Equitable resource allocation using all-pay auctions

Abstract

Auction theory is a very interesting topic which studies mechanisms of various formats for buying and selling goods. There are all kinds of mechanisms covered in the ambit of auction theory, ranging from sealed bid auctions like first-price or second price auctions, to open bid auctions like the English or Dutch auctions. One interesting kind of auction is the all-pay auction, in which, as the name suggests, all the players pay their bids. Analysis of all-pay auctions with virtual money has so far been neglected in the auction theory literature. However, it can be used to design a mechanism with a wide variety of applications including equitable resource allocation, and fairer systems for legislation and corporate management. In this thesis, we shall present this novel mechanism, analyze it in a game-theoretic framework and consider the variants of the problem including the perfect and imperfect information cases. Furthermore, we shall outline how to find the equilibrium bidding strategies for this mechanism which lead to equitable distribution of resources. One possible application of this is in equitable resource allocation, such as in a battlefield where different agents have competing needs for limited resources to complete their missions. Finally, we shall draw the connection between this mechanism, and the process of voting in the legislature or the company board rooms. Currently, a party needs just more than 50% of seats in the legislature to control 100% of the bills. Similarly, a shareholder needs just 51% of shares to completely control the company. We shall show how it is possible to modify these voting systems, using the proposed mechanism to enable even the minority players to have an equitable say in the decisions.