Selfish behavior in network-based games

It is a well known principle of economics that when members of society do not coordinate and instead act independently in a self-interested fashion, the resulting outcome typically does not achieve the maximum possible total social welfare. Thus, there is often a cost to competitive behavior. This phenomenon, often referred to as the "Tragedy of the Commons", can explain the underlying cause of many diverse problems, including industrial over-pollution, nuclear proliferation, and over-fishing. In all these settings, decentralized and selfish behavior leads to suboptimal outcomes in which all parties suffer. In this thesis, we explore the extent to which a similar lack of centralized control in the design, formation, and operation of the Internet might likewise lead to an inefficient, unreliable, and needlessly expensive network. To study such scenarios, we apply the tools of game theory. This branch of mathematics allows us to formally describe these competitive environments, which we call games. Self-interested agents are represented as players, who seek to maximize their own private welfare. The stable solutions reached by these competing players are called Nash equilibria. In this thesis, we consider a number of games which model various aspects of competition in the Internet, and seek to quantify the extent to which the lack of centralized control decreases social welfare. In particular, we study games that model the competitive creation of networks and the pricing of network services, and we examine how collusion can make matters even worse. Our primary goal is to compare the quality of Nash equilibria to that of centrally designed solutions. We first introduce a game that models network formation. We show that while worst case selfish behavior is very costly, in a broad class of games, the best stable solutions are just as good as those that are designed centrally. In other words, for a large class of network creation games, selfish behavior need not lessen social welfare. We then consider the computational complexity of finding such stable outcomes. We also explore how minor restrictions on players' choices can lead to dramatically better outcomes. In particular, we show that by enforcing a certain degree of "fairness" in our network formation game, the cost of solutions reached through selfish play improves dramatically. We next consider a game in which players set prices for network services, and compete with each other for customers. We provide conditions under which Nash equilibria are guaranteed to exist, and show that for a broader class of games, equilibria are always close to optimal. Lastly, we propose a framework to model the formation of coalitions, and study these coalitions in the context of a simple load-balancing game. We show that despite the apparent increase in the level of coordination, limited collusion can actually decrease the quality of solutions that are reachable through selfish play. However, we prove that for a large class of games, this increase is always small.