scholarly journals Efficient Computation of Semivalues for Game-Theoretic Network Centrality

2018 ◽  
Vol 63 ◽  
pp. 145-189 ◽  
Author(s):  
Mateusz K. Tarkowski ◽  
Piotr L. Szczepański ◽  
Tomasz P. Michalak ◽  
Paul Harrenstein ◽  
Michael Wooldridge
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Centrality Measures ◽  
Efficient Computation ◽  
Solution Concepts ◽  
Banzhaf Index ◽  
The Shapley Value ◽  
Game Theoretic ◽  
Theoretic Solution ◽  
Network Centralities

Some game-theoretic solution concepts such as the Shapley value and the Banzhaf index have recently gained popularity as measures of node centrality in networks. While this direction of research is promising, the computational problems that surround it are challenging and have largely been left open. To date there are only a few positive results in the literature, which show that some game-theoretic extensions of degree-, closeness- and betweenness-centrality measures are computable in polynomial time, i.e., without the need to enumerate the exponential number of all possible coalitions. In this article, we show that these results can be extended to a much larger class of centrality measures that are based on a family of solution concepts known as semivalues. The family of semivalues includes, among others, the Shapley value and the Banzhaf index. To this end, we present a generic framework for defining game-theoretic network centralities and prove that all centrality measures that can be expressed in this framework are computable in polynomial time. Using our framework, we present a number of new and polynomial-time computable game-theoretic centrality measures.

scholarly journals Game-theoretic Vocabulary Selection via the Shapley Value and Banzhaf Index

2021 ◽  
Author(s):  
Roma Patel ◽  
Marta Garnelo ◽  
Ian Gemp ◽  
Chris Dyer ◽  
Yoram Bachrach
Keyword(s):  
Shapley Value ◽  
Banzhaf Index ◽  
The Shapley Value ◽  
Game Theoretic

scholarly journals The Tractability of the Shapley Value over Bounded Treewidth Matching Games

2017 ◽  
Author(s):  
Gianluigi Greco ◽  
Francesco Lupia ◽  
Francesco Scarcello
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Open Problem ◽  
Positive Answer ◽  
Coalitional Games ◽  
Solution Concepts ◽  
Bounded Treewidth ◽  
The Shapley Value ◽  
Matching Games

Matching games form a class of coalitional games that attracted much attention in the literature. Indeed, several results are known about the complexity of computing over them {solution concepts}. In particular, it is known that computing the Shapley value is intractable in general, formally #P-hard, and feasible in polynomial time over games defined on trees. In fact, it was an open problem whether or not this tractability result holds over classes of graphs properly including acyclic ones. The main contribution of the paper is to provide a positive answer to this question, by showing that the Shapley value is tractable for matching games defined over graphs having bounded treewidth. The proposed technique has been implemented and tested on classes of graphs having different sizes and treewidth at most three.

scholarly journals Vitality Indices are Equivalent to Induced Game-Theoretic Centralities

2021 ◽  
Author(s):  
Oskar Skibski
Keyword(s):  
Game Theory ◽  
Theoretical Analysis ◽  
Shapley Value ◽  
Centrality Measures ◽  
Coalitional Game ◽  
The Shapley Value ◽  
Balanced Contributions ◽  
Game Theoretic ◽  
The Impact ◽  
Coalitional Game Theory

Vitality indices form a class of centrality measures that assess the importance of a node based on the impact its removal has on the network. To date, theoretical analysis of this class is lacking. In this paper, we show that vitality indices can be characterized using the axiom of Balanced Contributions proposed by Myerson in the coalitional game theory literature. We explore the link between both fields and show an equivalence between vitality indices and induced game theoretic centralities based on the Shapley value. Our characterization allows us to easily determine which known centrality measures are vitality indices.

DON and Shapley Value for Allocation among Cooperating Agents in a Network: Conditions for Equivalence

2017 ◽  
Vol 5 (2) ◽  
pp. 143-161 ◽  
Author(s):  
Sridhar Mandyam ◽  
Usha Sridhar
Keyword(s):  
Social Welfare ◽  
Shapley Value ◽  
Centrality Measures ◽  
Pareto Optimal ◽  
Undirected Network ◽  
Social Welfare Maximization ◽  
Optimal Allocations ◽  
Game Theoretic ◽  
Cooperating Agents ◽  
Pareto Optimal Allocations

In a paper appearing in a recent issue of this journal ( Studies in Microeconomics), the authors explored a new method to allocate a divisible resource efficiently among cooperating agents located at the vertices of a connected undirected network. It was shown in that article that maximizing social welfare of the agents produces Pareto optimal allocations, referred to as dominance over neighbourhood (DON), capturing the notion of dominance over neighbourhood in terms of network degree. In this article, we show that the allocation suggested by the method competes well with current cooperative game-theoretic power centrality measures. We discuss the conditions under which DON turns exactly equivalent to a recent ‘fringe-based’ Shapley Value formulation for fixed networks, raising the possibility of such solutions being both Pareto optimal in a utilitarian social welfare maximization sense as well as fair in the Shapley value sense.

The Heuristic Use of Game Theory: Insights for Conflict Resolution

2007 ◽  
Vol 3 (2) ◽  
Author(s):  
Ben D. Mor
Keyword(s):  
Game Theory ◽  
Conflict Resolution ◽  
Bargaining Game ◽  
Solution Concepts ◽  
Negotiated Settlement ◽  
Protracted Conflict ◽  
History Of ◽  
Game Theoretic ◽  
Three Stages ◽  
Theoretic Solution

This article illustrates the heuristic use of game theory by applying it to the analysis of conflict resolution. To this end, we will proceed in three stages. First, we will define a generic bargaining game, which confronts two states that share a history of protracted conflict. Second, we will then introduce a gradual and controlled change in the preferences of the two states for the outcomes that are generated by the bargaining game. Third, for the game series that will be produced, we will apply alternative game-theoretic solution concepts and examine the expected implications of different information conditions. That is, we will establish by means of the theory what the states are expected to do in response to the induced change in their own preferences, in those of the opponent—and in their perception of each other. By modifying these parameters, we will be able to analyze the obstacles that are expected to arise in the peacemaking process and the conditions that are required to attain and stabilize a negotiated settlement.

scholarly journals Complexity of Computing the Shapley Value in Games with Externalities

2020 ◽  
Vol 34 (02) ◽  
pp. 2244-2251 ◽  
Author(s):  
Oskar Skibski
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Marginal Contribution ◽  
The Shapley Value ◽  
Games With Externalities ◽  
Computational Properties

We study the complexity of computing the Shapley value in games with externalities. We focus on two representations based on marginal contribution nets (embedded MC-nets and weighted MC-nets) and five extensions of the Shapley value to games with externalities. Our results show that while weighted MC-nets are more concise than embedded MC-nets, they have slightly worse computational properties when it comes to computing the Shapley value: two out of five extensions can be computed in polynomial time for embedded MC-nets and only one for weighted MC-nets.

Sign in / Sign up

Export Citation Format

Share Document