-neutral model, Nash equilibrium predicts no difference in strategies between treatments with and without the externality. Our experimental results provide some support for this prediction, as average bids do not differ significantly across treatments and generally align with equilibrium benchmarks. However, bidding distributions in both treatments exhibit a pronounced bimodal pattern that is consistent with previous all-pay auction experiments but inconsistent with risk-neutral Nash predictions. To account for these features, we evaluate two models of bounded rationality, incorporating prospect theory-inspired preferences: quantal response equilibrium (QRE) and a variant on noisy introspection that we call Belief-Perturbed Logit (BPL). While both models can rationalize bimodal bidding, QRE provides the superior fit while also predicting the location of bid peaks across treatments. These results reinforce the growing evidence that while subjects may not mix strategies exactly as prescribed by Nash equilibrium, their bidding behavior remains broadly equilibrium-consistent. Our findings also support the role of reference dependence and loss aversion in explaining bimodal bidding and strategic behavior more generally.