Bayesian auctions with friends and foes

We study auctions whose bidders are embedded in a social or economic network. As a result, even bidders who do not win the auction themselves might derive utility from the auction, namely, when a friend wins. On the other hand, when an enemy or competitor wins, a bidder might derive negative utility. Such spite and altruism will alter the bidding strategies. A simple and natural model for bidders' utilities in these settings posits that the utility of a losing bidder i as a result of bidder j winning is a constant (positive or negative) fraction of bidder j's utility. We study such auctions under a Bayesian model in which all valuations are distributed independently according to a known distribution, but the actual valuations are private. We describe and analyze Nash Equilibrium bidding strategies in two broad classes: regular friendship networks with arbitrary valuation distributions, and arbitrary friendship networks with identical uniform valuation distributions.