A random walk model for studying allocation patterns in auction-based resource allocation

We consider users bidding in a series of multi-unit sealed-bid auctions, aiming at reserving the same amount of units of the resource auctioned, e.g. transmission slots in a wireless network. Each user attains from each successful allocation of resource units an instant marginal utility that depends on his history of resource allocation. The user's bid at each auction equals this marginal utility. We introduce a random walk model for transient analysis of this series of auctions, we study the properties of the resulting user resource allocation patterns and we provide a numerical and experimental evaluation of this model.