Essays in game theory: Social interactions, coordination and network formation

The first chapter in this dissertation studies long run equilibrium selection in 2 x 2 coordination games in a framework that accounts for the effect of mobility, local interact ion, and scale of interaction. I find that the stochastic stability of a particular convention depends both on the importance of scale effects relative to the degree of local interaction, and the efficiency and risk characteristics of a particular equilibrium. It is shown that less flexibility (increased costs of mobility) can help rather than hurt the chances of selecting efficient conventions. Allowing for heterogeneous matching characteristics, limit sets in which players of different characteristics coordinate on different actions can prevail in the long run. A tension between scale effects and the stability of the payoff dominant conventions is also identified: societies that enjoy the benefits of large scale effects and give up the stability of payoff dominant conventions can perform better in the long run.; The second chapter analyzes a social game where agents choose their partners as well as their actions. Players interact with direct and indirect neighbors in the endogenous network. It is shown that the architecture of any nontrivial Nash equilibrium is minimally connected, and equilibrium actions approximate a symmetric equilibrium of the underlying game. The model is then used to analyze stochastic stability in 2 x 2 coordination games. The main finding is that long run equilibrium selection depends on a trade-off between efficiency and risk dominance due to the presence of scale effects arising from network externalities.; The third chapter builds a non-cooperative model of network formation where network externalities exhibit decreasing returns and distant neighbors in the network yield no benefit. In this model, the unique non-empty equilibrium network architecture is a periphery-sponsored star: one player, the center, maintains no links, and all other players maintain a single link to the center. The model explains the emergence of a small number of central agents or "hubs", a pervasive pattern of many social and economic networks such as networks of advice, R&D alliances in innovative industries, and trade networks. It is shown that, consistent with evidence, central agents fare better. However, the unequal distribution of connections that results in equilibrium can be socially inefficient because of decreasing returns. Allowing for heterogeneous groups, interlinked stars or separation can emerge in equilibrium: small minorities favor integration while large minorities are self-sufficient. Although any player can be the center in a static equilibrium, evolution with persistent randomness selects the agent with most valuable resources as the center in the long run. As a result, even a small inequality in the pre-existing endowments can be greatly amplified by the endogenous determination of social connections.