Implementation and Computation of a Value for Generalized Characteristic Function Games

Michalak, Tomasz P.; Szczepański, Piotr L.; Rahwan, Talal; Chrobak, Agata; Brânzei, Simina; Wooldridge, Michael; Jennings, Nicholas R.

doi:10.1145/2665007

Cited by 6 publications

(1 citation statement)

References 45 publications

(57 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The contribution presented in this chapter is threefold, it formally proves that computing the Shapley value in connectivity games in NP-hard, it develops faster exact algorithm for connectivity games, and it develops one approximation algorithm for these family of games. -The final Chapter 8 is based on the second part of the publication Implementation and Computation of a Value for Generalized Characteristic Function Games [Michalak, Szczepański, Rahwan, Chrobak, Brânzei, Wooldridge, and Jennings, 2014] published in journal ACM Transactions on Economics and Computation (ACM TEAC). The technical content in the whole chapter is an exclusive contribution of the author.…”

Section: Publications and Author's Contributionmentioning

confidence: 99%

Fast Algorithms for Game-Theoretic Centrality Measures

Szczepański¹

2015

Preprint

View full text Add to dashboard Cite

In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each coalition of nodes is determined by certain graph properties. Next, the centrality of any individual node is determined by a chosen game-theoretic solution concept (notably, the Shapley value) in the same way as the payoff of a player in a cooperative game. On one hand, the advantage of game-theoretic centrality measures is that nodes are ranked not only according to their individual roles but also according to how they contribute to the role played by all possible subsets of nodes. On the other hand, the disadvantage is that the game-theoretic solution concepts are typically computationally challenging. The main contribution of this dissertation is that we show that a wide variety of game-theoretic solution concepts on networks can be computed in polynomial time.Our focus is on centralities based on the Shapley value and its various extensions, such as the Semivalues and Coalitional Semivalues. Furthermore, we prove #P-hardness of computing the Shapley value in connectivity games and propose an algorithm to compute it. Finally, we analyse computational properties of generalized version of cooperative games in which order of player matters. We propose a new representation for such games, called generalized marginal contribution networks, that allows for polynomial computation in the size of the representation of two dedicated extensions of the Shapley value to this class of games.

show abstract

Section: Publications and Author's Contributionmentioning

confidence: 99%

Fast Algorithms for Game-Theoretic Centrality Measures

Szczepański¹

2015

Preprint

View full text Add to dashboard Cite

show abstract

A Simple Mechanism for the Disaster Emergency Unit Scheduling Problem

Araya-Córdova

Vásquez

2017

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Measuring players’ importance in basketball using the generalized Shapley value

Metulini

Gnecco

2022

Ann Oper Res

View full text Add to dashboard Cite

Measuring players’ importance in team sports to help coaches and staff with the aim of winning the game is gaining relevance, mainly because of the advent of new data and advanced technologies. In this paper we evaluate each player’s importance - for the first time in basketball - as his/her average marginal contribution to the utility of an ordered subset of players, through a generalized version of the Shapley value, where the value assumed by the generalized characteristic function of the generalized coalitional game is expressed in terms of the probability a certain lineup has to win the game. In turn, such probability is estimated by applying a logistic regression model in which the response is represented by the game outcome and the Dean’s factors are used as explanatory features. Then, we estimate the generalized Shapley values of the players, with associated bootstrap confidence intervals. A novelty, allowed by explicitly considering single lineups, is represented by the possibility of forming best lineups based on players’ estimated generalized Shapley values conditional on specific constraints, such as an injury or an “a-priori” coach’s decision. A comparison of our proposed approach with industry-standard counterparts shows a strong linear relation. We show the application of our proposed method to seventeen full NBA seasons (from 2004/2005 to 2020/21). We eventually estimate generalized Shapley values for Utah Jazz players and we show how our method is allowed to be used to form best lineups.

show abstract

Implementation and Computation of a Value for Generalized Characteristic Function Games

Cited by 6 publications

References 45 publications

Fast Algorithms for Game-Theoretic Centrality Measures

Fast Algorithms for Game-Theoretic Centrality Measures

A Simple Mechanism for the Disaster Emergency Unit Scheduling Problem

Measuring players’ importance in basketball using the generalized Shapley value

Contact Info

Product

Resources

About