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Best response dynamics in simultaneous and sequential network design games

This thesis is concerned with the analysis of best response dynamics in simultaneous and sequential network design games with fair-cost sharing, for both capacitated and uncapacitated networks. We address questions related to the evolution of stable states through selfish updates. First, we examine in general what effects such updates can have, from various perspectives, on the quality of the solutions to a game. From this, we move on to a more specific analysis of updates which begin from an optimal profile, providing insight to the price of stability measure of network efficiency, from the perspective of the user incurring the highest cost in the game. Finally, we investigate the process of updates beginning from an empty strategy profile, and make some observations about the quality of the resultant profile in such situations.