Optimal market thickness and market design

© 2017 Dr. Ellen Victoria MuirIn this thesis we primarily focus on developing tractable dynamic market models, together with applications of these models. We also address several open questions concerning the statistical properties of static market models. The original research contained in this thesis begins when we define a new distribution, called a general non-central hypergeometric distribution, which models biased sampling without replacement. We then consider a classic mechanism design market model with unit traders in which buyer valuations and seller costs are independent and, on each side of the market, identically distributed. We show that the equilibrium quantity traded has a general non-central hypergeometric distribution under a broad class of mechanisms, where the sampling bias encodes information about the distribution of buyer values relative to seller costs, strategic behaviour of market participants and rent extraction by the market intermediary. We then extend this work by developing a general approach to approximating outcomes in large markets. In particular, we show that the joint distribution of the equilibrium quantity traded and welfare is asymptotically normal, compute the parameters of the approximating normal distribution and bound the approximation rate. We then turn our attention to dynamic market models in which traders with persistent types arrive over time and focus on optimally assessing the tradeoff between the benefits of increasing market thickness and the cost of delay. We start by considering a two-period extension of the classic model of Myerson and Satterthwaite and derive the class of Bayesian optimal mechanisms. Investigating the properties of these mechanisms, we compare them to benchmark static mechanisms and find that dynamics tends to increase the convexity of the region of trade in period one. Motivated by the computational complexity of these optimal mechanisms, we consider approximate implementation in the form of a price-posting mechanism, before turning our attention to models with simpler type spaces. Finally, we consider an infinite-horizon market model in which agents have binary type spaces. Assuming that a buyer-seller pair arrives in each period and agents are privately informed about their types, we introduce notions of dynamic efficiency and optimality and construct the class of Bayesian optimal mechanisms. We demonstrate that, provided the discount factor is sufficiently large, a profit-maximising two-sided platform creates higher welfare compared to a less centralised, welfare-targeting market maker. Further, the main benefits from dynamic mechanisms are reaped by clearing markets at fixed, optimally chosen frequencies. We consider a variety of economic applications including in-house production by the designer, taxation policy and asymptotically optimal prior-free mechanisms. With minor qualifications (including a dynamic generalisation of Myerson regularity), our analysis and main results apply to more general arrival processes and type spaces