Essays in applied microeconomic theory [electronic resource]

This dissertation examines a few theoretical questions in financial economics, mechanism design, and contract theory. Chapter 1 studies how competitive middlemen affect bid-ask spreads and investor welfare in a dynamic limit order market. Both middlemen and ordinary investors can choose between providing liquidity and taking liquidity. I find that although the presence of competitive middlemen tightens the average bid-ask spread, its consequence on total and investor welfare is mixed due to multiple competing effects. Middlemen provide counter-parties to investors when there is order imbalance, increasing total welfare. However, the uncertainty of their liquidity and their speed advantage relative to investors may crowd out liquidity-providing investors and/or create additional picking-off risk for investors, reducing social surplus and investor welfare. Moreover, although middlemen compete in price when supplying liquidity, the competition to pick off investors' stale orders is in speed. Thus, they may extract surplus from investors when taking liquidity, also reducing investor welfare. I characterize conditions under which each of the above effects dominates. Chapter 2 investigates implementability of allocation rules in quasilinear environments when the agent has private information about his preference. It is well known in static mechanism design that an allocation rule can be implemented if and only if it is monotonic. Recently, Pavan, Segal, and Toikka (2014) show that monotonicity is also sufficient for implementability in dynamic mechanism design if the environment is Markov. I show in an example that monotonicity is not sufficient for implementation in non-Markov environments due to the possibility of successive lying. The difference is that in Markov environments, if the agent does not want to lie after truthful reports, he does not want to lie after lies either. However, this is not true in non-Markov environments, where the agent's realized types in earlier periods directly affect his reporting incentive. In a 2-period non-Markov setting, I derive a sufficient condition for implementability in direct, deterministic and continuous mechanisms. It can be viewed as a generalized monotonicity condition on the allocation rule, taking into account the agent's optimal sequential lie after lying in the first period. Using this generalized monotonicity condition, I also derive two other sufficient conditions for implementability which do not directly use the agent's sequentially optimal reporting strategy and thus are easier to check. Chapter 3 studies the role of commitment in long-term agency relationships when the agent's efforts in each period affect both current and future output distributions. It is well known in the dynamic adverse selection literature that second-best contracts are often not implementable without commitment. Fudenberg, Holmstrom, and Milgrom (1990) provide conditions such that commitments are unnecessary in long-term agency relationships. One of the conditions is that recontracting takes place when preference and technology are common knowledge. Can second-best contracts still be implemented if this condition is not satisfied? In a finite horizon setting, I consider a simple history-dependent technology where the cumulative distribution function of outputs in each period is a linear combination of two cumulative distribution functions. These two functions are determined respectively by the effort exerted in the current period and the effort exerted in the previous period. I show that even with a history-dependent technology, second-best contracts can still be implemented in the absence of commitments if the history dependence is small enough. The intuition is that, when the effects of the agent's efforts on future outputs are small, the incentive compatibility constraints of the second-best contract are satisfied with equality. This implies that there is no excessive risk at the beginning of each period, and thus no need for the contracting parties to renegotiate.

Keywords: Economics.
Advisor: Segal Ilya primary advisor. Thesis advisor
Jackson Matthew O. advisor. Thesis advisor
Milgrom Paul R. (Paul Robert)