The Position Value and the Myerson Value for Hypergraph Communication Situations

2018 ◽  
pp. 237-250
Author(s):  
Erfang Shan ◽  
Guang Zhang
Keyword(s):  
Myerson Value ◽  
Position Value ◽  
Communication Situations

scholarly journals LINK MONOTONIC ALLOCATION SCHEMES

2005 ◽  
Vol 07 (04) ◽  
pp. 473-489 ◽  
Author(s):  
MARCO SLIKKER
Keyword(s):  
Allocation Scheme ◽  
Myerson Value ◽  
Allocation Rules ◽  
A Value ◽  
Position Value ◽  
Communication Situations ◽  
Fixed Set ◽  
Monotonic Allocation Scheme

A network is a graph where the nodes represent players and the links represent bilateral interaction between the players. A reward game assigns a value to every network on a fixed set of players. An allocation scheme specifies how to distribute the worth of every network among the players. This allocation scheme is link monotonic if extending the network does not decrease the payoff of any player. We characterize the class of reward games that have a link monotonic allocation scheme. Two allocation schemes for reward games are studied, the Myerson allocation scheme and the position allocation scheme, which are both based on allocation rules for communication situations. We introduce two notions of convexity in the setting of reward games and with these notions of convexity we characterize the classes of reward games where the Myerson allocation scheme and the position allocation scheme are link monotonic. As a by-product we find a characterization of the Myerson value and the position value on the class of reward games using potentials.

scholarly journals The Efficient Proportional Myerson Values for Hypergraph Games

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Guangming Wang ◽  
Lei Cai ◽  
Erfang Shan
Keyword(s):  
Numerical Results ◽  
Allocation Rule ◽  
Research Fund ◽  
Myerson Value ◽  
Measure Function ◽  
Axiomatic Characterizations ◽  
Communication Situations

This study deals with a class of efficient extensions of Myerson value for games with hypergraph communication situations in which the surplus is allocated proportionally. We introduce w -fairness of surplus and provide axiomatic characterizations of the new allocation rule. Furthermore, we give an example of research fund distribution amongst researchers, compare the numerical results with several values, and realize other efficient extensions of Myerson value can be obtained depending on the different measure function w on the hypergraph.

A Unified Approach To The Myerson Value And The Position Value

2004 ◽  
Vol 56 (1-2) ◽  
pp. 63-76 ◽  
Author(s):  
Daniel Gómez ◽  
Enrique González-Arangüena ◽  
Conrado Manuel ◽  
Guillermo Owen ◽  
Monica Del Pozo
Keyword(s):  
Unified Approach ◽  
Myerson Value ◽  
Position Value

scholarly journals A Decomposability Property to the Weighted Myerson Value and the Weighted Position Value

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Guangming Wang ◽  
Erfang Shan
Keyword(s):  
Cooperative Game ◽  
Graph Structure ◽  
Myerson Value ◽  
Position Value

Myerson value and position value are important values in a cooperative game with a graph structure. Usually, due to the differences of players in the game, the weighted Myerson value and weighted position value are more widely used in practical situations. This article offers a new calculation approach of the weighted Myerson value and weighted position value. Instead of using induced games (point game and edge game), we prove that the weighted Myerson value and weighted position value meet decomposability property.

On the position value for communication situations with fuzzy coalition

2017 ◽  
Vol 33 (1) ◽  
pp. 113-124 ◽  
Author(s):  
Xianghui Li ◽  
Hao Sun ◽  
Dongshuang Hou
Keyword(s):  
Position Value ◽  
Communication Situations

A Unified Approach to the Myerson Value and the Position Value

2004 ◽  
pp. 63-76
Author(s):  
Daniel Gómez ◽  
Enrique González-Arangüena ◽  
Conrado Manuel ◽  
Guillermo Owen ◽  
Monica del Pozo
Keyword(s):  
Unified Approach ◽  
Myerson Value ◽  
Position Value
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