The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure

McQuillin, Ben

doi:10.1016/j.jet.2008.05.010

Cited by 46 publications

(49 citation statements)

References 19 publications

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“…Now, let us consider a payoff of player 1 in this game that we will denote ϕ 1 (v). This payoff, according to the extensions of the Shapley value to games with externalities by Pham do and Norde [16], McQuillin [11], Bolger [2], Macho-Stadler et al [10], and Hu and Yang [9], respectively, is as follows:…”

Section: Marginality Approach and Axiomsmentioning

confidence: 99%

“…This property is called (Weak) Monotonicity. Indeed, the fact that Myerson's value violates Monotonicity is the main reason why it was criticized in the literature as unintuitive [10,3,11]. Formally, we have the following definition:…”

Section: Weak and Strong Monotonicitymentioning

confidence: 99%

“…This means that weights α f ree are interlace resistant. Skibski [18] used weights which are dual to the previous ones to derive McQuillin's value [11]:…”

Section: The Analysis Of Various Marginality Definitionsmentioning

confidence: 99%

“…McQuillin [11] analyzed extending the Shapley value to games with externalities combined with Owen generalization [14]. If we specify how the payoffs of players should be generalized for payoffs of coalition (to this end, McQuillin provided a Rule of Generalization), then we can treat the payoffs as a game (as all coalitions have assigned payoffs).…”

Section: Related Workmentioning

confidence: 99%

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Marginality Approach to Shapley Value in Games with Externalities

Michalak

2013

SSRN Journal

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One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities. In particular, when externalities occur, a direct translation of Shapley's axioms does not imply a unique value. In this paper we study the marginality approach to this problem, based on the idea of an α-parametrized definition of the marginal contribution, where α is a vector of weights associated with an agent joining/leaving a coalition. We prove that all values that satisfy the direct translation of Shapley's axioms can be obtained using the marginality approach. Moreover, we show that every such value can be uniquely derived using marginality approach by choosing appropriate weights α. Next, we analyze how properties of a value translate to the requirements on the definition of the marginal contribution (i.e. weights α). Building upon this analysis, we show that under certain conditions, two other axiomatizations of the Shapley value (i.e., Young's marginality axiomatization and Myerson's axiomatization based on the concept of balanced contributions), translated to games with externalities using the proper definition of the α-parametrized marginal contribution, are equivalent to Shapley's axiomatization.

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Section: Marginality Approach and Axiomsmentioning

confidence: 99%

Section: Weak and Strong Monotonicitymentioning

confidence: 99%

“…This means that weights α f ree are interlace resistant. Skibski [18] used weights which are dual to the previous ones to derive McQuillin's value [11]:…”

Section: The Analysis Of Various Marginality Definitionsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Marginality Approach to Shapley Value in Games with Externalities

Michalak

2013

SSRN Journal

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“…Recently, some game theorists study extensions of the Shapley value for games in partition function form. For instance, Potter (2000), Fujinaka (2004), Albizuri et al (2005), Macho-Stadler et al (2007), Dutta et al (2008) and McQuillin (2009) are contributions to this line of research. The axiomatic approach is one of methods to justify solution concepts for coalitional games.…”

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confidence: 99%

An axiomatic characterization of a value for games in partition function form

Yang

2010

SERIEs

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for n-Person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307-317, 1953) to characterize our value. In addition, we discuss a relationship between the a-Shapley values proposed by Fujinaka (On the marginality principle in partition function form games. Mimeo, Graduate School of Economics, Kobe University, Japan, 2004) and the values constructed through the average approach provided by Macho-Stadler et al. (J Econ Theory 135:339-356, 2007). Terms of use: Documents in EconStor may

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Shapley Value in Partition Function Form Games: New Research Perspectives for Features Selection

Bimonte

Senatore

2022

Mathematical and Statistical Methods for Actuarial Sciences and Finance

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The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure

Cited by 46 publications

References 19 publications

Marginality Approach to Shapley Value in Games with Externalities

Marginality Approach to Shapley Value in Games with Externalities

An axiomatic characterization of a value for games in partition function form

Shapley Value in Partition Function Form Games: New Research Perspectives for Features Selection

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