University Sétif 1 FERHAT ABBAS Faculty of Sciences
Détail de l'auteur
Auteur Abderrahmane Ziad |
Documents disponibles écrits par cet auteur
Ajouter le résultat dans votre panier Affiner la recherche
Titre : Congestion games and applications, nash equilibrium and anarchy price Type de document : document électronique Auteurs : Fatima KHANCHOUCHE, Auteur ; Abderrahmane Ziad, Directeur de thèse Editeur : Setif:UFA Année de publication : 2026 Importance : 1 vol (107 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Singleton congestion games
Classical Nash equilibrium
Strong Nash equilibrium
Price of Anarchy
Price of StabilityIndex. décimale : 510 - Mathématique Résumé :
This thesis examines singleton congestion games in the non-symmetric case. We proposed simplified analytical formulations that allow for an accurate description of the possible sets of equilibria, including the classical Nash equilibrium and the strong Nash equilibrium in the case of two resources. Furthermore, we developed a general methodology for computing the Nash equilibrium in the general case, supported by practical and efficient algorithms. These algorithms enabled the evaluation of the proposed solutions’ performance and the calculation of the difference between the Price of Anarchy and the Price of Stability, thereby highlighting the theoretical and practical value of this work.Note de contenu :
Sommaire
List ofFigures3
List ofTables4
List ofAcronyms5
1 Definitionsandnotations13
1.1 Non-cooperativegame......................... 15
1.1.1 Nashequilibriuminnon-cooperativegames.......... 16
1.1.2 Paretooptimuminnon-cooperativegames.......... 21
1.1.3 StrongNashequilibriuminnon-cooperativegames..... 22
1.2 Congestiongames............................ 24
1.2.1 Standardcongestiongames................... 25
1.2.2 Congestiongameswithspecificpaymentfunctions..... 26
1.2.3 Singletoncongestiongames.................. 30
1.3 potentialgames............................. 31
1.3.1 Exactpotentialgames..................... 31
1.3.2 Weightedpotentialfunction.................. 33
1.3.3 Ordinalpotentialfunction................... 34
1.3.4 Generalizedordinalpotentialfunction............. 35
1.4 Improvementpath........................... 36
1.5 Conclusion................................ 37
2 Nashequilibriuminsingletoncongestiongames38
2.1 Introduction............................... 38
2.2 Singletoncongestiongames....................... 39
2.3 Nashequilibriuminnon-symmetricgames.............. 41
2.3.1 Caseoftwostrategies...................... 42
2.3.2 Gameswithoutthefiniteimprovementproperty....... 42
2.4 Priceofanarchyandpriceofstability................. 43
2.4.1 Priceofanarchy......................... 44
2.4.2 Priceofstability........................ 45
2.5 Results:NovelproofsandcharacterizationofNashequilibria... 46
2.5.1 Thecaseoftworessources(m = (r1, r2)) ........... 46
2.6 Numericalexperiments......................... 54
2.7 Conclusion................................ 62
3 Computation ofNashequilibriumincongestiongamewithplayer
specificpayofffunctions63
3.1 Introduction............................... 63
3.2 Congestiongamewithexactpartition................. 64
3.2.1 Nash Equilibriumincongestiongameswithpreciseresource
allocation............................ 67
3.3 Nash Equilibriumincongestiongameswithimpreciseresourceallo-
cation .................................. 67
3.3.1 Existence ofNashequilibiriuminsingletoncongestiongame
with exactnon-partition.................... 70
3.4 Theresults:descriptionofNashequilibria.............. 72
3.5 Numericalexperiments......................... 81
3.6 Conclusion............................... 83
4 StrongNashequilibriuminsingletoncongestiongames84
4.1 Introduction............................... 84
4.2 Singletoncongestiongameswithplayernon-specificpayofffunctions 85
4.2.1 Existence ofSNEinsingletoncongestiongamewithplayer
non-specificpayofffunction.................. 86
4.3 The results:computationofstrongNashequilibriuminsingleton
congestion gameswithplayerspecificpayofffunction........ 88
4.4 Numericalexperiments......................... 92
4.5 Conclusion................................ 98
Bibliography102Côte titre : DM/0224 Congestion games and applications, nash equilibrium and anarchy price [document électronique] / Fatima KHANCHOUCHE, Auteur ; Abderrahmane Ziad, Directeur de thèse . - [S.l.] : Setif:UFA, 2026 . - 1 vol (107 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Singleton congestion games
Classical Nash equilibrium
Strong Nash equilibrium
Price of Anarchy
Price of StabilityIndex. décimale : 510 - Mathématique Résumé :
This thesis examines singleton congestion games in the non-symmetric case. We proposed simplified analytical formulations that allow for an accurate description of the possible sets of equilibria, including the classical Nash equilibrium and the strong Nash equilibrium in the case of two resources. Furthermore, we developed a general methodology for computing the Nash equilibrium in the general case, supported by practical and efficient algorithms. These algorithms enabled the evaluation of the proposed solutions’ performance and the calculation of the difference between the Price of Anarchy and the Price of Stability, thereby highlighting the theoretical and practical value of this work.Note de contenu :
Sommaire
List ofFigures3
List ofTables4
List ofAcronyms5
1 Definitionsandnotations13
1.1 Non-cooperativegame......................... 15
1.1.1 Nashequilibriuminnon-cooperativegames.......... 16
1.1.2 Paretooptimuminnon-cooperativegames.......... 21
1.1.3 StrongNashequilibriuminnon-cooperativegames..... 22
1.2 Congestiongames............................ 24
1.2.1 Standardcongestiongames................... 25
1.2.2 Congestiongameswithspecificpaymentfunctions..... 26
1.2.3 Singletoncongestiongames.................. 30
1.3 potentialgames............................. 31
1.3.1 Exactpotentialgames..................... 31
1.3.2 Weightedpotentialfunction.................. 33
1.3.3 Ordinalpotentialfunction................... 34
1.3.4 Generalizedordinalpotentialfunction............. 35
1.4 Improvementpath........................... 36
1.5 Conclusion................................ 37
2 Nashequilibriuminsingletoncongestiongames38
2.1 Introduction............................... 38
2.2 Singletoncongestiongames....................... 39
2.3 Nashequilibriuminnon-symmetricgames.............. 41
2.3.1 Caseoftwostrategies...................... 42
2.3.2 Gameswithoutthefiniteimprovementproperty....... 42
2.4 Priceofanarchyandpriceofstability................. 43
2.4.1 Priceofanarchy......................... 44
2.4.2 Priceofstability........................ 45
2.5 Results:NovelproofsandcharacterizationofNashequilibria... 46
2.5.1 Thecaseoftworessources(m = (r1, r2)) ........... 46
2.6 Numericalexperiments......................... 54
2.7 Conclusion................................ 62
3 Computation ofNashequilibriumincongestiongamewithplayer
specificpayofffunctions63
3.1 Introduction............................... 63
3.2 Congestiongamewithexactpartition................. 64
3.2.1 Nash Equilibriumincongestiongameswithpreciseresource
allocation............................ 67
3.3 Nash Equilibriumincongestiongameswithimpreciseresourceallo-
cation .................................. 67
3.3.1 Existence ofNashequilibiriuminsingletoncongestiongame
with exactnon-partition.................... 70
3.4 Theresults:descriptionofNashequilibria.............. 72
3.5 Numericalexperiments......................... 81
3.6 Conclusion............................... 83
4 StrongNashequilibriuminsingletoncongestiongames84
4.1 Introduction............................... 84
4.2 Singletoncongestiongameswithplayernon-specificpayofffunctions 85
4.2.1 Existence ofSNEinsingletoncongestiongamewithplayer
non-specificpayofffunction.................. 86
4.3 The results:computationofstrongNashequilibriuminsingleton
congestion gameswithplayerspecificpayofffunction........ 88
4.4 Numericalexperiments......................... 92
4.5 Conclusion................................ 98
Bibliography102Côte titre : DM/0224 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité DM/0224 DM/0224 Thèse Bibliothèque des sciences Anglais Disponible
Disponible
