This document summarizes a research paper on one-sided uncertainty and delay in reputational bargaining. It outlines the motivation, literature, models and equilibria discussed in the paper. The motivation is a two-person infinite bargaining model where one player may have one of two discount factors. The literature discussed includes previous work on adding behavioral types or incomplete information that results in unique equilibria with delay. The analysis of the models and equilibria is described as quite messy and the intuition for behavioral types is not entirely clear.

1. One-sided Uncertainty and Delay in Reputational
Bargaining
Dilip Abreu David Pearce Ennio Stacchetti
June, 2013
Abreu, Pearce and Stacchetti One-sided Uncertainty and Delay in Reputational Bargaining 1 / 7

2. Outline
1 Motivation and Literature
2 Models and Equilibria
3 Comments
Abreu, Pearce and Stacchetti One-sided Uncertainty and Delay in Reputational Bargaining 2 / 7

3. Motivation and Literature Motivation
Motivation
A two-person infinite-horizon bargaining model
If one of the players may have one of two discount factors, the model
has multiple equilibria
The equilibrium is unique if players are irrational with some probability
If “behavioral types” postpone making their offers, the equilibrium is
still unique, but the payoffs may be substantially different
Abreu, Pearce and Stacchetti One-sided Uncertainty and Delay in Reputational Bargaining 3 / 7

4. Motivation and Literature Literature
Literature
Abreu and Gul (2000):
• Add behavioral types to a continuous-time bargaining model
• A unique equilibrium with delay
• Inefficiency due to delay disappears in the limit
Rubinstein (1985):
• Add incomplete information about time preferences to Rubinstein
(1982)
• Define a set of “bargaining axioms”
• The uninformed player does as bad as she would in a full information
game against a “stronger” opponent
Abreu, Pearce and Stacchetti One-sided Uncertainty and Delay in Reputational Bargaining 4 / 7

5. Motivation and Literature Literature
Literature
Abreu and Gul (2000):
• Add behavioral types to a continuous-time bargaining model
• A unique equilibrium with delay
• Inefficiency due to delay disappears in the limit—not in this model
Rubinstein (1985):
• Add incomplete information about time preferences to Rubinstein
(1982)
• Define a set of “bargaining axioms”
• The uninformed player does as bad as she would in a full information
game against a “stronger” opponent
Abreu, Pearce and Stacchetti One-sided Uncertainty and Delay in Reputational Bargaining 5 / 7

6. Motivation and Literature Literature
Literature
Abreu and Gul (2000):
• Add behavioral types to a continuous-time bargaining model
• A unique equilibrium with delay
• Inefficiency due to delay disappears in the limit—not in this model
Rubinstein (1985):
• Add incomplete information about time preferences to Rubinstein
(1982)
• Define a set of “bargaining axioms”
• The uninformed player does as bad as she would in a full information
game against a “stronger” opponent—not in this model
Abreu, Pearce and Stacchetti One-sided Uncertainty and Delay in Reputational Bargaining 6 / 7

7. Comments Comments
Comments
The results are interesting
The analysis is quite messy
The intuition behind the second dimension of the behavioral types is
not that clear
Abreu, Pearce and Stacchetti One-sided Uncertainty and Delay in Reputational Bargaining 7 / 7