The balanced contributions property for equal contributors

Yokote, Koji; Kongo, Takumi; Funaki, Yukihiko

doi:10.1016/j.geb.2017.08.007

Cited by 21 publications

(14 citation statements)

References 22 publications

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“…Figure 4 depicts the fairness comparison among mobile devices in each relay operator. It is also estimated based on the J index in equation (15). As can be seen, the fairness among mobile devices is very similar to the performance trend in Figure 3.…”

Section: Simulation Results and Discussionmentioning

confidence: 56%

“…. . , a n is the set of players and v is the characteristic function, which assigns a real number v(C) to every coalition C ∈ N where N is the set of nonempty subsets of N. A transferable utility game is a pair (C, v) consisting of a set of players C, and a coalition ) and S ⊆ C, S ≠ ∅ , let (S, v) denote the game in which the domain of v is restricted from 2 C to 2 S , and the ESh r of a i is ESh r a i [15].…”

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confidence: 99%

“…e solution of ESh r assigns a payoff vector ESh r a i ∈C (C, v) ∈ R to each game (C, v). To define ESh r , the idea of rescaling the worth of coalitions is necessary [15]. Let L denote the set of finite sequences of real numbers:…”

mentioning

confidence: 99%

“…In the game v r , the worth of each coalition is rescaled by multiplying the s th entry of the sequence vector r, where s is the size of coalition S. is type of rescaling is often discussed in the context of the per-capita measure or discounting; v r can be interpreted as generalizing these ideas by allowing for any sequence of real numbers [15]. Finally, the ESh r is defined as follows:…”

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confidence: 99%

“…According to X r S,C and Y r S,a i , the original Shapley value is obtained based on the v r game [7,16]. erefore, we Mobile Information Systems can interpret ESh r a i as (i) the worth of coalitions are rescaled based on the sequence vector r, (ii) an imaginary v r game is constructed, (iii) the Shapley value idea is applied to the v r game, and (iv) the gap between the v(C) and v r (C) is equally divided among players [15].…”

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confidence: 99%

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A New Cooperative Dual-Level Game Approach for Operator-Controlled Multihop D2D Communications

Kim

2019

Mobile Information Systems

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With the development of wireless communications and the intellectualization of mobile devices, device-to-device (D2D) communications are considered as a standard part of future 5G networks. This new paradigm can provide better user experiences while improving the system performance such as network throughput, latency, fairness, and energy efficiency. In this study, we investigate a new dual-level D2D communication scheme consisting of multiple D2D operators and a group of mobile devices. To model the interaction among D2D operators and devices, we adopt two cooperative game approaches based on the incentive mechanism design and r-egalitarian Shapley value. At the upper level, routing paths and incentive payments for multihop relay services are decided using the incentive mechanism. At the lower level, mobile devices share the given incentive based on the r-egalitarian Shapley value. Both level control procedures are mutually dependent on each other by the proper coordination and collaboration. According to the main features of two cooperative game models, the proposed scheme takes various benefits in a fair-efficient way. Through the derived simulation results, we can verify the superiority of our proposed scheme comparing to the existing protocols. Finally, we propose further challenges and future opportunities in the research area of operator-controlled multihop D2D communications.

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Section: Simulation Results and Discussionmentioning

confidence: 56%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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A New Cooperative Dual-Level Game Approach for Operator-Controlled Multihop D2D Communications

Kim

2019

Mobile Information Systems

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Relationally equal treatment of equals and affine combinations of values for TU games

2019

Self Cite

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We axiomatize the set of affine combinations between the Shapley value, the equal surplus division value, and the equal division value in cooperative games with transferable utilities. The set is characterized by efficiency, linearity, the balanced contributions property for equal contributors and outsiders, and the differential null player out property. The balanced contributions property for equal contributors and outsiders requires the balance of contributions between two players who contribute the same amount to the grand coalition and whose singleton coalitions earn the same worth. The differential null player out property requires that an elimination of a null player affects the other players identically. These two relational axioms are obtained by investigating Myerson's (Int J Game Theory 9:169-182, 1980) balanced contributions property and Derks and Haller's (Int Game Theory Rev 1:301-314, 1999) null player out property, respectively, from the perspective of a principle of Aristotle's distributive justice, whereby "equals should be treated equally". JEL Classification D63 • C71B Takumi Kongo

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Core stability of the Shapley value for cooperative games

Abe

Nakada

2022

Soc Choice Welf

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The balanced contributions property for equal contributors

Cited by 21 publications

References 22 publications

A New Cooperative Dual-Level Game Approach for Operator-Controlled Multihop D2D Communications

A New Cooperative Dual-Level Game Approach for Operator-Controlled Multihop D2D Communications

Relationally equal treatment of equals and affine combinations of values for TU games

Core stability of the Shapley value for cooperative games

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