Méthodes pour jeux en forme extensive avec application au marché des réseaux mobiles

Methods for extensive-form games with application to the telecommunication market

• Auteur / Autrice : Paolo Zappala
• Direction : Francesco De pellegrini
• Type : Projet de thèse
• Discipline(s) : Informatique
• Date : Inscription en doctorat le ; Soutenance le 26/09/2024
• Etablissement(s) : Avignon
• Ecole(s) doctorale(s) : Agrosciences et Sciences
• Partenaire(s) de recherche : Laboratoire : LIA - Laboratoire d'Informatique d'Avignon
• Partenaire(s) de recherche : Equipe de recherche : CORNET - Complex systems, Operation Resarch and NETworking
• Jury : Président / Présidente : Michaël Poss
• Jury : Examinateurs / Examinatrices : Francesco De pellegrini, Stefano Moretti, Stéphane Gaubert, Rosa Figueiredo, Matthieu Chardy, Amal Benhamiche, Margarida Carvalho
• Jury : Rapporteur / Rapporteuse : Stefano Moretti, Stéphane Gaubert

Mots clés

Mots clés libres

Théorie des jeux

Optimisation

Télécommunication

Game theory

Optimisation

Telco

Résumé

La thèse étudie les algorithmes pour la résolution des jeux en forme extensive, avec une application aux marché des télécommunications.

This thesis aims at providing new methods to solve large generic extensive-form games. Extensive-form games are game-theoretical objects that model competitive contexts with two or more agents (partially or fully) observing the actions of their opponents. The solutions of extensive-form games are the Nash equilibria, which represent the foreseeable outcomes of competitive scenarios. The known methods to identify the Nash equilibria of generic extensive-form games are utterly inadequate, because they are inefficient for practical applications and by no means scalable. Indeed, a generic extensive-form game can be solved with the current methods, only if it has fewer than 20 outcomes. It is possible to remark a significant gap in the literature of algorithmic game theory for what concerns games with a generic number of agents and a generic utility function. This thesis introduces new efficient and scalable methods to identify the Nash equilibria of extensive-form games, which can be applied to games having up to thousands of outcomes. Motivation. The interest for extensive-form games comes from a specific application: the analysis of the competition in the telecommunication market. More specifically, mobile network operators invest a significant amount of their budget (in the order of billions euros in France only in investments for the update of their networks. The motivation of this thesis rises especially from the need of models for the optimization of the investments for the newest mobile technology, the 5G. This topic is complex and requires the involvement of different domains of research, namely microeconomics, telecommunication networks, combinatorial optimization and game theory. Faced to the impossibility of covering all these fields, this thesis presents some significant abstractions in the modeling. Eventually, we show how a competition in mobile networks can be rightly modeled with discrete timing games, a specific category of extensive-form games. The innovative character of our research lies in the introduction of new methods for extensive-form games and in the adoption of a large game-theoretical model to approach a competitive context, such as the market of mobile networks. Games of such size have never been applied to the analysis of a competitive market. To make a comparison, a chess player takes actions on a 8x8 board with 16 pieces of her own. Even if the description of chess is concise, the game has more than 10^35 possible outcomes. The simplicity of chess, a zero-sum 2-player game, allows to at least vaguely approximate its optimal strategies. On the other hand, a stakeholder in the market of mobile networks operates on a chessboard having the size of a country, with thousands of assets to be considered. The combinations of strategies available to her are way more than a chess player's, by some orders of magnitude 10^(10^40) possible outcomes. Moreover, the structure of the model is more complex than chess: there are more than 2 stakeholders involved and the market dynamics are more faceted than a zero-sum game. This thesis is a joint work with Orange Innovation and Laboratoire Informatique d'Avignon. Orange is one of the largest telecommunication company in the world. Orange Innovation is the division of Orange dedicated to theoretical and applied research and innovation. Laboratoire Informatique d'Avignon (LIA) is the IT laboratory of Avignon Université.