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What Have We Learned From Market Design?
 ECONOMIC JOURNAL
, 2008
"... This essay discusses some things we have learned about markets, in the process of designing marketplaces to fix market failures. To work well, marketplaces have to provide thickness, i.e. they need to attract a large enough proportion of the potential participants in the market; they have to overco ..."
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Cited by 29 (8 self)
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This essay discusses some things we have learned about markets, in the process of designing marketplaces to fix market failures. To work well, marketplaces have to provide thickness, i.e. they need to attract a large enough proportion of the potential participants in the market; they have to overcome the congestion that thickness can bring, by making it possible to consider enough alternative transactions to arrive at good ones; and they need to make it safe and sufficiently simple to participate in the market, as opposed to transacting outside of the market, or having to engage in costly and risky strategic behavior. I'll draw on recent examples of market design ranging from labor markets for doctors and new economists, to kidney exchange, and school choice in New York City and Boston.
The Speed of Learning in Noisy Games: Partial Reinforcement and the Sustainability of Cooperation
"... In an experiment, players’ ability to learn to cooperate in the repeated prisoner’s dilemma was substantially diminished when the payoffs were noisy, even though players could monitor one another’s past actions perfectly. In contrast, in onetime play against a succession of opponents, noisy payoffs ..."
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Cited by 29 (2 self)
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In an experiment, players’ ability to learn to cooperate in the repeated prisoner’s dilemma was substantially diminished when the payoffs were noisy, even though players could monitor one another’s past actions perfectly. In contrast, in onetime play against a succession of opponents, noisy payoffs increased cooperation, by slowing the rate at which cooperation decays. These observations are consistent with the robust observation from the psychology literature that partial reinforcement (adding randomness to the link between an action and its consequences while holding expected payoffs constant) slows learning. This effect is magnified in the repeated game: when others are slow to learn to cooperate, the benefits of cooperation are reduced, which further hampers cooperation. These results show that a small change in the payoff environment, which changes the speed of individual learning, can have a large effect on collective behavior. And they show that there may be interesting comparative dynamics that can be derived from careful attention to the fact that at least some economic behavior is learned from experience.
The dynamics of law clerk matching: An experimental and computational investigation of proposals for reform of the market
, 2006
"... ..."
Mix and Match
, 2010
"... Consider a matching problem on a graph where disjoint sets of vertices are privately owned by selfinterested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to maximize the number of matches despite selfinterest, with agents ..."
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Cited by 18 (5 self)
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Consider a matching problem on a graph where disjoint sets of vertices are privately owned by selfinterested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to maximize the number of matches despite selfinterest, with agents that each want to maximize the number of their own vertices that match. Each agent can choose to hide some of its vertices, and then privately match the hidden vertices with any of its own vertices that go unmatched by the mechanism. A prominent application of this model is to kidney exchange, where agents correspond to hospitals and vertices to donorpatient pairs. Here hospitals may game an exchange by holding back pairs and harm social welfare. In this paper we seek to design mechanisms that are strategyproof, in the sense that agents cannot benefit from hiding vertices, and approximately maximize efficiency, i.e., produce a matching that is close in cardinality to the maximum cardinality matching. Our main result is the design and analysis of the eponymous MixandMatch mechanism; we show that this randomized mechanism is strategyproof and provides a 2approximation. Lower bounds establish that the mechanism is near optimal.
Making Decisions Based on the Preferences of Multiple Agents
"... People often have to reach a joint decision even though they have conflicting preferences over the alternatives. Examples range from the mundane—such as allocating chores among the members of a household—to the sublime—such as electing a government and thereby charting the course for a country. The ..."
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Cited by 14 (6 self)
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People often have to reach a joint decision even though they have conflicting preferences over the alternatives. Examples range from the mundane—such as allocating chores among the members of a household—to the sublime—such as electing a government and thereby charting the course for a country. The joint decision can be reached by an informal negotiating process or by a carefully specified protocol. Philosophers, mathematicians, political scientists, economists, and others have studied the merits of various protocols for centuries. More recently, especially over the course of the past decade or so, computer scientists have also become deeply involved in this study. The perhaps surprising arrival of computer scientists on this scene is due to a variety of reasons, including the following. 1. Computer networks provide a new platform for communicating
Almost stable” matchings in the roommates problem
 In Approximation and online algorithms
, 2006
"... Abstract. An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an sr instance with n agents, i ..."
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Cited by 11 (3 self)
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Abstract. An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an sr instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NPhard and not approximable within n 1 2 −ε, for any ε> 0, unless P=NP. If the preference lists contain ties, we improve this result to n 1−ε. Also, we show that, given an integer K and an sr instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NPcomplete. By contrast, if K is constant, we give a polynomialtime algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an sr instance I. 1
Local Matching Dynamics in Social Networks
, 2012
"... We study stable marriage and roommates problems under locality constraints. Each player is a vertex in a social network and strives to be matched to other players. The value of a match is specified by an edge weight. Players explore possible matches only based on their current neighborhood. We study ..."
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Cited by 10 (0 self)
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We study stable marriage and roommates problems under locality constraints. Each player is a vertex in a social network and strives to be matched to other players. The value of a match is specified by an edge weight. Players explore possible matches only based on their current neighborhood. We study convergence of natural betterresponse dynamics that converge to locally stable matchings – matchings that allow no incentive to deviate with respect to their imposed information structure in the social network. If we have global information and control to steer the convergence process, then quick convergence is possible and for every starting state we can construct in polynomial time a sequence of polynomially many betterresponse moves to a locally stable matching. In contrast, for a large class of oblivious dynamics including random and concurrent betterresponse the convergence time turns out to be exponential. In such distributed settings, a small amountof randommemorycan ensure polynomialconvergence time, even for manytomany matchings and more general notions of neighborhood. Here the type of memory is crucial as for several variants of cache memory we provide exponential lower bounds on convergence times. 1
The stable roommates problem with globallyranked pairs
 IN PROC. OF THE 3RD INT. WORKSHOP ON INTERNET AND NETWORK ECONOMICS (WINE
, 2007
"... We introduce a restriction of the stable roommates problem in which roommate pairs are ranked globally. In contrast to the unrestricted problem, weakly stable matchings are guaranteed to exist, and additionally, can be found in polynomial time. However, it is still the case that strongly stable matc ..."
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Cited by 7 (1 self)
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We introduce a restriction of the stable roommates problem in which roommate pairs are ranked globally. In contrast to the unrestricted problem, weakly stable matchings are guaranteed to exist, and additionally, can be found in polynomial time. However, it is still the case that strongly stable matchings may not exist, and so we consider the complexity of finding weakly stable matchings with various desirable properties. In particular, we present a polynomialtime algorithm to find a rankmaximal (weakly stable) matching. This is the first generalization of the algorithm due to Irving et al. [17] to a nonbipartite setting. Also, we prove several hardness results in an even more restricted setting for each of the problems of finding weakly stable matchings that are of maximum size, are egalitarian, have minimum regret, and admit the minimum number of weakly blocking pairs.
An improved 2agent kidney exchange mechanism
"... Abstract. We study a mechanism design version of matching computation in graphs that models the game played by hospitals participating in pairwise kidney exchange programs. We present a new randomized matching mechanism for two agents which is truthful in expectation and has an approximation ratio o ..."
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Cited by 7 (4 self)
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Abstract. We study a mechanism design version of matching computation in graphs that models the game played by hospitals participating in pairwise kidney exchange programs. We present a new randomized matching mechanism for two agents which is truthful in expectation and has an approximation ratio of 3/2 to the maximum cardinality matching. This is an improvement over a recent upper bound of 2 [Ashlagi et al., EC 2010] and, furthermore, our mechanism beats for the first time the lower bound on the approximation ratio of deterministic truthful mechanisms. We complement our positive result with new lower bounds. Among other statements, we prove that the weaker incentive compatibility property of truthfulness in expectation in our mechanism is necessary; universally truthful mechanisms that have an inclusionmaximality property have In an attempt to address the wide need for kidney transplantation and the scarcity of cadaver kidneys, several countries have launched, or are considering,
Inapproximability of the kidney exchange problem
 Information Processing Letters
, 2007
"... Abstract. To overcome the shortage of kidneys available for transplantation, several countries have started various programmes of kidney exchanges between incompatible patientdonor pairs. This situation can be modelled as a cooperative game in which the players are the patientdonor pairs and their ..."
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Cited by 4 (1 self)
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Abstract. To overcome the shortage of kidneys available for transplantation, several countries have started various programmes of kidney exchanges between incompatible patientdonor pairs. This situation can be modelled as a cooperative game in which the players are the patientdonor pairs and their preferences are derived in the first step from the suitability of the donated kidney and in the second step from the length of the obtained cycle of exchanges. Although the core of such a cooperative game is always nonempty and one core solution can be found by the famous Top Trading Cycles algorithm, many questions concerning the structure of the core are NPhard. In this paper we show that the problem of finding a core permutation that maximizes the number of patients who obtain a suitable kidney is not approximable within n 1−ε for any ε> 0 unless P = NP.