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J.R. van den Brink

Bio: J.R. van den Brink is an academic researcher. The author has contributed to research in topics: Shapley value & Example of a game without a value. The author has an hindex of 8, co-authored 16 publications receiving 327 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors assume that the players who participate in such a game are part of some permission structure, which means there are players who need permission from one or more other players before they can act or cooperate.

135 citations

Journal ArticleDOI
TL;DR: In this article, an axiomatization of the Shapley value for TU-games using a fairness property is provided. But this property states that if to a game we add another game in which two players are symmetric then their payoffs change by the same amount.
Abstract: In this paper we provide an axiomatization of the Shapley value for TU-games using a fairness property. This property states that if to a game we add another game in which two players are symmetric then their payoffs change by the same amount. We show that the Shapley value is characterized by this fairness property, efficiency and the null player property. These three axioms also characterize the Shapley value on the class of simple games.

105 citations

Posted Content
TL;DR: In this paper, the cardinal ranking of the nodes in a digraph competition is modeled as an allocation problem where the initial weights on the nodes are redistributed on the basis of insights from cooperative game theory.
Abstract: A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph.Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory.After describing the resulting procedure of redistributing the initial weights, we describe an iterative process is described which repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights.Existence and uniqueness of the limit is established for arbitrary digraphs.Applications to the evaluation of e.g. sport competitions and paired comparison experiments are discussed.

26 citations

Journal ArticleDOI
TL;DR: In this article, the cardinal ranking of the nodes in a directed graph is modelled as an allocation problem where the initial weights on the nodes are redistributed on the basis of insights from cooperative game theory.
Abstract: A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.

25 citations


Cited by
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Journal ArticleDOI
TL;DR: The theory and applications of random walks on networks are surveyed, restricting ourselves to simple cases of single and non-adaptive random walkers, and three main types are distinguished: discrete-time random walks, node-centric continuous-timerandom walks, and edge-centric Continuous-Time random walks.
Abstract: Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

397 citations

Journal ArticleDOI
TL;DR: Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures as discussed by the authors, and they are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can extract information about important entities or dense groups of entities in networks.

375 citations

Posted Content
TL;DR: In this paper, it is shown that the Shapley value of these projected games can be interpreted as an index that measures the power of the players in the permission structure, and that the collection of these games forms a subspace of the vector space of all games with side payments on a specified player set.
Abstract: This paper is devoted to the game theoretic analysis of decision situations, in which the players have veto power over the actions undertaken by certain other players. We give a full characterization of the dividends in these games with a permission structure. We find that the collection of these games forms a subspace of the vector space of all games with side payments on a specified player set. Two applications of these results are provided. The first one deals with the projection of additive games on a permission structure. It is shown that the Shapley value of these projected games can be interpreted as an index that measures the power of the players in the permission structure. The second application applies the derived results on games, where the organization structure can be analysed separately from the production capacities of the participating players.

189 citations

Journal Article
TL;DR: In this article, the Shapley value is defined as the expected marginal contribution of a player to a feasible random coalition in a cooperative game, which is a generalization of the permission value of Gilles and van den Brink.
Abstract: Cooperative games are considered where only those coalitions of players are feasible that respect a given precedence structure on the set of players. Strengthening the classical symmetry axiom, we obtain three axioms that give rise to a unique Shapley value in this model. The Shapley value is seen to reflect the expected marginal contribution of a player to a feasible random coalition, which allows us to evaluate the Shapley value nondeterministically. We show that every exact algorithm for the Shapley value requires an exponential number of operations already in the classical case and that even restriction to simple games is #P-hard in general. Furthermore, we outline how the multi-choice cooperative games of Hsiao and Raghavan can be treated in our context, which leads to a Shapley value that does not depend on pre-assigned weights. Finally, the relationship between the Shapley value and the permission value of Gilles, Owen and van den Brink is discussed. Both refer to formally similar models of cooperative games but reflect complementary interpretations of the precedence constraints and thus give rise to fundamentally different solution concepts.

182 citations

Posted Content
TL;DR: A preventive maintenance policy is considered, which is based not only on the information about the age of the installation but also on the content of the subsequent buffer, based on the embedding technique from Markov decision theory.
Abstract: Abstract We consider a deteriorating installation, which supplies input to a subsequent production system. The installation is provided with a buffer to cope with unexpected failures of the installation, which may cause interruptions of the production process. By preventive maintenance on the installation a further improvement of the production process can be obtained. In this paper we consider a preventive maintenance policy, which is based not only on the information about the age of the installation but also on the content of the subsequent buffer. For this integrated maintenance-production problem, we analyse a class of control limit policies which are nearly optimal and easy to implement. The analysis is based on the embedding technique from Markov decision theory. In addition, we provide a characterization of the overall optimal policy and report on numerical comparisons of the best control limit policy with the overall optimal policy and other reference policies.

167 citations