Essays on Housing Market Problem
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In my dissertation, I focus on resource reallocation problem. Specifically, I consider the housing market problem. In this problem, there is a group of agents and a group of objects. Each agent owns at most one object and each object is owned by at most one agent. Agents have preferences over objects. The goal is to reallocate these objects among agents while satisfying desirable properties; Pareto efficiency (not possible to make someone better-off without making someone worse-off), individual rationality (each agent is assigned an object at least as good as her endowment), strategy proofness (no agent has an incentive to lie) and weak-core selection (no group of agents can trade among themselves such that each of them becomes better-off). In addition, I consider this problem while allowing agents to be indifferent between objects. Recently, favorable results have been established for such problems. It has been proved that Pareto efficient, weak-core selecting (hence, individually rational) and strategy proof rules exist for such problems. I consider additional properties for the housing market problem with indifferences. I show that there are rules which, in addition to the aforementioned properties, satisfy no justified-envy for agents with identical endowments and weak group strategy proofness even though Pareto efficiency and group strategy proofness are incompatible under the assumption of indifferences. I achieve this by providing sufficient conditions for weak group strategy proofness. Then, I propose a procedural enhancement which prioritizes the outcome achieved without violating strategy proofness. I show that some of the existing rules do not satisfy this criterion. So, I propose a new mechanism which satisfies this property in addition to other desirable results. Additionally, I present an amended version of sufficient condition for strategy proofness for housing market problem with weak preferences. I also consider random assignment solutions to housing market problem which is referred to as fractional housing market problem in literature. For general and strict preferences, several impossibility results have been established for such problems. I show that for a restricted class of preferences, trichotomous preferences, these impossibility results do not hold.
Ahmad, Ghufran (2017). Essays on Housing Market Problem. Doctoral dissertation, Texas A & M University. Available electronically from