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Theses

Nonatomic strategic games and network applications

Thomas Boulogne 1
1 C&O - Equipe combinatoire et optimisation
IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche
Abstract : This thesis has two parts: the first is about nonatomic strategic games, and the second is about applications of game theory to telecommunication networks. In the first part, the models of Schmeidler (1973) and of Mas-Colell (1984) of nonatomic games are described and compared. It is then shown that these models are good approximations of games having a large number of players in which the influence of each player on the other players is vanishing. An extension and some variations of Mas-Colell's model are presented in order to obtain a unifying framework for various applications of non-atomic games, such as routing games, crowding games and evolutionary games. These three types of game are analyzed in detail. Finally, the evolutionarily stable strategy is extended to Schmeidler's model, which yields an equilibrium refinement. The second part of the thesis deals with routing in networks. Some situations in which a network is shared by two types of user are considered: some users have an influence on the state of the network while others do not. The convergence of best-reply dynamics is then studied in networks that have a simple topology. Finally, multipoint-to-multipoint routing is modelled.
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https://tel.archives-ouvertes.fr/tel-00008759
Contributor : Thomas Boulogne <>
Submitted on : Friday, March 11, 2005 - 5:00:39 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:39 PM
Long-term archiving on: : Friday, September 14, 2012 - 11:55:46 AM

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  • HAL Id : tel-00008759, version 1

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Thomas Boulogne. Nonatomic strategic games and network applications. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2004. English. ⟨tel-00008759⟩

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