Shapley-Based Analysis of the Leadership Formation in Social Networks

2019 ◽  
pp. 357-390
Author(s):  
Ivan Belik
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Real Life ◽  
Importance Measure ◽  
Theory Theory ◽  
Leadership Position ◽  
Leadership Formation ◽  
Game Theoretic ◽  
As Graph ◽  
Research Domains

The dynamic nature of networks formation requires the development of multidisciplinary methods for the effective social network analysis. The research presented in this chapter is motivated by the necessity to overcome the limitation of using analytical methods from the originally disconnected research domains. Hence, the authors present an approach based on techniques from different areas, such as graph theory, theory of algorithms, and game theory. Specifically, this chapter is based on the analysis of how an agent can move towards leadership in real-life socioeconomic networks. For the agent's importance measure, the authors employed a Shapley value concept from the area of cooperative games. Shapley value is interpreted as the node centrality that corresponds to the significance of the agent within a socioeconomic network. Employing game theoretic concept, the authors introduced an algorithmic approach that detects the potential connectivity modifications required to increase an agent's leadership position.

APPLICATIONS OF GAME THEORY TO ECONOMIC EQUILIBRIUM

1999 ◽  
Vol 01 (01) ◽  
pp. 1-8 ◽  
Author(s):  
GUILLERMO OWEN
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Cooperative Games ◽  
Competitive Equilibrium ◽  
Random Variable ◽  
Market Games ◽  
The Core ◽  
Thin Markets ◽  
Shapley Values ◽  
Game Theoretic

One of the original expectations for the theory of cooperative games was that it would give us results valid for thin markets (where the number of traders is too small for an equilibrium to be reached). Over a period of years, however, it has been shown that, for market games, both the core and the Shapley values converge, in some sense, to the competitive equilibrium. Thus, the feeling arises that for large market games, the game-theoretic concepts yield nothing other than the equilibrium. In this article, we study the question of convergence of the Shapley value to the equilibrium and show that in some cases the convergence can be extremely slow. A very simple example (the "shoe" game) suggests that replacing the value by the equilibrium is in some sense akin to replacing a random variable by its mean.

Importance measures for degrading components based on cooperative game theory

2019 ◽  
Vol 37 (2) ◽  
pp. 189-206
Author(s):  
Yingsai Cao ◽  
Sifeng Liu ◽  
Zhigeng Fang
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
System Reliability ◽  
Design Methodology ◽  
System Structure ◽  
Importance Measure ◽  
Engineering Systems ◽  
Content Type ◽  
Timely Feedback ◽  
Degradation Models

Purpose The purpose of this paper is to propose new importance measures for degrading components based on Shapley value, which can provide answers about how important players are to the whole cooperative game and what payoff each player can reasonably expect. Design/methodology/approach The proposed importance measure characterizes how a specific degrading component contributes to the degradation of system reliability by using Shapley value. Degradation models are also introduced to assess the reliability of degrading components. The reliability of system consisting independent degrading components is obtained by using structure functions, while reliability of system comprising correlated degrading components is evaluated with a multivariate distribution. Findings The ranking of degrading components according to the newly developed importance measure depends on the degradation parameters of components, system structure and parameters characterizing the association of components. Originality/value Considering the fact that reliability degradation of engineering systems and equipment are often attributed to the degradation of a particular or set of components that are characterized by degrading features. This paper proposes new importance measures for degrading components based on Shapley value to reflect the responsibility of each degrading component for the deterioration of system reliability. The results are also able to give timely feedback of the expected contribution of each degrading component to system reliability degradation.

scholarly journals A Game Theoretic Model of Choosing a Valuable Good via a Short List Heuristic

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 199 ◽  
Author(s):  
David M. Ramsey
Keyword(s):  
Real Life ◽  
Decision Makers ◽  
The Internet ◽  
Theoretic Model ◽  
Final Decision ◽  
Search Procedure ◽  
Short List ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
High Level

The Internet gives access to a huge amount of data at the click of a mouse. This is very helpful when consumers are making decisions about which product to buy. However, the final decision to purchase is still generally made by humans who have limited memory and perception. The short list heuristic is often used when there are many offers on the market. Searchers first find information about offers via the Internet and on this basis choose a relatively small number of offers to view in real life. Although such rules are often used in practice, little research has been carried out on determining, for example, what the size of the short list should be depending on the parameters of the problem or modelling how the short list heuristic can be implemented when there are multiple decision makers. This article presents a game theoretic model of such a search procedure with two players. These two players can be interpreted, for example, as a couple searching for a flat or a second-hand car. The model indicates that under such a search procedure the roles of searchers should only be divided when the preferences of the players are coherent or there is a high level of goodwill between them. In other cases, dividing the roles leads to a high level of conflict.

STABLE COOPERATION UNDER ENVIRONMENTAL CONSTRAINTS

2010 ◽  
Vol 12 (04) ◽  
pp. 453-470 ◽  
Author(s):  
NADEZHDA KOZLOVSKAYA ◽  
NIKOLAY ZENKEVICH
Keyword(s):  
Shapley Value ◽  
Stable Distribution ◽  
Theoretic Model ◽  
Cooperative Solution ◽  
Irrational Behavior ◽  
Game Theoretic ◽  
The Common ◽  
Game Theoretic Model ◽  
Cooperative Differential Game ◽  
Total Stock

A game-theoretic model of territorial environmental production under Cournot competition is studied. The process is modeled as cooperative differential game. The stable distribution mechanism of the common cooperative benefit among players is proposed. We proved that the cooperative total stock of accumulated pollution is strictly less then the pollution under Nash equilibrium for the whole duration of the game. We design a stable Shapley value as a cooperative solution, which is time-consistent. The Shapley value is also strategic stable and satisfies the irrational-behavior-proofness condition. The numerical example is given.

scholarly journals Game-Theoretic Principles of Decision Management Modeling Under the Coopetition

2020 ◽  
pp. 2050010
Author(s):  
Iryna Heiets ◽  
Tamara Oleshko ◽  
Oleg Leshchinsky
Keyword(s):  
Infinite Number ◽  
Cooperative Games ◽  
Characteristic Functions ◽  
Optimal Distribution ◽  
Collective Rationality ◽  
Decision Management ◽  
Game Theoretic ◽  
The Individual ◽  
Additional Income

The paper considers the two main game-theoretic models, such as coalition and cooperative. The authors are of the opinion that definitions and notions of cooperative games and coalition games are different, but both games are coopetitive games. Transitivity and superadditivity are presented as the main characteristic functions of coopetitive games. The individual and collective rationality were identified as unconditional requirements for the optimal distribution between players. Furthermore, the additional income added to the guaranteed amount occurs in the event of coopetition. Any substantial coopetitive game has an infinite number of transactions. The authors highlighted that the dominant transaction is the transaction that is better for all coalition numbers without exceptions and it can be reached by the coalition. In addition, the authors propose using Shapley system of axioms to identify coopetitive game results.

AN AXIOM SYSTEM FOR A VALUE FOR GAMES IN PARTITION FUNCTION FORM

2005 ◽  
Vol 07 (01) ◽  
pp. 63-72 ◽  
Author(s):  
M. J. ALBIZURI ◽  
J. ARIN ◽  
J. RUBIO
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Cooperative Games ◽  
Axiom System ◽  
Axiomatic Characterization ◽  
Transferable Utility ◽  
Function Form ◽  
A Value ◽  
The Shapley Value ◽  
Partition Function Form

Lucas and Trall (1963) defined the games in partition function form as a generalization of the cooperative games with transferable utility. In our work we propose by means of an axiomatic characterization a solution for such games in partition function form. This solution will be a generalization of the Shapley value (1953).

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