Bargaining Under Strategic Uncertainty: The Role of Second-Order Optimism

This paper shows that bargainers may reach delayed agreements even in environments where there is no uncertainty about payoffs or feasible actions. Under such conditions, delay may arise when bargainers face direct forms of strategic uncertainty—that is, uncertainty about the opponent's play. The paper restricts the nature of this uncertainty in two important ways. First, it assumes on-path strategic certainty: Bargainers face uncertainty only after surprise moves. Second, it assumes Battigalli and Siniscalchi's (2002) rationality and common strong belief of rationality (RCSBR)—a requirement that bargainers are “strategically sophisticated.” The main result characterizes the set of outcomes consistent with on-path strategic certainty and RCSBR. It shows that these assumptions allow for delayed agreement, despite the fact that the bargaining environment is one of complete information. The source of delay is second-order optimism: Bargainers do not put forward “good” offers early in the negotiation process because they fear that doing so will cause the other party to become more optimistic about her future prospects.