We propose a new algorithm in the two-sided marriage market wherein both sides of the market propose in each round. The algorithm always yields a stable matching. Moreover, the outcome is a Rawlsian stable matching if...
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We propose a new algorithm in the two-sided marriage market wherein both sides of the market propose in each round. The algorithm always yields a stable matching. Moreover, the outcome is a Rawlsian stable matching if the number of men and women is equal. Lastly, the algorithm can be computed in polynomial time and, from a practical standpoint, can be used in markets where fairness considerations are important.
Kojima and Manea (Econometrica 78(2):633-653, 2010) present two characterizations of when an allocation rule corresponds to the agent-proposing deferredacceptance (DA) algorithm for some substitutable priority rule o...
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Kojima and Manea (Econometrica 78(2):633-653, 2010) present two characterizations of when an allocation rule corresponds to the agent-proposing deferredacceptance (DA) algorithm for some substitutable priority rule of the objects being assigned. Building on their results we characterize when an allocation rule is outcome equivalent to the DA algorithm for every substitutable priority rule. In particular, an assignment rule satisfies mutual best (MB) if an agent is always assigned her most preferred object whenever she has the highest priority for it. This mild requirement is a necessary but far from sufficient condition for an assignment rule to be stable. We demonstrate that any allocation mechanism that satisfies MB along with non-wastefulness, population monotonicity and either individually rational monotonicity or weak Maskin monotonicity not only is a stable assignment mechanism but is equivalent to the agent proposing DA algorithm.
This paper proposes an intelligent reflecting surface (IRS)-assisted wireless inland ship multi-access edge computing (MEC) network architecture with time windows, where UAV is deployed to serve time-constrained unman...
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ISBN:
(纸本)9798350311143
This paper proposes an intelligent reflecting surface (IRS)-assisted wireless inland ship multi-access edge computing (MEC) network architecture with time windows, where UAV is deployed to serve time-constrained unmanned surface vehicles (USVs) with IRS. The task execution efficiency maximization optimization problem is formulated by joint considering IRS phase-shift vector, UAVs hovering coordinates and the task execution indicator. To tackle the formulated challenging problem, a heuristic solution is proposed. First, an enhanced differential evolution algorithm is proposed to optimize UAVs hovering coordinates. Moreover, IRS phase-shift vector and task execution indicator are jointly optimized in an iterative manner by the proposed modified deferred acceptance algorithm. Numerical results verify the effectiveness of the proposed algorithm in comparison with some selected advanced algorithms in terms of task execution efficiency.
Network virtualization (NV) can provide greater flexibility, better control, and improved quality of service (QoS) for the existing Internet architecture by enabling heterogeneous virtual network requests (VNRs) to sh...
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ISBN:
(纸本)9781665477062
Network virtualization (NV) can provide greater flexibility, better control, and improved quality of service (QoS) for the existing Internet architecture by enabling heterogeneous virtual network requests (VNRs) to share the substrate network (SN) resources. The efficient assignment of the SN resources catering to the demands of virtual machines (VMs) and virtual links (VLs) of the VNRs is known as virtual network embedding (VNE) and is proven to be NP-Hard. Deviating from the literature, this paper proposes a framework MatchVNE that is focused on maximizing the revenue-to-cost ratio of VNRs by considering a blend of system and topological attributes that better capture the inherent dependencies among the VMs. MatchVNE performs a stable VM embedding using the deferred acceptance algorithm (DAA). The preference of the VMs and servers are generated using a hybrid entropy, and the technique for order of preference by similarity to ideal solution (TOPSIS) based ranking strategy for VMs and servers. The attribute weights are determined using entropy, whereas the server and VM ranking are obtained via TOPSIS. The shortest path, VL-embedding, follows VM-embedding. The simulation results show that MatchVNE outperforms the baselines by achieving a 23% boost in the average revenue-to-cost-ratio and 44% improvement in the average acceptance ratio.
We incorporate externalities into the stable matching theory of two-sided markets. Extending the classical substitutes condition to markets with externalities, we establish that stable matchings exist when agent choic...
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We incorporate externalities into the stable matching theory of two-sided markets. Extending the classical substitutes condition to markets with externalities, we establish that stable matchings exist when agent choices satisfy substitutability. We show that substitutability is a necessary condition for the existence of a stable matching in a maximal-domain sense and provide a characterization of substitutable choice functions. In addition, we extend the standard insights of matching theory, like the existence of side-optimal stable matchings and the deferred acceptance algorithm, to settings with externalities even though the standard fixed-point techniques do not apply.
We study multistage centralized assignment systems to allocate scarce resources based on priorities in the context of school choice. We characterize schools' capacity-priority profiles under which an additional st...
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We study multistage centralized assignment systems to allocate scarce resources based on priorities in the context of school choice. We characterize schools' capacity-priority profiles under which an additional stage of assignment may improve student welfare when the deferred acceptance algorithm is used at each stage. If the capacity-priority profile is acyclic, then no student prefers any subgame-perfect Nash equilibrium (SPNE) outcome of the 2-stage system to the truthful dominant-strategy equilibrium outcome of the 1-stage system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage system may Pareto dominate the truthful dominant-strategy equilibrium outcome of the 1-stage system. If students are restricted to playing truncation strategies, an additional stage unambiguously improves student welfare: no student prefers the truthful dominant-strategy equilibrium outcome of the 1-stage system to any SPNE outcome of the 2-stage system.
This paper proposes a practical and data-driven preference estimation method from reported lists in a deferredacceptance mechanism when there are incentives to report these lists strategically. Data on centralized co...
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This paper proposes a practical and data-driven preference estimation method from reported lists in a deferredacceptance mechanism when there are incentives to report these lists strategically. Data on centralized college admissions from Turkey show many pieces of evidence that students construct their lists strategically according to their admission chances and previous years' admission outcomes. We develop a preference estimation method to evaluate reported lists within the set of colleges that are considered accessible to each student. This method allows us to create personal choice sets and to estimate student preferences by making valid utility comparisons that are supported by data and theory. We show the robustness of our estimation method compared to the existing estimation methods. A counterfactual admission analysis based on our preference estimates suggests that students from low-SES households are better off under a student sorting rule only based on high school GPAs.
We study the trade-off between stability and students' welfare in school choice problems. We call a matchingweakly stableif none of its blocking pairs can be matched in a more stable matching-one with a weakly sma...
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We study the trade-off between stability and students' welfare in school choice problems. We call a matchingweakly stableif none of its blocking pairs can be matched in a more stable matching-one with a weakly smaller set of blocking pairs. A matching is said to beself-constrained efficientif for students it is not Pareto dominated by any more stable matching, and it isself-constrained optimalif it weakly Pareto dominates all such matchings. We show that the following are equivalent for any matching: (1) It is weakly stable and self-constrained efficient;(2) it is self-constrained optimal;(3) it is an efficiency-adjusted deferredacceptance mechanism (EADAM) outcome under some consenting constraints;and (4) it is exactly the EADAM outcome when its own set of blocking pairs is used as consenting constraint.
We analyze a three-sided matching market where institutions own objects and individuals belong to institutions. Institutions pool their objects to enlarge the choice set of individuals. For any institution, the number...
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We analyze a three-sided matching market where institutions own objects and individuals belong to institutions. Institutions pool their objects to enlarge the choice set of individuals. For any institution, the number of individuals who receive an object must be equal to the number of objects initially owned. Under this distributional constraint, individually rational and fair assignments may fail to exist. However, when the number of individuals is sufficiently large, fair assignments exist and can be found using a new algorithm, called the Nested deferred acceptance algorithm with interrupters (NDAI). This procedure nests a one-to-one matching between agents and objects and a one-to-many matching between objects and institutions. We show that it outputs a matching which is Pareto optimal among fair matchings and strategy-proof for individuals. When agents belong to several institutions, the NDAI results in assignments which are fair for agents of the same institution. (C) 2020 Elsevier Inc. All rights reserved.
For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof (Ergin, 2002)...
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For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof (Ergin, 2002). We reveal a hidden iterative removal structure behind such deferred acceptance algorithms. A nonempty set of students is called a top fair set(TFS) if when all students apply to their most preferred schools and all schools accept the best applicants up to their quotas, students in the set are always accepted, regardless of other students' preferences. We provide an elimination process to find the maximal TFS, if any TFS exists. We show that for any priority structure, iterative removal of TFS is equivalent to the associated deferred acceptance algorithm if and only if the latter is a Pareto efficient mechanism. (C) 2020 Elsevier Inc. All rights reserved.
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