Collusion in Second‐Price Auctions under Minimax Regret Criterion

Collusion in auctions, with different assumptions on distributions of bidders' private valuation, has been studied extensively over the years. With the recent development of on‐line markets, auctions are becoming an increasingly popular procurement method. The emergence of Internet marketplaces makes auction participation much easier and more convenient, since no physical presence of bidders is required. In addition, bidders in on‐line auctions can easily switch their identities. Thus, it may very well happen that the bidders in an auction have very little, if any, prior knowledge about the distributions of other bidders' valuations. We are proposing an efficient distribution of collusive profit for second‐price sealed bid auctions in such an environment. Unlike some known mechanism, which balance the budget only in expectation, our approach (which we call Random k) balances the budget ex‐post. While truth‐telling is not a dominant strategy for Random k, it is a minimax regret equilibrium.