Essays on Multi-Dimensional Obviously Regret-Proof Mechanisms

Abstract

This dissertation study strategically simple mechanisms for problems of multi-dimensional allocation. Strategic simplicity is crucial to make mechanisms robust to avoid mistakes and manipulation. However, the current literature on the analysis and implementation of strategically simple mechanisms is limited, especially for markets with many goods and services. This dissertation fills this gap with three complementary but stand-alone chapters. In Chapter 1, we identify and formalize the criteria for strategic simplicity. Then we combine those criteria into a new solution concept and propose a new class of mechanism that satisfies these criteria. In Chapter 2, we analyze the cost of enforcing this new notion of simplicity. In Chapter 3, we show that the new mechanism is a good candidate in an application with substantial welfare implications.

The solution concept we propose in Chapter 1 is called obvious regret-proofness (ORP). It describes conditions that regulate both the extensive form of a dynamic game and the communication between the auctioneer and the bidders. Those conditions make sure that there is a simple rule for bidders to determine his best action each time he is called to play. Also, it is easy for the bidder to understand and to verify that he will not regret choosing this action because the optimality of this action does not depend on the choices of other bidders. We then translate those requirements into auction rules and propose a new class of mechanisms called Persistent Exit Descending (PED) mechanisms.

Then in Chapter 2, we analyze the cost of pursuing strategic simplicity by implementing the PED mechanism. We first show that for an efficient strategy-proof mechanism, the allocation and payment to a bidder can be dependent on the reports of other bidders. This influence is monotonic and mutual. Therefore, the externality of a bidder’s choice can be internalized. In contrast, the influence in PED implementable mechanisms is restricted once the reports of other bidders exceed some certain thresholds. Moreover, the influence can only be one-sided, which means that if a bidder has influence over the other bidder, only if that bidder cannot influence him. Lacking the channel to influence, the decision of a bidder cannot take into account his externality to other bidders. This is the primary source of welfare loss in a PED mechanism.

In Chapter 3, we show that the PED mechanism proposed in Chapter 1 is a good candidate for land assembly problems. It has the properties that most of the land assembly mechanisms in the literature fail to have, but are fundamental to land assembly problems. First, it is strategically simple. Second, its allocation rule is combinatorial. Third, it can assign non-monetary compensations to a bidder. Finally, it fully respects the owners' property rights, and it is ex-post individual rational. We then tailor the PED mechanism to the land assembly problem and apply the analytical framework from Chapter 2 to discuss the advantages and limitations of using the PED mechanism in land assembly problems.