Strategyproof matching with regional minimum and maximum quotas

This paper considers matching problems with individual/regional minimum/maximum quotas. Although such quotas are relevant in many real-world settings, there is a lack of strategyproof mechanisms that take such quotas into account. We first show that without any restrictions on the regional structure, checking the existence of a feasible matching that satisfies all quotas is NP-complete. Then, assuming that regions have a hierarchical structure (i.e., a tree), we show that checking the existence of a feasible matching can be done in time linear in the number of regions. We develop two strategyproof matching mechanisms based on the Deferred Acceptance mechanism (DA), which we call Priority List based Deferred Acceptance with Regional minimum and maximum Quotas (PLDA-RQ) and Round-robin Selection Deferred Acceptance with Regional minimum and maximum Quotas (RSDA-RQ). When regional quotas are imposed, a stable matching may no longer exist since fairness and nonwastefulness, which compose stability, are incompatible. We show that both mechanisms are fair. As a result, they are inevitably wasteful. We show that the two mechanisms satisfy different versions of nonwastefulness respectively; each is weaker than the original nonwastefulness. Moreover, we compare our mechanisms with an artificial cap mechanism via simulation experiments, which illustrate that they have a clear advantage in terms of nonwastefulness and student welfare

Developments in Multi-Agent Fair Allocation

Fairness is becoming an increasingly important concern when designing markets, allocation procedures, and computer systems. I survey some recent developments in the field of multi-agent fair allocation

Approximately Stable Matchings with Budget Constraints

This paper considers two-sided matching with budget constraints where one side (firm or hospital) can make monetary transfers (offer wages) to the other (worker or doctor). In a standard model, while multiple doctors can be matched to a single hospital, a hospital has a maximum quota: the number of doctors assigned to a hospital cannot exceed a certain limit. In our model, a hospital instead has a fixed budget: the total amount of wages allocated by each hospital to doctors is constrained. With budget constraints, stable matchings may fail to exist and checking for the existence is hard. To deal with the nonexistence of stable matchings, we extend the "matching with contracts" model of Hatfield and Milgrom, so that it handles approximately stable matchings where each of the hospitals' utilities after deviation can increase by factor up to a certain amount. We then propose two novel mechanisms that efficiently return such a stable matching that exactly satisfies the budget constraints. In particular, by sacrificing strategy-proofness, our first mechanism achieves the best possible bound. Furthermore, we find a special case such that a simple mechanism is strategy-proof for doctors, keeping the best possible bound of the general case.Comment: Accepted for the 32nd AAAI Conference on Artificial Intelligence (AAAI2018). arXiv admin note: text overlap with arXiv:1705.0764

Decentralized and stable matching in Peer-to-Peer energy trading

In peer-to-peer (P2P) energy trading, a secured infrastructure is required to manage trade and record monetary transactions. A central server/authority can be used for this. But there is a risk of central authority influencing the energy price. So blockchain technology is being preferred as a secured infrastructure in P2P trading. Blockchain provides a distributed repository along with smart contracts for trade management. This reduces the influence of central authority in trading. However, these blockchain-based systems still rely on a central authority to pair/match sellers with consumers for trading energy. The central authority can interfere with the matching process to profit a selected set of users. Further, a centralized authority also charges for its services, thereby increasing the cost of energy. We propose two distributed mechanisms to match sellers with consumers. The first mechanism doesn't allow for price negotiations between sellers and consumers, whereas the second does. We also calculate the time complexity and the stability of the matching process for both mechanisms. Using simulation, we compare the influence of centralized control and energy prices between the proposed and the existing mechanisms. The overall work strives to promote the free market and reduce energy prices

Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties

Motivated by the serious problem that hospitals in rural areas suffer from a shortage of residents, we study the Hospitals/Residents model in which hospitals are associated with lower quotas and the objective is to satisfy them as much as possible. When preference lists are strict, the number of residents assigned to each hospital is the same in any stable matching because of the well-known rural hospitals theorem; thus there is no room for algorithmic interventions. However, when ties are introduced to preference lists, this will no longer apply because the number of residents may vary over stable matchings. In this paper, we formulate an optimization problem to find a stable matching with the maximum total satisfaction ratio for lower quotas. We first investigate how the total satisfaction ratio varies over choices of stable matchings in four natural scenarios and provide the exact values of these maximum gaps. Subsequently, we propose a strategy-proof approximation algorithm for our problem; in one scenario it solves the problem optimally, and in the other three scenarios, which are NP-hard, it yields a better approximation factor than that of a naive tie-breaking method. Finally, we show inapproximability results for the above-mentioned three NP-hard scenarios

Strategyproof and fair matching mechanism for ratio constraints

We introduce a new type of distributional constraints called ratio constraints, which explicitly specify the required balance among schools in two-sided matching. Since ratio constraints do not belong to the known well-behaved class of constraints called M-convex set, developing a fair and strategyproof mechanism that can handle them is challenging. We develop a novel mechanism called quota reduction deferred acceptance (QRDA), which repeatedly applies the standard DA by sequentially reducing artificially introduced maximum quotas. As well as being fair and strategyproof, QRDA always yields a weakly better matching for students compared to a baseline mechanism called artificial cap deferred acceptance (ACDA), which uses predetermined artificial maximum quotas. Finally, we experimentally show that, in terms of student welfare and nonwastefulness, QRDA outperforms ACDA and another fair and strategyproof mechanism called Extended Seat Deferred Acceptance (ESDA), in which ratio constraints are transformed into minimum and maximum quotas