Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities

Sedakov, Artem A.

doi:10.3390/math8010038

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…In this section, we establish the relationship between the cores for a class of cooperative two-stage network games studied in [20,21] for a general model and in [22] for their applications in public goods provision and market competition. We will define the characteristic functions in the two-stage cooperative network game according to transformation rule (2) when implementing the cooperative agreement.…”

Section: Two-stage Network Gamesmentioning

confidence: 99%

The Relationship between the Core and the Modified Cores of a Dynamic Game

Sedakov

Sun

2020

Mathematics

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The core as a solution to a cooperative game has the advantage that any imputation from it is undominated. In cooperative dynamic games, there is a known transformation that demonstrates another advantage of the core—time consistency—keeping players adhering to it during the course of the game. Such a transformation may change the solution, so it is essential that the new core share common imputations with the original one. In this paper, we will establish the relationship between the original core of a dynamic game and the core after the transformation, and demonstrate that the latter can be a subset of the former.

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Section: Two-stage Network Gamesmentioning

confidence: 99%

The Relationship between the Core and the Modified Cores of a Dynamic Game

Sedakov

Sun

2020

Mathematics

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“…To determine the importance of a node in a given network, we use centrality or power measures (see [10,11] for a general review of centrality measures). When it comes to problems modeled by a network, it is very common to use some tools inherited from game theory [12,13]. In particular, cooperative game theory has been used as natural approach to represent the power or centrality of nodes in a network (see for example [14,15]), or also the cohesion of a set of nodes [16].…”

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confidence: 99%

A New Edge betweenness Measure Using a Game Theoretical Approach : An Application to Hierarchical Community Detection

Gómez¹,

Castro²,

García-Pardo³

et al. 2021

Preprint

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In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.

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