Difference between the position value and the Myerson value is due to the existence of coalition structures

In game theory agents have the possibility to make binding agreements. The agents are assumed to determine their strategies based on intended but bounded rationality. The field of strategic games provides the possibility to an agent to understand the optimality of his behaviour. In coalition and network games stability, Pareto‐efficiency and fairness of agreements is investigated. The paper shows the relationship between the different fields of game theory in the case of 3 agents. On that basis it shows the ubiquity of time‐inconsistency in dynamic setting due to bounded rationality, deception and environment changes. The paper explains why allocation rules like the Shapley‐based Aumann‐Drèze‐value and the Myerson‐value for coalition structures must be modified in dynamic setting in order to consider the influence of excluded agents, the outside option. An accordingly modified allocation rule is introduced and investigated. It is shown that the “Aumann‐Drèze‐value” and the “Myerson‐value for coalition structures” remains relevant for the case that the switching of the partner is connected with high costs. It is shown through the example of enterprise cooperation in supply chains that low partner switching costs require the introduced allocation rule that considers the outside option. Santrauka Žaidimu teorijoje agentai turi galimybe sudaryti isipareigojančius susitarimus. Agentai, kaip yra mano‐ma, numato savo strategijas riboto racionalumo salygomis. Strateginiu žaidimu sritis sudaro galimybe agentui suvokti optimalios elgsenos krypti. Straipsnyje tyrinejamas ryšys tarp skirtingu žaidimu teo‐rijos sričiu tuo atveju, kai susitarimuose dalyvauja trys agentai. Atskleidžiamas neišvengiamas agentu elgsenos nesuderinamumas del riboto racionalumo, apgavysčiu bei aplinkos pokyčiu. Straipsnyje aiš‐kinama, kad žaidimu teorijos numatomos agentu susitarimu taisykles turetu būti modifikuotos siekiant ivertinti papildomu susitarimu alternatyvu galimybe.

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The Position Value and the Myerson Value for Hypergraph Communication Situations

Static & Dynamic Game Theory: Foundations & Applications - Frontiers of Dynamic Games ◽

10.1007/978-3-319-92988-0_14 ◽

2018 ◽

pp. 237-250

Author(s):

Erfang Shan ◽

Guang Zhang

Keyword(s):

Myerson Value ◽

Position Value ◽

Communication Situations

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Stable Cooperation in a Game with a Major Player

International Game Theory Review ◽

10.1142/s0219198916400053 ◽

2016 ◽

Vol 18 (02) ◽

pp. 1640005 ◽

Cited By ~ 4

Author(s):

Elena Parilina ◽

Artem Sedakov

Keyword(s):

Nash Equilibrium ◽

Cooperative Games ◽

Coalition Structure ◽

Star Graph ◽

Communication Structure ◽

Myerson Value ◽

Coalition Structures ◽

Restricted Cooperation ◽

Major Player ◽

Analytical Expressions

The theory of cooperative games with restricted cooperation has been rapidly developing over the last decades. In our study, we present a special game with restricted cooperation — a game with a major player — a modified version of the landlord game presented in Moulin [1988]. Cooperation of players is supposed to be restricted by a communication structure (a star-graph) as well as a coalition structure. We adopt two well-known cooperative allocations — the Myerson value and the ES-value — to the case when there exist restrictions on the cooperation of players and provide their analytical expressions. Additionally, we examine stability of coalition structures using the concept of the Nash equilibrium and formulate conditions guaranteeing such stability for a given coalition structure.

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ALLOCATION RULES WITH OUTSIDE OPTION IN COOPERATION GAMES WITH TIME‐INCONSISTENCY

Journal of Business Economics and Management ◽

10.3846/jbem.2010.04 ◽

2010 ◽

Vol 11 (1) ◽

pp. 56-96 ◽

Cited By ~ 9

Author(s):

Harald D. Stein

Keyword(s):

Game Theory ◽

Bounded Rationality ◽

Time Inconsistency ◽

Allocation Rule ◽

Network Games ◽

Myerson Value ◽

Allocation Rules ◽

Outside Option ◽

Coalition Structures ◽

Dynamic Setting

In game theory agents have the possibility to make binding agreements. The agents are assumed to determine their strategies based on intended but bounded rationality. The field of strategic games provides the possibility to an agent to understand the optimality of his behaviour. In coalition and network games stability, Pareto‐efficiency and fairness of agreements is investigated. The paper shows the relationship between the different fields of game theory in the case of 3 agents. On that basis it shows the ubiquity of time‐inconsistency in dynamic setting due to bounded rationality, deception and environment changes. The paper explains why allocation rules like the Shapley‐based Aumann‐Drèze‐value and the Myerson‐value for coalition structures must be modified in dynamic setting in order to consider the influence of excluded agents, the outside option. An accordingly modified allocation rule is introduced and investigated. It is shown that the “Aumann‐Drèze‐value” and the “Myerson‐value for coalition structures” remains relevant for the case that the switching of the partner is connected with high costs. It is shown through the example of enterprise cooperation in supply chains that low partner switching costs require the introduced allocation rule that considers the outside option. Santrauka Žaidimu teorijoje agentai turi galimybe sudaryti isipareigojančius susitarimus. Agentai, kaip yra mano‐ma, numato savo strategijas riboto racionalumo salygomis. Strateginiu žaidimu sritis sudaro galimybe agentui suvokti optimalios elgsenos krypti. Straipsnyje tyrinejamas ryšys tarp skirtingu žaidimu teo‐rijos sričiu tuo atveju, kai susitarimuose dalyvauja trys agentai. Atskleidžiamas neišvengiamas agentu elgsenos nesuderinamumas del riboto racionalumo, apgavysčiu bei aplinkos pokyčiu. Straipsnyje aiš‐kinama, kad žaidimu teorijos numatomos agentu susitarimu taisykles turetu būti modifikuotos siekiant ivertinti papildomu susitarimu alternatyvu galimybe.

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LINK MONOTONIC ALLOCATION SCHEMES

International Game Theory Review ◽

10.1142/s021919890500065x ◽

2005 ◽

Vol 07 (04) ◽

pp. 473-489 ◽

Cited By ~ 20

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.

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

Mathematical Problems in Engineering ◽

10.1155/2021/5082947 ◽

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.

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