Coalitions interrelations and coevolutions

One of the fundamental objectives of game theory is to study equilibrium and stability points embodying situations from which no deviation is optimal for players. Since the early development of the theory, a major concern has been to develop formalisms where agents are able to cooperate and form groups among them. In this respect, network and coalition theories have developed new stability and equilibrium notions in the realm of non-cooperative game theory using graphs and sets. This thesis enriches these theories by proposing stability concepts suited to analyse models where agents can form coalitions of different types.
The first part of this thesis examines an applied framework where firms can cooperate in R&D and form collusive agreements to share the markets among them. To understand the interrelations between these two types of cooperation, the concept of stable pairs of coalition structures is introduced. Taken independently, no R&D structure is stable. Nonetheless, when collusion is allowed in the model, stable pairs of structures emerge.
In the second chapter, the stability concept of Δ-stable pairs of coalition structures is considered to analyse models on contests. With this notion, the alteration of one structure can modify the topology of the other. Δ-stable pairs of structures that are not stable, as defined in the first part, are found.
For each of these stability concepts, the agents could only be part of one coalition of a given type. The third chapter relaxes this assumption by formalising coalitions as edges of a hypergraph. The concept of setwise stability is introduced and its existence is established when agents can form edges from one or two types of hypergraphs.


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Gegevens


Uitgever
Presses universitaires de Louvain
Auteur
Jérôme Dollinger,
Set
Taal
Engels
BISAC Subject Heading
BUS069030 BUSINESS & ECONOMICS / Economics / Theory
BIC subject category (UK)
KCA Economic theory & philosophy
Onix Audience Codes
06 Professional and scholarly
CLIL (2013)
3320 Économie théorique et expérimentale > 3327 Théorie des jeux
Voor het eerst gepubliceerd
30 januari 2025
Subject Scheme Identifier Code
: Sciences économiques
: Théories économiques

Paperback


Publicatie datum
30 januari 2025
ISBN-13
9782390615330
Omvang
Aantal pagina's hoofdinhoud : 148
Code
107862
Formaat
16 x 24 cm
Gewicht
247 grams
Packaging Type
No outer packaging
Aanbevolen verkoopprijs
14,00 €
ONIX XML
Version 2.1, Version 3

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Introduction 3
1 R&D and market sharing agreements 8
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Incentives for enlarging R&D alliances . . . . . . . . . . . . . . . . . . . . 16
1.4 Incentives for dissolving MS agreements . . . . . . . . . . . . . . . . . . . . 19
1.5 Stable R&D and MS Agreements . . . . . . . . . . . . . . . . . . . . . . . 21
1.5.1 No stable structures without MS agreement . . . . . . . . . . . . . 23
1.5.2 Main result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.3 Proof of the main result . . . . . . . . . . . . . . . . . . . . . . . . 25
1.5.4 Stable pairs of symmetric coalition structures . . . . . . . . . . . . 28
1.5.5 Policy implications and consumer surplus . . . . . . . . . . . . . . . 29
1.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.6.1 -stability versus -stability . . . . . . . . . . . . . . . . . . . . . . 30
1.6.2 Identical R&D alliance structure and MS structure . . . . . . . . . 31
1.6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2 Alliances and Technological Partnerships in Contests 54
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.3 Stabilisation of the grand alliance . . . . . . . . . . . . . . . . . . . . . . . 63
2.3.1 Stability with linear costs . . . . . . . . . . . . . . . . . . . . . . . 63
2.3.2 Stability with quadratic costs . . . . . . . . . . . . . . . . . . . . . 73
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.4.1 -stability versus 
 stability . . . . . . . . . . . . . . . . . . . . . . 74
2.4.2 Harshness of the contest . . . . . . . . . . . . . . . . . . . . . . . . 75
2.4.3 Implications of the results . . . . . . . . . . . . . . . . . . . . . . . 76
2.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3 On the existence of setwise stable hypergraphs of relationships 100
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.3 Formation of one hypergraph . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.3.1 Existence of Nash-setwise stable profiles . . . . . . . . . . . . . . . 105
3.3.2 Applications to formalisms in coalition theory . . . . . . . . . . . . 111
3.3.3 Relationship with others equilibrium concepts . . . . . . . . . . . . 115
3.4 Formation of two hypergraphs . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.4.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.4.2 Existence results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
A.1. Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
A.2. Proof of Corollary 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.3. Setwise stability under subgroups decision rules . . . . . . . . . . . . 127
A.4. Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.5. Proof of Corollary 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138