L'abbé Marenne

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.