Absorbing sets in roommate problems

Iñarra, Elena; Larrea, Concepción; Molis, Elena

doi:10.1016/j.geb.2013.04.008

Cited by 17 publications

(6 citation statements)

References 18 publications

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“…Roth and Vande Vate (1990) demonstrate a random blocking pair dynamic that leads almost surely to the core in such games. Chung (2000), Diamantoudi et al (2004) and Inarra et al (2008Inarra et al ( , 2013 establish similar results for nontransferable-utility roommate problems, while Klaus and Klijn (2007) and Kojima andÜnver (2008) treat the case of many-to-one and many-to-many nontransferable-utility matchings. Another branch of the literature considers stochastic updating procedures that place high probability on core solutions, that is, the stochastically stable set is contained in the core of the game (Jackson and Watts 2002, Klaus et al 2010, Newton and Sawa 2013.…”

Section: Related Literaturementioning

confidence: 83%

Evolutionary dynamics and equitable core selection in assignment games

Nax

Pradelski

2014

Int J Game Theory

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We study evolutionary dynamics in assignment games where many agents interact anonymously at virtually no cost. The process is decentralized, very little information is available and trade takes place at many different prices simultaneously. We propose a completely uncoupled learning process that selects a subset of the core of the game with a natural equity interpretation. This happens even though agents have no knowledge of other agents' strategies, payoffs, or the structure of the game, and there is no central authority with such knowledge either. In our model, agents randomly encounter other agents, make bids and offers for potential partnerships and match if the partnerships are profitable. Equity is favored by our dynamics because it is more stable, not because of any ex ante fairness criterion.JEL classifications: C71, C73, C78, D83

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Section: Related Literaturementioning

confidence: 83%

Evolutionary dynamics and equitable core selection in assignment games

Nax

Pradelski

2014

Int J Game Theory

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“…Unsolvable roommate problems have been long studied in economics and other related fields, and several more solution concepts have been proposed. These include maximum stable matchings (Tan, 1990), almost stable matchings (Abraham et al, 2006), Pstable matchings (Inarra et al, 2008), absorbing sets (Iñarra et al, 2013), and Q-stable matchings (Biró et al, 2016). Each of those solutions focuses on a part of the properties that a stable matching satisfies, and extends it to unsolvable problems.…”

Section: Related Literaturementioning

confidence: 99%

Stability against robust deviations in the roommate problem

Hirata

Kasuya

Tomoeda

2021

Games and Economic Behavior

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We propose a new solution concept in the roommate problem, based on the "robustness" of deviations (i.e., blocking coalitions). We call a deviation from a matching robust up to depth k, if none of the deviators gets worse off than at the original matching after any sequence of at most k subsequent deviations. We say that a matching is stable against robust deviations (for short, SaRD) up to depth k, if there is no robust deviation up to depth k. As a smaller k imposes a stronger requirement for a matching to be SaRD, we investigate the existence of a matching that is SaRD with a minimal depth k. We constructively demonstrate that a SaRD matching always exists for k = 3, and establish sufficient conditions for k = 1 and 2.

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“…Kalai, Pazner, and Schmeidler (1976) studied the "admissible set" in various bargaining situations and Shenoy (1979) defined the "elementary dynamic solution" for coalitional games. More recently, Inarra, Larrea and Molis (2013) studied the absorbing set for the roommate problem, and Jackson and Watts (2002) the "closed cycle" for network formation.…”

Section: Introductionmentioning

confidence: 99%

An Implementation Approach to Rotation Programs

Submitter¹,

Korpela²,

Lombardi

et al. 2021

SSRN Journal

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Rotation programs are widely used in societies. Some examples are job rotations, rotation schemes in the management of common-pool resources, and rotation procedures in fair division problems. We study rotation programs via the implementation of Pareto efficient social choice rules under complete information. The notion of the rotation program predicts the outcomes. A rotation program is a myopic stable set whose states are arranged circularly, and agents can effectively move only between two consecutive states. We provide characterizing conditions for the implementation in rotation programs and show that, for multi-valued rules, our notion of rotation monotonicity is necessary and sufficient for implementation. Finally, we identify two classes of assignment problems that are implementable in rotation programs.

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Absorbing sets in roommate problems

Cited by 17 publications

References 18 publications

Evolutionary dynamics and equitable core selection in assignment games

Evolutionary dynamics and equitable core selection in assignment games

Stability against robust deviations in the roommate problem

An Implementation Approach to Rotation Programs

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