Mergers and collusion in all-pay auctions and crowdsourcing contests

We study the effects of bidder collaboration in all-pay auctions. We analyse both mergers, where the remaining players are aware of the agreement between the cooperating participants, and collusion, where the remaining players are unaware of this agreement. We examine two scenarios: the sum-profit model where the auctioneer obtains the sum of all submitted bids, and the max-profit model of crowdsourcing contests where the auctioneer can only use the best submissions and thus obtains only the winning bid. We show that while mergers do not change the expected utility of the participants, or the principal's utility in the sum-profit model, collusion transfers the utility from the non-colluders to the colluders. Surprisingly, we find that in some cases such collaboration can increase the social welfare. Moreover, mergers and, curiously, also collusion can even be beneficial to the auctioneer under certain conditions.