Student-Project-Resource Matching-Allocation Problems: Game Theoretic Analysis

In this work, we consider a three sided student-project-resource matching-allocation problem, in which students have preferences on projects, and projects on students. While students are many-to-one matched to projects, indivisible resources are many-to-one allocated to projects whose capacities are thus endogenously determined by the sum of resources allocated to them. Traditionally, this problem is divided into two separate problems: (1) resources are allocated to projects based on some expectations (resource allocation problem), and (2) students are matched to projects based on the capacities determined in the previous problem (matching problem). Although both problems are well-understood, unless the expectations used in the first problem are correct, we obtain a suboptimal outcome. Thus, it is desirable to solve this problem as a whole without dividing it in two. In this paper, we first show that a stable (i.e., fair and nonwasteful) matching does not exist in general (nonwastefulness is a criterion related to efficiency). Then, we show that no strategyproof mechanism satisfies fairness and very weak efficiency requirements. Given this impossibility result, we develop a new strategyproof mechanism that strikes a good balance between fairness and efficiency, which is assessed by experiments.