Resource Allocation to Agents with Restrictions: Maximizing Likelihood with Minimum Compromise

TL;DR

This paper studies how to advise agents to relax restrictions in resource allocation problems to maximize their chances of being matched, considering budget constraints and computational complexity.

Contribution

It formulates a new problem of guiding agents to relax restrictions within budgets to improve matching probabilities and provides hardness results and algorithms for this problem.

Findings

Hardness results for certain variants of the problem

Algorithmic solutions for other variants

Experimental validation on synthetic and real-world datasets

Abstract

Many scenarios where agents with restrictions compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have restrictions that make them incompatible with some resources. We assume that a Principle chooses a maximum matching randomly so that each agent is matched to a resource with some probability. Agents would like to improve their chances of being matched by modifying their restrictions within certain limits. The Principle's goal is to advise an unsatisfied agent to relax its restrictions so that the total cost of relaxation is within a budget (chosen by the agent) and the increase in the probability of being assigned a resource is maximized. We establish hardness results for some variants of this budget-constrained maximization problem and present algorithmic results for other variants. We experimentally evaluate our methods on synthetic datasets as well as on two novel real-world datasets: a vacation activities dataset and a classrooms dataset.