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. 
Po-An Chen, David Kempe
cs.GT