Matching with Contracts: Comment

2013 ◽  
Vol 103 (5) ◽  
pp. 2050-2051 ◽  
Author(s):  
Orhan Aygün ◽  
Tayfun Sönmez
Keyword(s):  
Matching Theory ◽  
Stable Allocation ◽  
Stable Allocations

The matching with contracts model (Hatfield and Milgrom 2005) is widely considered to be one of the most important advances of the last two decades in matching theory. One of their main messages is that the set of stable allocations is non-empty under a substitutes condition. We show that an additional irrelevance of rejected contracts (IRC) condition is implicitly assumed throughout their analysis, and in the absence of IRC several of their results, including the guaranteed existence of a stable allocation, fail to hold. (JEL C78, D86)

scholarly journals Matching with Contracts: Comment

2008 ◽  
Vol 98 (3) ◽  
pp. 1189-1194 ◽  
Author(s):  
John William Hatfield ◽  
Fuhito Kojima
Keyword(s):  
Unified Model ◽  
The Other ◽  
Auction Models ◽  
Stable Allocation ◽  
Stable Allocations ◽  
Package Auction

Hatfield and Milgrom (2005) present a unified model of matching with contracts phrased in terms of hospitals and doctors, which subsumes the standard two-sided matching and some package auction models. They show that a stable allocation exists if contracts are substitutes for each hospital. They further claim that if a hospital's preferences violate the substitutes condition, there exist singleton preferences for the other hospitals and doctors such that no stable allocation exists. We show this last claim does not hold in general. We further present a weaker condition that is necessary to guarantee the existence of stable allocations. (JEL C78, D86, J41)

Stable Governments and the Allocation of Policy Portfolios

1990 ◽  
Vol 84 (3) ◽  
pp. 891-906 ◽  
Author(s):  
David Austen-Smith ◽  
Jeffrey Banks
Keyword(s):  
Government Policy ◽  
Policy Decision ◽  
Portfolio Allocation ◽  
Policy Outcomes ◽  
Allocation Model ◽  
Coalition Governments ◽  
The Core ◽  
Stable Allocation ◽  
Usual Concept ◽  
Stable Allocations

Different members of coalition governments typically have responsibility for different aspects, or dimensions, of policy. Such responsibilities are allocated as portfolios to government members. Given a distribution of such portfolios, final government policy is derived as the accumulation of individual members' decisions in regard to their respective responsibilities. We develop a portfolio allocation model of government formation and policy decision in multiparty legislatures. In particular, we focus on stable portfolio allocations, where a stable allocation is one that yields a policy that no legislative coalition is willing or able to overturn. Several notions of stability are considered and related to the usual concept of the core. Among the results are that although stable allocations are not guaranteed, such allocations can exist with minority governments; and that final policy outcomes associated with stable governments need not be “centrist.“

scholarly journals Graphical One-Sided Markets

2019 ◽  
Author(s):  
Sagar Massand ◽  
Sunil Simon
Keyword(s):  
Solution Concept ◽  
Weighted Graph ◽  
Rational Agents ◽  
Indivisible Objects ◽  
Stable Allocation ◽  
Np Complete ◽  
Neighbourhood Graph ◽  
Stable Allocations ◽  
Rational Players

We study the problem of allocating indivisible objects to a set of rational agents where each agent's final utility depends on the intrinsic valuation of the allocated item as well as the allocation within the agent's local neighbourhood. We specify agents' local neighbourhood in terms of a weighted graph. This extends the model of one-sided markets to incorporate neighbourhood externalities. We consider the solution concept of stability and show that, unlike in the case of one-sided markets, stable allocations may not always exist. When the underlying local neighbourhood graph is symmetric, a 2-stable allocation is guaranteed to exist and any decentralised mechanism where pairs of rational players agree to exchange objects terminates in such an allocation. We show that computing a 2-stable allocation is PLS-complete and further identify subclasses which are tractable. In the case of asymmetric neighbourhood structures, we show that it is NP-complete to check if a 2-stable allocation exists. We then identify structural restrictions where stable allocations always exist and can be computed efficiently. Finally, we study the notion of envy-freeness in this framework.

Reforming the Labour Market in Good and Bad Times

2018 ◽  
Author(s):  
Britta Gehrke ◽  
Enzo Weber
Keyword(s):  
Time Series ◽  
Business Cycle ◽  
Labour Market ◽  
Markov Switching ◽  
Matching Theory ◽  
Market Reforms ◽  
Structural Reforms ◽  
Labour Market Reforms ◽  
Short Run ◽  
The Business Cycle

This chapter discusses how the effects of structural labour market reforms depend on whether the economy is in expansion or recession. Based on an empirical time series model with Markov switching that draws on search and matching theory, we propose a novel identification of reform outcomes and distinguish the effects of structural reforms that increase the flexibility of the labour market in distinct phases of the business cycle. We find in applications to Germany and Spain that reforms which are implemented in recessions have weaker expansionary effects in the short run. For policymakers, these results emphasize the costs of introducing labour market reforms in recessions.

scholarly journals ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS

2021 ◽  
pp. 1-37
Author(s):  
Florian F. Gunsilius
Keyword(s):  
Convergence Rate ◽  
Poincaré Inequality ◽  
Optimal Transportation ◽  
Matching Theory ◽  
Economic Research ◽  
Poincare Inequality ◽  
Optimal Transportation Problem ◽  
Minimax Rate ◽  
The Cost ◽  
Kantorovich Problem

The theory of optimal transportation has experienced a sharp increase in interest in many areas of economic research such as optimal matching theory and econometric identification. A particularly valuable tool, due to its convenient representation as the gradient of a convex function, has been the Brenier map: the matching obtained as the optimizer of the Monge–Kantorovich optimal transportation problem with the euclidean distance as the cost function. Despite its popularity, the statistical properties of the Brenier map have yet to be fully established, which impedes its practical use for estimation and inference. This article takes a first step in this direction by deriving a convergence rate for the simple plug-in estimator of the potential of the Brenier map via the semi-dual Monge–Kantorovich problem. Relying on classical results for the convergence of smoothed empirical processes, it is shown that this plug-in estimator converges in standard deviation to its population counterpart under the minimax rate of convergence of kernel density estimators if one of the probability measures satisfies the Poincaré inequality. Under a normalization of the potential, the result extends to convergence in the $L^2$ norm, while the Poincaré inequality is automatically satisfied. The main mathematical contribution of this article is an analysis of the second variation of the semi-dual Monge–Kantorovich problem, which is of independent interest.

The Effect of Under- and Over-Benefited Support Gaps on Hurt Feelings, Esteem, and Relationships

2015 ◽  
Vol 46 (6) ◽  
pp. 785-810 ◽  
Author(s):  
Rachel M. McLaren ◽  
Andrew C. High
Keyword(s):  
Matching Theory ◽  
Informational Support ◽  
Negative Outcomes ◽  
Supportive Communication ◽  
Optimal Matching ◽  
Network Support ◽  
Different Types ◽  
Hurt Feelings ◽  
Tangible Support

Although the supportive communication people receive from others during stressful times can be helpful, it can also result in negative outcomes. One explanation for these different effects might be how closely the support people receive matches their desires. This study extends optimal matching theory and examines how the discrepancy between the support people want and what they receive (called support gaps) corresponds with hurt feelings, perceived negative relational consequences, and esteem improvement. People can either receive less support than the desire (i.e., be under-benefited) or receive more support than they desire (i.e., be over-benefited), and these different types of support gaps produce distinct patterns of results. Specifically, action-facilitating support, which includes informational and tangible support, and nurturant support, which includes emotional, esteem, and network support, were studied. Results showed that being over-benefited in informational support and being under-benefited in emotional and esteem support is hurtful, and hurt corresponded with negative relational consequences and reduced esteem improvement. Implications for research on support gaps and hurt feelings are discussed.

scholarly journals The integral stable allocation problem on graphs

2010 ◽  
Vol 7 (1-2) ◽  
pp. 64-73 ◽  
Author(s):  
Péter Biró ◽  
Tamás Fleiner
Keyword(s):  
Allocation Problem ◽  
Stable Allocation
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