Essay on Strategic Behavior of Heterogeneous Agents

This dissertation studies how heterogeneity across interacting parties affects their strategic behavior and their equilibrium implications. I divide my dissertation into three chapters. The first chapter studies how an initial asymmetry in the production costs between two firms affects aggregate R&D investment and equilibrium welfare under non-cooperative R&D and under a research joint venture. Under both regimes, increasing the initial cost asymmetry reduces welfare. If there exists a spillover value for which welfare under the two regimes is the same, then increasing the initial cost asymmetry has an ambiguous effect on this critical spillover value.

The second chapter studies how private information affects the stability of a network of heterogeneous agents in the coauthor model. I introduce private information in the node linkformation decisions and endow each node with complete information in their link-severing decisions. A node's incentive to form a link increases with its type if, and only if, the increase of the magnitude of the negative externality induced by a new link is small relative to the benefit of a new interaction. A node's incentive to form a new link decreases with each of the neighbors' types. Adding information can maintain or undermine the stability of a network. Therefore a stable star network under incomplete information can be unstable under complete information.

The third chapter analyzes a communication game with two types of players: loyals and traitors. Conditional on his type after privately observing a noisy signal about the state of the world, each player sends a message to an uninformed decision maker. Necessary and sufficient conditions for the existence of equilibria where every player sends the same message regardless of his signal, equilibria where each loyal truthfully reveals his signal and equilibria where each loyal lies with some probability for some signal are provided. The conditions that provide the incentives to the loyals to truthfully reveal their signals in equilibrium may contradict the conditions under which a Byzantine Agreement can exist. Moreover, having each loyal revealing their signals in equilibrium does not guarantee the decision maker's maximum welfare ex-ante.