We study a school choice problem under affirmative action policies where authorities reserve a certain fraction of the slots at each school for specific student groups, and where students have preferences not only over the schools they are matched to but also the type of slots they receive. Such reservation policies might cause waste in instances of low demand from some student groups. To propose a solution to this issue, we construct a family of choice functions, dynamic reserves choice functions, for schools that respect within-group fairness and allow the transfer of otherwise vacant slots from low-demand groups to high-demand groups. We propose the cumulative offer mechanism (COM) as an allocation rule where each school uses a dynamic reserves choice function and show that it is stable with respect to schools' choice functions, is strategy-proof, and respects improvements. Furthermore, we show that transferring more of the otherwise vacant slots leads to strategy-proof Pareto improvement under the COM.
Along with the energy transition, the energy markets change their organization toward more decentralized and self-organized structures, striving for locally optimal profits. These tendencies may endanger the physical grid stability. One realistic option is the exhaustion of reserve energy due to an abuse by arbitrageurs. We map the energy market to different versions of a minority game and determine the expected amount of arbitrage as well as its fluctuations as a function of the model parameters. Of particular interest are the impact of heterogeneous contributions of arbitrageurs, the interpl…
For a many-to-many matching market, we study the lattice structure of the set of random stable matchings. We define a partial order on the random stable set and present two intuitive binary operations to compute the least upper bound and the greatest lower bound for each side of the matching market. Then, we prove that with these binary operations the set of random stable matchings forms two dual lattices.
We study dynamic matching in exchange markets with easy- and hard-to-match agents. A greedy policy, which attempts to match agents upon arrival, ignores the positive externality that waiting agents generate by facilitating future matchings. We prove that this trade-off between a ``thicker'' market and faster matching vanishes in large markets; A greedy policy leads to shorter waiting times, and more agents matched than any other policy. We empirically confirm these findings in data from the National Kidney Registry. Greedy matching achieves as many transplants as commonly-used policies (1.6\% …
For a many-to-one matching model, we study the matchings obtained through the restabilization of stable matchings that had been disrupted by a change in the population. We include a simple representation of the stable matching obtained in terms of the initial stable matching (i.e., before being disrupted by changes in the population) and the firm-optimal stable matching. (We used Lattice Theory to characterize the outcome of the restabilization process.) We also describe the connection between the original stable matching and the one obtained after the restabilization process in the new market…
Profit-Oriented Planning and Multi-Market Operation Model for Hybrid Energy Storage Systems
School of Economics and Management, Beihang University（北京航空航天大学经济管理学院）；School of Systems Science, Beijing Normal University（北京师范大学系统科学学院）；National Engineering Laboratory for Big Data Analysis and Applications, Peking University（北京大学大数据分析与应用国家工程实验室）；National Safety and Emergency Management, Beijing Normal University（北京师范大学国家安全与应急管理学院）
Although the integration of two-sided matching markets using stable mechanisms generates expected gains from integration, I show that there are worst-case scenarios in which these are negative. The losses from integration can be large enough that the average rank of an agent's spouse decreases by 37.5% of the length of their preference list in any stable matching mechanism.
In a many-to-one matchingmodel with responsive preferences in which indifferences are allowed, we study three notions of core, three notions of stability, and their relationships. We show that (i) the core contains the stable set, (ii) the strong core coincides with the strongly stable set, and (iii) the super core coincides with the super stable set. We also show how the core and the strong core in markets with indifferences relate to the stable matchings of their associated tie-breaking strict markets.
This paper studies a delegation problem faced by the planner who wants to regulate receivers' reaction choices in markets for matching between receivers and senders with signaling. We provide a noble insight into the planner's willingness to delegate and the design of optimal (reaction) interval delegation as a solution to the planner's general mechanism design problem. The relative heterogeneity of receiver types and the productivity of the sender' signal are crucial in deriving optimal interval delegation in the presence of the trade-off between matching efficiency and signaling costs.
This paper studies matching markets in the presence of middlemen. In our framework, a buyer-seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer-seller pairs. Direct trade between a buyer and a seller is costlier than a trade mediated by a middleman. For each such market, we examine an associated cooperative game with transferable utility. First, we show that an optimal matching for a matching market with middlemen can be obtained by considering the two-sided assignment market where each buyer-seller pair is allowed to use the media…
This paper develops a framework for repeated matching markets. The model departs from the Gale-Shapley matching model by having a fixed set of long-lived hospitals match with a new generation of short-lived residents in every period. I show that there are two kinds of hospitals in this repeated environment: some hospitals can be motivated dynamically to voluntarily reduce their hiring capacity, potentially making more residents available to rural hospitals; the others, however, are untouchable even with repeated interaction and must obtain the same match as they do in a static matching. In lar…
We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets, with each agent having an average degree $d$ in a random (undirected) graph, and a uniformly random preference ranking over their neighbors in the graph. We formally characterize stable matchings in large markets random with small imbalance and find a threshold in the connectivity $d$ at $\log^2 n$ (where $n$ is the number of agents on one side of the market) …
We introduce a new algorithm for finding stable matchings in multi-sided matching markets. Our setting is motivated by a PhD market of students, advisors, and co-advisors, and can be generalized to supply chain networks viewed as $n$-sided markets. In the three-sided PhD market, students primarily care about advisors and then about co-advisors (consistent preferences), while advisors and co-advisors have preferences over students only (hence they are cooperative). A student must be matched to one advisor and one co-advisor, or not at all. In contrast to previous work, advisor-student and stude…
