Auctions, public tenders, and fair division games: An axiomatic approach

Abstract

Auctions, public tenders, and fair division games are considered as special classes of games with incomplete information. The specialty of these games is that choosing a strategy in such a game amounts to displaying (the not necessarily true) preferences. Our main axiom of displayed envy-freeness states that according to his displayed preferences no player should prefer another player's net trade to his own. This axiom and the well-known property of incentive compatibility imply the rules of auctions and public tenders which are originally discussed by Vickrey. We consider our axiomatic characterization as a strong support for the Vickrey-rules. There is no obvious reason why the actually applied rules (e.g. the rules of public tenders in the Federal Republic of Germany) do often violate these rules. For fair division problems the two axioms are shown to be mutually inconsistent. By weakening the requirement of incentive compatibility we, nevertheless, can determine rules for fair division problems which are a reasonable analogue of the Vickrey-rules. Finally, it is discussed how our ideas can be extended to other allocation problems.