Fairness in Assignment Markets with Dual Decomposition

In this work, we present a market design for assignment problems that computes a globally optimal solution by adjusting incentives. Such markets can help in settings such as the assignment of peer-reviewers to submitted academic articles, assignment of tutors to students, or online matchmaking services. In these settings, each assignment has some reward value, and existing strategies for achieving high global reward involve either adjustments to greedy choices by agents or global optimization of estimated reward values. The benefit of maintaining a market is that we combine benefits from these methods in a principled way. The agents make incentivized greedy decisions, which is ideal because they understand their reward functions best, while the incentives push their decisions toward the global optimum. We update the incentives by relating the assignment market to the standard dual of the (b-) matching linear programming relaxation. We evaluate our proposed system on simulations, demonstrating that the market quickly improves the global reward.