Assignment games with externalities revisited

Gudmundsson, Jens; Habis, Helga

doi:10.1007/s40505-017-0117-4

Cited by 10 publications

(4 citation statements)

References 14 publications

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“…In markets with externalities, the utility of a user depends not only on the shared resources with its matched user but also generally depends on the existing matching [11]. The main difficulty in dealing with externalities lies in the fact that the core of a cooperative game might be empty in the presence of externalities [33]. Furthermore, the very concept of stability and of blocking pairs is not well defined.…”

Section: Discussionmentioning

confidence: 99%

BLMA: A Blind Matching Algorithm With Application to Cognitive Radio Networks

Hamza

Shamma

2017

IEEE J. Select. Areas Commun.

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We consider a two-sided matching problem with a defined notion of pairwise stability. We propose a distributed blind matching algorithm (BLMA) to solve the problem. We prove the solution produced by BLMA will converge to an -pairwise stable outcome with probability one. We then consider a matching problem in cognitive radio networks. Secondary users (SUs) are allowed access time to the spectrum belonging to the primary users (PUs) provided that they relay primary messages. We propose a realization of the BLMA to produce an -pairwise stable solution assuming quasi-convex and quasiconcave utilities. In the case of more general utility forms, we show another BLMA realization to provide a stable solution. Furthermore, we propose negotiation mechanism to bias the algorithm towards one side of the market. We use this mechanism to protect the exclusive rights of the PUs to the spectrum. In all such implementations of the BLMA, we impose a limited information exchange in the network so that agents can only calculate their own utilities, but no information is available about the utilities of any other users in the network.

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Section: Discussionmentioning

confidence: 99%

BLMA: A Blind Matching Algorithm With Application to Cognitive Radio Networks

Hamza

Shamma

2017

IEEE J. Select. Areas Commun.

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“…Since Shapley and Shubik [1972], where cooperative assignment games associated with assignment problems were introduced, different generalizations have been developed. Three of these extensions are quasi-assignment games [Auriol and Marchi, 2002], infinite assignment games [Llorca et al, 2004] and assignment games with externalities [Eriksson et al, 2011;Gudmundsson and Habis, 2017]. Quasi-assignment games are assignment games in which some inequalities are converted into equalities.…”

Section: Literature Reviewmentioning

confidence: 99%

A Solution Concept Related to “Bounded Rationality” for some Two-Echelon Models

Sánchez-Soriano

Llorca

2019

Int. Game Theory Rev.

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Two-echelon models describe situations in which there are two differentiated groups of agents. Some examples of these models can be found in supply chain problems, transportation problems or two-sided markets. In this paper, we deal with two-sided transportation problems which can be used to describe a wide variety of logistic and market problems. We approach the problem from the perspective of cooperative games and study some solution concepts closely related to the game theoretical concept of core, but rather than focus specifically on the core of a transportation game, we introduce and study a new solution concept, a core catcher, which can be motivated by a kind of bounded rationality which can arise in these cooperative contexts.

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“…They also proposed a weak stability concept that allows a pair of agents to block a matching only if they benefit from the block under all possible rematches of the remaining agents and showed that such weak stable matchings exist in one-to-one environments. Much of the subsequent literature-e.g., Chowdhury (2004); Hafalir (2008); Eriksson, Jansson and Vetander (2011); Chen (2013); Gudmundsson and Habis (2017); Salgado-Torres (2011a,b); Bodine-Baron et al…”

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confidence: 99%