The goal of this paper is to propose a language for representing and reasoning about the rules governing an auction-based market. Such language is at first interest as long as we want to build up digital market places based on auction, a widely used framework for automated transactions. Auctions may differ in several aspects: single or double-side, ascending or descending, single or multi-unit, open cry or sealed-bid, and so on. This variety prevents an agent to easily switch between different (auction-based) markets. The first requirement for building such agents is to have a general language for describing auction-based markets. Second, this language should also allow the reasoning about the key issues of a specific market, namely the allocation and payment rules. To do so, we define a language in the spirit of the Game Description Language (GDL): the Auction Description Language (ADL) is the first language for describing auctions in a logical framework. In this paper, we illustrate this general dimension by representing two different types of well-known auctions: an English Auction and a Multi-Unit Vickrey Auction. We show the benefit of ADL by deriving properties about these two auction protocols. It also enables us to show in an explicit way what should be assumed about the behavior of a rational bidder.
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