An Approximate Model for Bidders in Sequential Automated Auctions

In this paper, we propose a probabilistic model to study the interaction of bidder and seller agents in sequential automated auctions. We consider a designated “special bidder” (SB) who arrives at an auction and observes the ongoing activities among a number of bidders and the seller jointly, as a stochastic system that is parameterised by the rate of the bidding and selling events. The auction is modelled as a random process with discretised state-space, where the state-space represents the recently attained price for the good. We distinguish the statistical properties of the SB from that of the others, and isolate the system states that denote the desirable outcomes for the SB. In this manner, we define the measures that are of interest to the SB: its winning probability, the average time it takes to purchase an item, and its expected savings with respect to the maximum payable. For tractability, we introduce an approximately equivalent model that yields convenient and closed form expressions of these measures with minimal loss in the accuracy. We examine the effects of the SB’s time to bid, and study how decisions may be taken to balance the trade-offs between its interests.