Representing and Reasoning about Auctions

Munyque Mittelmann, Laurent Perrussel, Sylvain Bouveret

Abstract: In this paper, we propose a framework for representing and reasoning about auction-based protocols. Such a framework is of interest for building digital marketplaces based on auctions and should fulfill two requirements: (i) it should enable bidders to express their preferences over combinations of items and (ii) it should allow the mechanism designer to describe the rules governing the market, namely the legality of bids, the allocative choice, and the payment rule. To do so, we define a logical language in the spirit of the Game Description Language, namely Auction Description Language with a set of functions FB (ADL[FB]). ADL[FB] is expressive enough to represent different kinds of protocols and enables reasoning about auction properties, including playability, termination, and budget-balance. We also study the complexity of model-checking ADL[FB].