Dynamic strategic interaction in networks

Abstract

In this thesis, dynamic strategic interaction in networks is analyzed. In reality, economic agents frequently are organized in networks, in which links capture social ties of people or relationships between companies and other organizations. The agents strategically interact with each other over time. The network gives a structure to the observability of agents' action choices and to communication in a group. In similar setups, imperfect monitoring is often modelled by letting each agent obtain a perturbed signal of the actions chosen by other agents or no informational restrictions are imposed. A network provides an intuitive and realistic way to model such imperfections. It helps to explain why market outcomes often fail to be as efficient in reality as predicted in models. The first part, "Repeated Games Played in a Network", analyzes an infinitely repeated discounted game which all players in a connected network play. Each player only observes his neighbors' actions. By communicating, the players obtain the entire history over time. However, under strategic cortimunication additional conditions need to hold. A Folk Theorem given any stage-game and network obtains, though for impatient players the set of sequential equilibria and the corresponding payoff set may be reduced. The network's diameter is decisive for cooperation to be sustainable and not its clustering coefficient as in other models. In the second part, 'The Prisoner's Dilemma in a Network", this result is extended to strategic communication for a specific game, and further results are obtained, such as reduction in the set of equilibrium payoff vectors for impatient players. This is illustrated analytically and graphically for a star versus a complete network, each formed by three players. In the thrid part, 'Team Formation in a Network", two project leaders in a network recruit players in a strategic, competitive and time-limited process. Each project's optimal size depends on its quality. This is a random variable whose distribution is commonly known. Only the corresponding project leader observes its realization. Any decision is only observed by the involved agents. A pure strategy Sequential Equilibrium always exists. It may produce inefficient unemployment and allow for Pareto improvements which are prevented by the network's geography. An agent's payoff is related to his position in the petworlc This leads to a categorization of players which is unrelated to existent concepts in the network literature. In all three papers, a fixed network is assumed but the impact of the addition or destruction of links on the equilibrium outcome is analyzed. In reality, a network formation game in which all agents literally enter a room and see each other for the first time rarely takes place. Marginal link creation and severance is more likely to occur. The approach taken in this thesis can be extended to many other interesting situations of dynamic strategic interaction and existing models can be checked for their robustness using it.DD