Public resources are closely related to residents' daily lives. Because of their scarcity, it has become a big challenge for the government, or resource holder, to properly allocate limited resources to large amount of applicants who desire for them. In this thesis, we focus on mechanism design in allocating public resources, when multiple objectives are tried to achieve, and applicants' strategic behaviors are taken into consideration.

This first work studies the problem of allocating a set of homogenous resources (goods) between multiple strategic players while balancing both efficiency and equality from a game-theoretic perspective. We develop a general truthful mechanism framework for two very general classes of efficiency measures and equality measures which optimally maxi...[ Read more ]

Public resources are closely related to residents' daily lives. Because of their scarcity, it has become a big challenge for the government, or resource holder, to properly allocate limited resources to large amount of applicants who desire for them. In this thesis, we focus on mechanism design in allocating public resources, when multiple objectives are tried to achieve, and applicants' strategic behaviors are taken into consideration.

This first work studies the problem of allocating a set of homogenous resources (goods) between multiple strategic players while balancing both efficiency and equality from a game-theoretic perspective. We develop a general truthful mechanism framework for two very general classes of efficiency measures and equality measures which optimally maximizes the resource holders efficiency while guaranteeing certain equality levels. We characterize the optimal allocation rule fully, showing that there exists an optimal allocation where all the players can be divided into at most four groups and players in the same group have the same winning probability. Although there is no closed-form solution for the optimal allocation and truthful payments, we present polynomial-time algorithms to compute them. We also illustrate how the optimal efficiency changes for varying equality levels. For some special cases of efficiency measures or equality measures, we show that the optimal allocation and payments can be computed more efficiently.

The second work studies the waitlist design, a commonly used mechanism to allocate scarce public resources, especially for public housing allocation. Under the waitlist mechanism, the decision is the number of deferral chances, i.e., refusal of a housing unit randomly selected from a pool of available ones, an eligible applicant or agent is allowed. By a Markov decision process, we analyze the agents' behaviors under different deferral numbers. Then we investigate the performance of the waitlist mechanisms under four evaluating metrics: idle waiting time (time until the first offer), match value (matching efficiency), match distribution (how urgent needs are met) and social welfare. We establish some monotonicity properties of the impact of the number of deferral chances on the performance. Numerical studies further reveal the sensitivities of the model parameters on the idle waiting time and social welfare. A case study on the public housing allocation in Hong Kong suggests that increasing the number of referral chances from the current 2 to 5 would increase the social welfare by 10% without violating the government's idle waiting time target.