False-name bidding in first-price combinatorial auctions with incomplete information

False-name bids are bids submitted by a single agent under multiple fictitious names such as multiple e-mail addresses. False-name bidding can be a serious fraud in Internet auctions since identifying each participant is virtually impossible. It is shown that even the theoretically well-founded Vickrey-Clarke-Groves auction (VCG) is vulnerable to false-name bidding. Thus, several auction mechanisms that cannot be manipulated by false-name bids, i.e., false-name-proof mechanisms, have been developed. This paper investigates a slightly different question, i.e., how do they affect (perfect) Bayesian Nash equilibria of first-price combinatorial auctions? The importance of this question is that first-price combinatorial auctions are by far widely used in practice than VCG, and can be used as a benchmark for evaluating alternate mechanisms. In an environment where false-name bidding are possible, analytically investigating bidders' behaviors is very complicated, since nobody knows the number of real bidders. As a first step, we consider a kind of minimal settings where false-name bids become effective, i.e., an auction with two goods where one naive bidder competes with one shill bidder who may pretend to be two distinct bidders. We model this auction as a simple dynamic game and examine approximate Bayesian Nash equilibria by utilizing a numerical technique. Our analysis revealed that false-name bidding significantly affects the first-price auctions. Furthermore, the shill bidder has a clear advantage against the naive bidder.