Essays on network formation

The importance of networks has been highlighted in numerous economic studies. To address the key question of how networks emerge, several models have been developed to examine equilibrium networks and assess the efficiency of various network structures. This thesis presents our research on network formation, organized into three chapters. In Chapter 1, we consider a non-cooperative model of network formations where agents decide on whom to form costly links to. Links are unilaterally formed and payoff flows one way to the active side. We study discontinuous information flows where agents only receive benefits from other agents at a distance of two in the network. For the static game, we show that the set of strict Nash equilibria encompasses a multiplicity of core-periphery network structures. We further study a noisy best response process to obtain long-run predictions. By doing so, we find that the set of stochastically stable states retains a multiplicity of network structures, many of which are not efficient. Chapter 2 provides supportive simulation evidence for the theoretical model of evolutionary network formation, where agents form unilateral links and receive payoffs from others within distance two. We present a MatLab program to mimic both unperturbed and perturbed myopic best learning dynamics. The simulation of unperturbed dynamics shows that core-periphery networks are absorbing when agents never make mistakes. Further, when there is a small probability that agents make mistakes, the simulation of perturbed dynamics shows that core-periphery networks are uniquely stochastically stable. In Chapter 3, we present an evolutionary model of coordination and network formation where there are two groups of agents who face either high or low linking constraints on the number of links. We study the agents’ choices of actions in the 2×2 coordination game and the set of agents to whom they link. For the static game, we show that both monomorphic states (all agents play the same action) and polymorphic states (agents play different actions) are Nash equilibria. We then study a noisy best response learning dynamics to select among multiple Nash equilibria in the static game. We find that if both low and high constraints are loose, the risk-dominant strategy is selected. In contrast, if both low and high constraints are tight, the payoff-dominant action arises. Moreover, we present that the co-existence of the risk- and payoff-dominant actions can be observed for some game parameters. In summary, the thesis contributes to the literature on network formation in both theoretical and simulation respects by considering the constraints of information transmission distance. Additionally, Furthermore, the work also adds to the literature on the coevolution of social coordination and network formation by incorporating heterogeneous linking constraints.