Games and network formation
Creators: name: Horowitz, Basak
Publisher: name: No Publisher Supplied
Year: 2017

description: This dissertation consists of three studies in communication and information networks. The first chapter analyzes formation of networks when players choose how much time to invest in other players. I assume the information can be transferred using all possible paths in the network and study the model under two different link strength functions. First, under the assumption that the link strength is the arithmetic mean of agents' investment levels, which allows players to form links unilaterally to other players, every player is connected to another either directly or indirectly with no more than two links under any Nash equilibrium. Moreover, the strict Nash equilibrium structure is a star network. Second,under the assumption that the link strength function is Cobb-Douglas in which players have to have bilateral agreement to form links with each other, I show that paired networks in which players are matched in pairs, are Nash equilibria. Moreover, I consider a sequential game in which players choose and announce their investments publicly according to a random ordering. I show that an Assortative Pair Equilibrium, in which players are assortatively matched in pairs according to their information levels, is the only strongly robust Nash equilibrium.      In the second chapter, I consider the model introduced in the first chapter and fully characterize the Nash equilibria and surplus-maximizing outcomes for a three-player game, in order to investigate how equilibrium structures are different from the efficient outcomes and how these structures differ under different link strength functions. At equilibrium, the agents choose to invest all their time with only one agent regardless of the link strength function. More links are formed when the agents are perfect substitutes compared to Cobb-Douglas link strength, in which bilateral agreement is required for link formation. Moreover, the results show that the agents have a tendency to connect to fewer agents with higher investment levels from an efficiency perspective.      In the third chapter, I investigate a model of communication with two agents and a principal, allowing for asymmetric interdependencies between the agents. Each agent has private information on different dimensions of the state of nature. The interdependencies are characterized as action complementarities or substitutabilities between the agents within the same economic environment. I model the communication as cheap talk messages, assuming the information is not verifiable. I look at two decision mechanisms. First, under the centralized decision mechanism, in which agents communicate vertically with the principal and the principal makes the decisions for the agents after observing the reported private information, the communication takes form of a partition equilibrium. Second, under the decentralized mechanism, the agents communicate horizontally with each other via cheap talk and then make the decision for themselves. Under this protocol, I show that when there are strategic interaction between the agents, there are at most two on-the-equilibrium path conditional expectations for each agent. Thus, centralization allows more informative communication compared to decentralization. Moreover, I show that if the agents are strategic complements, it is not possible to have an informative horizontal communication.