Uncoordinated two-sided matching markets

Ackermann, Heiner; Goldberg, Paul W.; Mirrokni, Vahab; Röglin, Heiko; Vöcking, Berthold

doi:10.1145/1598780.1598788

Cited by 18 publications

(51 citation statements)

References 15 publications

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“…In Section 2 we concentrate on stable matching with correlated preferences, in which each matched pair generates a single number that represents the utility of the match to both agents. Blocking pair dynamics in stable matching with correlated preferences give rise to a lexicographical potential function [1,2]. In Section 2.1 we present a general approach on coalition formation games with constraints.…”

Section: Contribution and Outlinementioning

confidence: 99%

“…Surprisingly, it also applies to ordinary two-sided stable matching games that have either correlated preferences with ties, or non-correlated strict preferences. Observe that the problem is trivially solvable for ordinary stable matching and correlated preferences without ties, as in this case there is a unique stable matching that can always be reached using the greedy construction algorithm [2]. Theorem 3.…”

Section: Reaching a Given Matchingmentioning

confidence: 99%

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Matching Dynamics with Constraints

Hoefer

Wagner

2014

Web and Internet Economics

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We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times. For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of "consistent" instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated. We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.

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Section: Contribution and Outlinementioning

confidence: 99%

Section: Reaching a Given Matchingmentioning

confidence: 99%

Matching Dynamics with Constraints

Hoefer

Wagner

2014

Web and Internet Economics

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“…In fact, for random memory this result holds even in general when links exist among or between both partitions. However, using known results on stable marriage with full information [2], convergence time can be exponential with high probability, independently of any memory.…”

Section: Results and Contributionmentioning

confidence: 99%

Locally Stable Marriage with Strict Preferences

Hoefer

Wagner²

2017

SIAM J. Discrete Math.

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We study stable matching problems with locality of information and control. In our model, each agent is a node in a fixed network and strives to be matched to another agent. An agent has a complete preference list over all other agents it can be matched with. Agents can match arbitrarily, and they learn about possible partners dynamically based on their current neighborhood. We consider convergence of dynamics to locally stable matchings -states that are stable with respect to their imposed information structure in the network. In the two-sided case of stable marriage in which existence is guaranteed, we show that the existence of a path to stability becomes NP-hard to decide. This holds even when the network exists only among one partition of agents. In contrast, if one partition has no network and agents remember a previous match every round, a path to stability is guaranteed and random dynamics converge with probability 1. We characterize this positive result in various ways. For instance, it holds for random memory and for cache memory with the most recent partner, but not for cache memory with the best partner. Also, it is crucial which partition of the agents has memory. Finally, we present results for centralized computation of locally stable matchings, i.e., computing maximum locally stable matchings in the two-sided case and deciding existence in the roommates case. * An extended abstract of this paper has been published in the proceedings of the 40th Intl. Colloquium on Automata, Languages, and Programming (ICALP 2013) [21].

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“…The graph pictured on Figure 2 is not correlated: edges (j 3 m 3 , j 4 m 3 , j 4 m 2 , j 3 m 2 ) build a preference cycle. Ackermann et al [2] were the first to prove that random better and best response dynamics reach a stable matching on correlated markets in expected polynomial time. Using a similar argumentation, we extend their result to allocation instances.…”

Section: Definition 3 (Correlated Market) An Allocation Instance Ismentioning

confidence: 99%

“…Polynomial time convergence cannot be shown, since better response strategies need exponential time to converge even in matching instances [2].…”

Section: Theorem 2 For Every Allocation Instance With Rational Data mentioning

confidence: 99%

Paths to Stable Allocations

Cseh

Skutella

2014

Algorithmic Game Theory

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The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case of uncoordinated processes in stable allocation instances. In this setting, a feasible allocation is given and the aim is to reach a stable allocation by raising the value of the allocation along blocking edges and reducing it on worse edges if needed. Do such myopic changes lead to a stable solution? In our present work, we analyze both better and best response dynamics from an algorithmic point of view. With the help of two deterministic algorithms we show that random procedures reach a stable solution with probability one for all rational input data in both cases. Surprisingly, while there is a polynomial path to stability when better response strategies are played (even for irrational input data), the more intuitive best response steps may require exponential time. We also study the special case of correlated markets. There, random best response strategies lead to a stable allocation in expected polynomial time.

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Uncoordinated two-sided matching markets

Cited by 18 publications

References 15 publications

Matching Dynamics with Constraints

Matching Dynamics with Constraints

Locally Stable Marriage with Strict Preferences

Paths to Stable Allocations

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