Date of Award
Doctor of Philosophy
We analyze dynamic equilibria of a multiple markets model with sparsely allocated participants. An example of such a market is the secondary radio spectrum market. In the first chapter a general model is represented by an allocation of a good from sellers to buyers where purchases can only occur if a buyer and seller are linked or if a buyer is located in the seller's coverage area. First, we study the static part of the model and show an optimal auction design for price efficiency. Second, we assume a dynamic structure where buyers can reallocate and show sufficient conditions to reach equilibrium. Finally, we consider the speed of convergence to an equilibrium and prove the equilibrium is allocation efficient. The second chapter expands the idea of a location based market. We consider a mechanism of allocating a differentiated good. To capture this, we use the idea of a Generalized Second Price Auction that is used extensively in online search auctions. Buyers in this market are competing for various goods that are ranked based on their quality (known as the click-through rate in online advertisement). Network formation is also assumed to capture different accessibility of participants to the market. In terms of secondary spectrum auctions, this mechanism can be thought of as competition of various wireless devices (such as cognitive radio) over broadcast priority from the base station. We provide the conditions and subset of networks that will lead to an equilibrium in this market. We also show how different constraints, such as transaction costs and interference, have an impact on this equilibrium. In the third chapter, we study two mechanisms of secondary allocation for trading spectrum in a dynamic setting. The two models considered are the "exclusive-use" model, where spectrum is traded on the open market, and the "commons-use" model, where spectrum is available freely in a non-coordinated way. We show that firms have more incentive to innovate and to acquire higher capital in the "exclusive-use" case, which results in higher welfare. We test these results with both numerical simulations and with a laboratory experiment to simulate the conditions of such markets and show that the theoretical results hold true.
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