The priority value for cooperative games with a priority structure

Béal, Sylvain; Ferrières, Sylvain; Solal, Philippe

doi:10.1007/s00182-021-00799-5

Cited by 6 publications

(6 citation statements)

References 32 publications

(51 reference statements)

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“…Note that an ordered partition over the agent set is a special case of a poset: it corresponds to a specific ranked poset where each agent with the same rank dominates, and so has priority over, each other agent with a lower rank, and agents with the same rank are incomparable with respect to the poset. As Kalai and Samet (1987), Béal et al (2022) consider that the priority structure does not influence the coalition formation process but the distribution of payoffs. They propose the Priority value which shares the Harsanyi dividend of a coalition in a game equally to its priority members.…”

Section: Introductionmentioning

confidence: 99%

“…There are many axiomatic foundations for the Shapley value, the Positively weighted Shapley values, and the Weighted Shapley values, and Béal et al (2022) propose two axiomatic characterizations of the Priority value. Recently, Casajus and Yokote (2017) provide a characterization of the Shapley value by three properties: Efficiency, Null agent, and Weak differential marginality.…”

Section: Introductionmentioning

confidence: 99%

“…If the ordered partition is the coarsest one, then the Weighted Shapley values coincide with the Positively weighted Shapley values. Béal et al (2022) define a nonsymmetric version of the Shapley value by endowing a game with a priority structure represented by a partially ordered set (a poset henceforth) over the agent set. The poset reflects the asymmetries that may exist between agents, for example, different needs, unequal merits, beyond the parameters of the game.…”

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confidence: 99%

“…To complete the characterization of Weighted priority values we use two other axioms. The first one is borrowed from Béal et al (2022). The Priority agent out axiom indicates that removing an agent does not affect the payoffs of the agents over which it has 1 Differential marginality is itself a weak version of Strong differential monotonicity introduced by Casajus and Huettner (2013).…”

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confidence: 99%

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Axiomatic characterizations of the family of Weighted priority values

Béal

Ferrières²,

Navarro-Ramos³

et al. 2023

Int J of Economic Theory

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We introduce a new family of values for TU‐games with a priority structure, which both contains the Priority value recently introduced by Béal et al. and the Weighted Shapley values (Kalai & Samet). Each value of this family is called a Weighted priority value and is constructed as follows. A strictly positive weight is associated with each agent and the agents are partially ordered according to a binary relation. An agent is a priority agent with respect to a coalition if it is maximal in this coalition with respect to the partial order. A Weighted priority value distributes the dividend of each coalition among the priority agents of this coalition in proportion to their weights. We provide an axiomatic characterization of the family of the Weighted Shapley values without the additivity axiom. To this end, we borrow the Priority agent out axiom from Béal et al., which is used to axiomatize the Priority value. We also reuse, in our domain, the principle of Superweak differential marginality introduced by Casajus to axiomatize the Positively weighted Shapley values. We add a new axiom of Independence of null agent position which indicates that the position of a null agent in the partial order does not affect the payoff of the other agents. Together with Efficiency, the above axioms characterize the Weighted Shapley values. We show that this axiomatic characterization holds on the subdomain where the partial order is structured by levels. This entails an alternative characterization of the Weighted Shapley values. Two alternative characterizations are obtained by replacing our principle of Superweak differential marginality by Additivity and invoking other axioms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Axiomatic characterizations of the family of Weighted priority values

Béal

Ferrières²,

Navarro-Ramos³

et al. 2023

Int J of Economic Theory

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“…Faigle and Kern [48] considered restricted structures modelling precedence constraints where the set of players is (partially) ordered by some precedence relations. Algaba et al [3] developed the so-called antimatroid which generalizes the concept of permission structures, and Béal et al [18] developed priority structures which are mathematically identical to the acyclic conjunctive permission structures in [55] and the structure of precedence constraints. Furthermore, several other combinatorial structures are incorporated into general TU-games, such as union stable systems [2], convex geometries [23,24], augmenting systems [25], regular set systems [78], union closed systems [113], accessible union stable network structures [4], voting structures [1], intersection closed system [19], etc.…”

Section: Introductionmentioning

confidence: 99%