Strategic Negotiations in Endogenous Network Formation

Abstract

In network formation games, agents form edges with each other to maximize their utility. Each agent's utility depends on its private beliefs and its edges in the network. Strategic agents can misrepresent their beliefs to get a better resulting network. Most prior works in this area consider honest agents or a single strategic agent. Instead, we propose a model where any subset of agents can be strategic. We provide an efficient algorithm for finding the set of Nash equilibria, if any exist, and certify their nonexistence otherwise. We also show that when several strategic agents are present, their utilities can increase or decrease compared to when they are all honest. Small changes in the inter-agent correlations can cause such shifts. In contrast, the simpler one-strategic-agent setting explored in the literature lacks such complex patterns. Finally, we develop an algorithm by which new agents can learn the information needed for strategic behavior. Our algorithm works even when the (unknown) strategic agents deviate from the Nash-optimal strategies. We verify these results on both simulated networks and a real-world dataset on international trade.