Bargaining, Strategic Timing and Network Formation

Using a continuous time framework, this paper proves existence of Markov Perfect equilibria in a strategic network formation game where opportunities to propose new links follow a Poisson process whose intensity is jointly controlled by the players. This allows network activity to systematically vary across states, with calm periods where there are few changes to the network structure as well as periods of frantic activity where agents seek out scarce opportunities. If action on the part of another player would raise an agent’s discounted expected value relative to the current state, intensities are strategic substitutes; otherwise they are strategic complements. Thus, players who benefit from each others’ actions crowd one another out in equilibrium, while players whose actions have negative consequences for each other compete more aggressively. The model allows for side-payments and bargaining, where agents bargaining positions are endogenously determined by their expectations about the future value of their relationships. Finally, a class of games is characterized in which myopic behavior is optimal, and a repeated auction game with an endogenous buyer-seller network is analyzed as an example.