Cooperative Game as Non-Additive Measure

Fujimoto, Katsushige

doi:10.1007/978-3-319-03155-2_6

Cited by 11 publications

(3 citation statements)

References 42 publications

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“…In what follows, we express the MI k -value of a TU game in terms of the Shapley values of a class of associated games. For any T ⊆ N denote by [T ] a single hypothetical player (Fujimoto, 2014) Let with an abuse of notation 2 N denote the power set of all coalitions of the player setN that includes the players in T as a single hypothetical player.…”

Section: Representation Of the The MI K -Value In Terms Of The Shapley Valuementioning

confidence: 99%

Solidarity induced by group contributions: the MI$$^k$$-value for transferable utility games

et al. 2020

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The most popular values in cooperative games with transferable utilities are perhaps the Shapley and the Shapley like values which are based on the notion of players' marginal productivity. The equal division rule on the other hand, is based on egalitarianism where resource is equally divided among players, no matter how productive they are. However none of these values explicitly discuss players' multilateral interactions with peers in deciding to form coalitions and generate worths. In this paper we study the effect of multilateral interactions of a player that accounts for her contributions with her peers not only at an individual level but also on a group level. Based on this idea, we propose a value called the MI k -value and characterize it by the axioms of linearity, anonymity, efficiency and a new axiom: the axiom of MN k -player. An MN kplayer is one whose average marginal contribution due to her multilateral interactions upto level k is zero and can be seen as a generalization of the standard null player axiom of the Shapley value. We have shown that the MI k -value on a variable player set is asymptotically close to the equal division rule. Thus our value realizes solidarity among players by incorporating both their individual and group contributions.

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Section: Representation Of the The MI K -Value In Terms Of The Shapley Valuementioning

confidence: 99%

Solidarity induced by group contributions: the MI$$^k$$-value for transferable utility games

et al. 2020

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“…Moreover, multi-choice games assign zero worth to the lowest level of participation of the players, while bi-cooperative games have the option of assigning negative worth to players (Labreuche and Grabisch 2008). Fujimoto (2014) surveys the recent developments in bi-cooperative games as a special type of non-additive measure. Thus we find in Labreuche and Grabisch (2008) a new bi-cooperative game model (in contrast to Bilbao et al 2008a) that preserves such bipolarity and is not isomorphic to a multi-choice game.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The characteristic function (equivalently bi‐characteristic function; see Fujimoto ) representing the game assigns a value to the positive players that depends on their opponents, the negative players. Network games à la Jackson and Wolinsky () are graph‐restricted cooperative games, where players can generate a value only when they are linked through networks.…”

Section: Introductionmentioning

confidence: 99%

Bi‐cooperative network games: A link‐based allocation rule

Borkotokey

Gogoi

Mukherjee

2018

Int J of Economic Theory

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We study the notion of a bi‐cooperative network game and obtain a link‐based allocation rule for the corresponding class. Unlike classical network games where players have single motive of forming (or not forming) a network, a player under a bi‐cooperative set up has two more variations: all her links attribute exclusively to her positive or negative contributions, or few links are positive while few others are negative. We extend the position value, an important link‐based allocation rule in classical network games, and show that it is the only rule for all the three variations of a bi‐cooperative network game.

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