Partition decision trees: representation for efficient computation of the Shapley value extended to games with externalities

2019 ◽  
Vol 34 (1) ◽  
Author(s):  
Oskar Skibski ◽  
Tomasz P. Michalak ◽  
Yuko Sakurai ◽  
Michael Wooldridge ◽  
Makoto Yokoo
Keyword(s):  
Decision Trees ◽  
Shapley Value ◽  
Efficient Computation ◽  
The Shapley Value ◽  
Games With Externalities

A Note on a Class of Solutions for Games with Externalities Generalizing the Shapley Value

2015 ◽  
Vol 17 (03) ◽  
pp. 1550003 ◽  
Author(s):  
Joss Sánchez-Pérez
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Complete Characterization ◽  
Function Form ◽  
Characterization Result ◽  
The Shapley Value ◽  
Games With Externalities ◽  
Partition Function Form

In this paper we study a family of extensions of the Shapley value for games in partition function form with n players. In particular, we provide a complete characterization for all linear, symmetric, efficient and null solutions in these environments. Finally, we relate our characterization result with other ways to extend the Shapley value in the literature.

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 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.

scholarly journals Efficient Computation and Estimation of the Shapley Value for Traveling Salesman Games

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 129119-129129
Author(s):  
Chaya Levinger ◽  
Noam Hazon ◽  
Amos Azaria
Keyword(s):  
Shapley Value ◽  
Traveling Salesman ◽  
Efficient Computation ◽  
The Shapley Value

scholarly journals Efficient Computation of the Shapley Value for Centrality in Networks

2010 ◽  
pp. 1-13 ◽  
Author(s):  
Karthik V. Aadithya ◽  
Balaraman Ravindran ◽  
Tomasz P. Michalak ◽  
Nicholas R. Jennings
Keyword(s):  
Shapley Value ◽  
Efficient Computation ◽  
The Shapley Value

scholarly journals Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality

2013 ◽  
Vol 46 ◽  
pp. 607-650 ◽  
Author(s):  
T. P. Michalak ◽  
K. V. Aadithya ◽  
P. L. Szczepanski ◽  
B. Ravindran ◽  
N. R. Jennings
Keyword(s):  
Monte Carlo ◽  
Communication Networks ◽  
Shapley Value ◽  
Biological Networks ◽  
Real Life ◽  
Exact Algorithms ◽  
Collaboration Network ◽  
Efficient Computation ◽  
Exact Answer ◽  
The Shapley Value

The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. For instance, in the case of unweighted networks our algorithms are able to return the exact solution about 1600 times faster than the Monte Carlo approximation, even if we allow for a generous 10% error margin for the latter method.

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.

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