Essays in Mechanism and Market Design

Abstract

This thesis consists of three essays on mechanism and market design.

The first chapter studies the question of when we can eliminate investment inefficiency in a general mechanism design model with transferable utility. We show that when agents make investments only before participating in the mechanism, inefficient investment equilibria cannot be ruled out whenever an allocatively efficient social choice function is implemented. We then allow agents to make investments before and after participating in the mechanism. When ex post investments are possible and an allocatively constrained-efficient social choice function is implemented, efficient investments can be fully implemented in perfect Bayesian Nash equilibria if and only if the social choice function is commitment-proof (a weaker requirement than strategy-proofness). Our result implies that in the provision of public goods, implementation of efficient investments and efficient allocations is possible even given a budget-balance requirement.

The second chapter analyzes the implementability of efficient investments for two commonly used mechanisms in single-item auctions: the first-price auction and the English auction. We allow uncertain ex ante investment and further ex post investment. Under private values, we show that both the first-price auction and the English auction implement efficient investments in equilibrium.

In the third chapter, we study the controlled school choice problem employing the lower and upper bounds of type-specific constraints. In such a problem, it is known that the set of feasible, fair and non-wasteful assignments may be empty (Ehlers et al., 2014). We find that a common priority condition of a schools’ priority profile plays a key role for the non-emptiness. A schools’ priority profile is said to have a common priority order if a student has higher priority than any given student of the same type whenever she does so in some other school. We show that this condition is sufficient for the existence of a feasible assignment that is fair and non-wasteful, and also that it is necessary in a weak sense. To show the sufficiency part, we introduce an algorithm called the type-proposing deferred acceptance (TDA) algorithm.