Mathematical modelling, analysis, and optimisation in automated auctions

Auctions are convenient mechanisms that formalise the rules with which automated trading schemes can be conducted, and are increasingly important in the Internet-based economy. This thesis proposes probabilistic models of bidder and seller agents’ interactions in sequential computerised auctions. We consider a designated “special bidder” (SB), who arrives at an auction and observes ongoing activities among other bidders and seller, and study the outcome of strategies that it may follow. Bidding and sale events are modelled as continuous time random processes with discrete state-space, where the state-space represents the current value of the most recent bid and the identity of the bidder who makes that offer. 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, the measures that are of interest to the SB are defined: the average time spent waiting to purchase an item, and, in the event of winning, the expected savings with respect to the maximum payable amount. The observation here leads to the problem of how a bidder that is pressed for time can address the trade-off between a good quickly and the price that it pays to make a successful bid. For tractability, we introduce an approximate model that allows closed form expressions of the SB’s measures of interest. Using these to explore the optimisation problem faced by the SB, our approximation yields an analytical solution that characterises the trade-off. The approximate solutions are benchmarked against exact results and validated with simulations. Several variations of the model are also studied, such as the networked auctions in which multiple sellers offer similar goods concurrently in an interconnected environment, so that bidders are able to circulate in the network and place bids following a Markovian process.EThOS - Electronic Theses Online ServiceGBUnited Kingdo