Marginality and Myerson values

Manuel, Conrado; Ortega, Edwin M. M.; Pozo, Mónica del

doi:10.1016/j.ejor.2019.12.021

Cited by 10 publications

(10 citation statements)

References 21 publications

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“…iv) satisfies the superfluous link property (Borm et al 1992), if for all (N, v, ) ∈ CS N 0 and every l ∈ superfluous link in (N, v, ) (i.e., a null player in the link game), then (N, v, ) = (N, v, ⧵ {l}). v) verifies PL-marginality (Manuel et al 2020) Borm et al (1992) characterized the position value only on the domain consisting of communication situations with a fixed player set and a cycle-free graph. Then, the position value is the unique allocation rule in such a domain that satisfies component efficiency, additivity, the superfluous link property, and the link anonymity.…”

Section: Preliminariesmentioning

confidence: 88%

“…To prove that it also satisfies PL-marginality, we will use the following lemma whose proof is straightforward. This lemma states that if the PL-marginal contributions of player i and his subset of links to 𝜂 ⊆ 𝛾 ⧵ 𝛾 i (Manuel et al 2020) coincide for games (N, v) and (N, w), ceteris paribus, then the change in the PL-marginal contributions corresponding to and * of this player in both games also coincide. In other words, if the change in the value of the game does not affect the PL-marginal contributions, neither will it affect their variations.…”

Section: A New Characterization Of the Position Valuementioning

confidence: 98%

“…Gómez et al (2003) and González-Arangüena et al (2017) additively decomposed the Myerson value into the WG-Myerson value that measures the productivity of the player via the characteristic function (for symmetric games, the communication centrality), and the BG-Myerson value that evaluates the ability of the player to intermediate among others (betweenness centrality). Manuel et al (2020) introduced different types of marginal contributions for communication situations as well as the corresponding marginality properties. When the cooperation in a game is restricted by means of a graph, in addition to the classic marginal contribution of a player to a coalition, it is possible to consider that a player can contribute to a coalition by lending it his links to increase the connectedness, but without joining himself (L-marginal contribution), and also the possibility of joining with his relationships (PL-marginal contributions).…”

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confidence: 99%

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Marginality and the position value

Manuel

Ortega²,

Pozo³

2022

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We present a new characterization of the position value, one of the most prominent allocation rules for communication situations (graph-games or games with restricted communication). This characterization includes the PL-marginality property, an extension for communications situations of the classic marginality for TU-games, as well as component efficiency and balanced link contributions for necessary players.

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Section: Preliminariesmentioning

confidence: 88%

Section: A New Characterization Of the Position Valuementioning

confidence: 98%

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confidence: 99%

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Marginality and the position value

Manuel

Ortega²,

Pozo³

2022

TOP

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“…In the course of finding solutions for graph games, Myerson analyzed situations in which communication between players is restricted in TU games [261] and introduced the graph-restricted game, where the outcome of a coalition is determined by the total payoffs obtained in the original game by its connected subcoalitions [262]. Then, he proposed a solution concept -known as Myerson value [263] -for graphrestricted games.…”

Section: ) Coalition Graph Gamesmentioning

confidence: 99%

A Survey of Cyber-Physical Systems From a Game-Theoretic Perspective

et al. 2023

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With the emergence of the Internet-of-Things (IoT), artificial intelligence, and communication technologies, cyber-physical systems (CPS) have revolutionized the engineering paradigm with profound applications in many aspects of society including homes, energy, agriculture, health-care, transportation, business, and manufacturing. A CPS uses suitable computational techniques such as game theory to enable different entities to interact with one another for taking necessary actions to obtain selected objectives. Recent literature on CPS has extensively used game theory to approach a variety of technical challenges. In order to make these contributions more accessible to a broader audience, there is a need for studies that can provide readers with a comprehensive understanding of different types of CPS and their attributes, then clearly outline why game theory is relevant for modeling different aspects of CPS, and also discuss how game theory has been used in relevant literature to date. This paper bridges this gap by 1) providing a general discussion of different types of CPS and their characteristics; 2) giving an overview of different types of game-theoretic approaches; 3) explaining why game theory is appropriate for modeling different types of CPS; and 4) finally, studying how game theory has been used in different CPS types to address their challenges. Further, we also identify some key research challenges for future investigation where game theory could be applied as a potential solution.

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“…The axiom of equal treatment of necessary players has already been studied recently by Navarro (2019) for cooperative games enriched by a communication graph, who shows that this axiom is at the origin of the fairness axiom satisfied by the Myerson value (Myerson, 1977). It has also been used by Manuel et al (2020) to offer a characterization of the Myerson value, the between groups Myerson value and the within groups Myerson value (González-Arangüena et al, 2017).…”

Section: Introductionmentioning

confidence: 99%