Three essays on collusion-proof mechanism design

Abstract

Collusion is a serious concern in real-life allocation problems. Auctions, for example, often create incentives for the bidders to compete less fiercely so as to increase their profits. This thesis contributes to the theoretical literature on how to design collusion-proof mechanisms. Each of the three chapters addresses this question in a specific economic environment, namely multidimensional bargaining (Chapter 1), multi-unit procurement (Chapter 2) and single-good allocation (Chapter 3). A common feature, apart from collusion, is the presence of asymmetric information. In other words, the key problem is that the mechanism designer (e.g. the auctioneer) does not know the agents’ preferences (e.g. the bidders’ values) and is concerned that they might coordinate their strategies. As is conventional in the mechanism design literature, we assume the agents’ utility functions to be quasilinear in money. The implementation concept is pure dominant-strategy equilibrium. Accordingly, we focus on deterministic mechanisms that are strategy-proof in the sense that each agent’s optimal decision is independent of the other agents’ strategies. A mechanism is considered to be collusion-proof if no group of agents find it profitable to jointly deviate from their dominant strategies. Exactly what constitutes a joint deviation hinges on how sophisticated a collusive arrangement can be. The central notion studied in this thesis assumes that the colluding agents cannot reallocate among each other after the mechanism has been executed. In particular, they are not able to exchange money. This limited form of collusion is characteristic of a weak cartel. The corresponding concept of collusion-proofness is usually referred to as group strategy-proofness in the literature. Chapter 2 additionally considers strong cartels, whose members can reallocate among each other. This capability increases the scope for collusive behavior and, therefore, restricts the set of collusion-proof mechanisms.