Fair Optimal Stopping Policy for Matching with Mediator

In this paper we study an optimal stopping policy for a multi-agent delegated sequential matching system with fairness constraints. We consider a setting where a mediator/decision maker matches a sequence of arriving assignments to multiple groups of agents, with agents being grouped according to certain sensitive attributes that needs to be protected. The decision maker aims to maximize total rewards that can be collected from above matching process (from all groups), while making the matching fair among groups. We discuss two types of fairness constraints: (i) each group has a certain expected deadline before which the match needs to happen; (ii) each group would like to have a guaranteed share of average reward from the matching. We present the exact characterization of fair optimal strategies. Example is provided to demonstrate the computation efficiency of our solution.