Bounded Rationality and Alternating-Offer Bargaining

One form of bounded rationality is a breakdown in the commonality of the knowledge that the players are rational. In Rubinstein’s two-person alternating-offer bargaining game, assuming time preferences with constant discount factors, common knowledge of rationality is necessary for an agreement on a subgame perfect equilibrium (SPE) partition to be reached (if ever). In this note, assuming time preferences with constant costs of delay, we show that common knowledge of rationality is not necessary to reach always an agreement on a SPE partition. This result is robust to a generalisation, time preferences with constant discount factors and costs of delay, if the players are sufficiently patient.