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.

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 Quantifying Algorithmic Improvements over Time

2018 ◽  
Author(s):  
Lars Kotthoff ◽  
Alexandre Fréchette ◽  
Tomasz Michalak ◽  
Talal Rahwan ◽  
Holger H. Hoos ◽  
...  
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Constraint Programming ◽  
State Of The Art ◽  
The State ◽  
General Idea ◽  
Coalitional Game ◽  
The Shapley Value ◽  
Over Time ◽  
Made In

Assessing the progress made in AI and contributions to the state of the art is of major concern to the community. Recently, Frechette et al. [2016] advocated performing such analysis via the Shapley value, a concept from coalitional game theory. In this paper, we argue that while this general idea is sound, it unfairly penalizes older algorithms that advanced the state of the art when introduced, but were then outperformed by modern counterparts. Driven by this observation, we introduce the temporal Shapley value, a measure that addresses this problem while maintaining the desirable properties of the (classical) Shapley value. We use the tempo- ral Shapley value to analyze the progress made in (i) the different versions of the Quicksort algorithm; (ii) the annual SAT competitions 2007–2014; (iii) an annual competition of Constraint Programming, namely the MiniZinc challenge 2014–2016. Our analysis reveals novel insights into the development made in these important areas of research over time.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

Shapley Ranking of Wines

2012 ◽  
Vol 7 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Victor Ginsburgh ◽  
Israël Zang
Keyword(s):  
Game Theory ◽  
Unique Solution ◽  
Cooperative Game ◽  
Shapley Value ◽  
Rank Order ◽  
Jel Classification ◽  
Ranking Method ◽  
The Shapley Value ◽  
Shapley Values

AbstractWe suggest a new game-theory-based ranking method for wines, in which the Shapley Value of each wine is computed, and wines are ranked according to their Shapley Values. Judges should find it simpler to use, since they are not required to rank order or grade all the wines, but merely to choose the group of those that they find meritorious. Our ranking method is based on the set of reasonable axioms that determine the Shapley Value as the unique solution of an underlying cooperative game. Unlike in the general case, where computing the Shapley Value could be complex, here the Shapley Value and hence the final ranking, are straightforward to compute. (JEL Classification: C71, D71, D78)

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