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Sequential Auctions with Budget-Constrained Bidders

In this paper, we examine a setting in which a number of goods are sold in sequential single unit auctions and the agents who bid for these items have a hard budget constraint, i.e. a preset amount of money to use for all their purchases, which cannot not be exceeded. Each auction is run as a second price sealed bid (Vickrey) auction. Analyzing sequential auctions is very important, because they appear often in reality, however very little work has been done on how budget affects the bidding strategies in this setting. This is the contribution of this paper, we present a theoretical analysis of this problem, with the limitation that closing prices and the winners of each auction are not announced, which limits the reasoning that is necessary to analyze this setting. More specifically, initially, we characterize the equilibrium bidding strategies for a general model of valuations where it is assumed that the items sold could be substitutes or complementary. Then, we will concentrate on cases where, first, the valuations for the items are additive, and, second, items are partial substitutes to the point that the bidder needs to buy exactly one of these. In each of these, we examine how the budget constraints (being looser or more tight) affect the bidding strategies of the participating bidders graphing the bidding strategy for some particular cases. While we have fully characterized the equilibria with equations, from the work presented in this paper, we can see that the computation of these in practice is challenging, which explains the lack of previous results.