The Dollar Auction with Spiteful Bidders

Shubik's (all-pay) dollar auction is a simple yet powerful auction model that aims to shed light on the motives and dynamics of conflict escalation. Common intuition suggests that the dollar auction is a trap, inducing conflict by its very design. However, O'Neill proved that, contrary to the experimental results and the intuition, the dollar auction has an immediate solution in pure strategies, i.e., theoretically it should not lead to conflict escalation.

Inspired by the recent literature on spiteful bidders, we ask whether the escalation in the dollar auction can be induced by meanness. Our results confirm this conjecture in various scenarios. We investigate this model both for the complete information setting, and for the situation where one player does not know the spitefulness level of her opponent. 

We also investigate the repeated version of Shubik's dollar auctions, in which the type of the opponent and her level of rationality is not known in advance. We formulate the problem as an adversarial multi-armed bandit, and we tailor the ELP algorithm to our setting.