Two Coalitional Models for Network Formation and Matching Games

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis comprises of two separate game theoretic models that fall under the general umbrella of network formation games. The first is a coalitional model of interaction in social networks that is based on the idea of social distance, in which players seek interactions with similar others. Our model captures some of the phenomena observed on such networks, such as homophily driven interactions and the formation of small worlds for groups of players. Using social distance games, we analyze the interactions between players on the network, study the properties of efficient and stable networks, relate them to the underlying graphical structure of the game, and give an approximation algorithm for finding optimal social welfare. We then show that efficient networks are not necessarily stable, and stable networks do not necessarily maximise welfare. We use the stability gap to investigate th