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

Abstract

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.

Costly miscalibration

“…How to extend such a definition to sender–receiver games with a continuum message space is not obvious. (See Remark 2 in the Appendix and Friedenberg 2019, for example, where similar issues arise.) However, the issue is somewhat simpler in our setup, because each player takes action only once.…”

Personal Power Dynamics in Bargaining

“…Uncertainty about the bargaining strength of agents has been previously proposed as a rationale for delay in bargaining. This has been explored in the seminal works of Admati and Perry (1987), Cramton (1992) and more recently by Friedenberg (2019). We do not seek to explain delay in this paper, but rather we seek to explain when we expect compromise to arise, or when we expect a challenge to ensue.…”

Positive and Negative Selection in Bargaining: An Experiment

“…Yildiz (2011) reviews the drivers of costly delays in negotiations and claims that the deadline effect and the learning about bargaining power would make optimistic players delay the agreement to a later period. The second-order optimism-belief about the other party's optimism toward her prospects-could also play a role in causing a delay (Friedenberg, 2019). Li and Wong (2009) show that mutual optimism is a source of delayed agreement and substantial efficiency loss in the Rubinstein bargaining environment.…”