A Theory of Disagreement in Repeated Games With Bargaining

Abstract

This paper proposes a new approach to equilibrium selection in repeated games with transfers, supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (following a generalized alternating-offer protocol), sharp predictions arise from three axioms. Two axioms allow the players to meaningfully discuss whether to deviate from their plan; the third embodies a "theory of disagreement"-that play under disagreement should not vary with the manner in which bargaining broke down. Equilibria that satisfy these axioms exist for all discount factors and are simple to construct; all equilibria generate the same welfare. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efficiency depends on both the stage game and the bargaining protocol. The theory extends naturally to games with imperfect public monitoring and heterogeneous discount factors, and yields new insights into classic relational contracting questions.

Past and Future Developments in the Economics of Relational Contracts

“…Neither of these approaches explicitly incorporates notions of bargaining power. The goal of Miller and Watson (2013) and Watson, Miller, and Olsen (2020) is to develop an approach to relational contracting that takes into account that parties discuss and bargain about their relationship, and these meaningful discussions should actually affect outcomes. Miller and Watson (2023) review this approach to modeling relational contracts that they call a "contractual equilibrium".…”

When Protection Becomes Exploitation: The Impact of Firing Costs on Present-Biased Employees

“…This feature is different fromMiller andWatson (2013) andFahn (2017). In these papers, the inability of parties to commit not to renegotiate any agreement undermines the efficiency of long-term employment relationships.…”

Self-enforcing agreement in cooperative teams: an agent-based modeling approach

“…In addition, the conclusion could vary when more complicated issues, for instance, the problem of renegotiationproofness, are taken into consideration. Over the past 20 years, much progress has been made on developing the original model (for example, Bond 2009;Faillo et al 2015;Goldlücke and Kranz 2013;Miller and Watson 2013;Ray 2002). The two competing arguments have never been formally tested and thus the debate has never been concluded.…”