Lecture Bargaining Theory

In the module we explore quantitative and mathematical methods of economic theory. We focus on decision processes involving multiple stakeholders, their negotiations and their agreements. Even with conflicting interests, decision makers can reach mutually beneficial outcomes through negotiation and compromise. We discuss what makes some decision makers more willing to cooperate and make commitments, and what makes other decision makers more reluctant to compromise. Understanding the negotiation and decision-making processes that shape sustainable outcomes supports the understanding of topics like climate negotiations, the management of shared resources, the participation of stakeholders and the balancing of diverse interests

Online teaching:

The module will be offered online.

This is a course with a more technical topic. For this course the online format offers benefits for learning that we miss in a traditional lecture room. Online videos allow you to follow your own learning speed. You can (and you should) pause your video, slow down or fast forward according to your individual learning speed. Weekly online homeworks give you regular feedback and help you to engage with the material. Online discussions and exercises provide and enhance interaction.

As a result, the online format gives you a much better learning experience and more room to interact. For this course, students are clearly more successful with online teaching than students with traditional teaching. In the past, with traditional classroom teaching, about 25% of the students failed the course. Now, with on-line teaching, fewer than 5% of the students fail.

🎥 Lecture:

During the term you will in each week obtain a new set of videos. You can choose when (and how) you watch these videos. These videos will remain available until the end of the term. I recommend to follow a routine: Watch the weekly videos on always the same day at always the same time.

Homework:

Each week you submit a brief homework (see the Moodle-page of the course). The homework counts for the final grade.

Discussion board:

Please use the discussion board in Moodle.

Online Q+A:

You find the details for the Q+A meeting in Moodle.

Exam:

04.08.2025, 08:30.
The final grade is 2/3 the result of a final take-home exam and 1/3 the weekly homework. I assume that, pursuant to the »Prüfungsordnung«, the weekly homework and the take home exam constitute a single partial exam.

Preparing for the exam: During the term you should solve the problems from the weekly homework. During the last weeks of the term, you will find in Moodle “extra questions”. This is a quiz, similar in style to the exam, that you can take as often as you want. Each time you take this quiz you get a new collection of problems. When you submit these extra questions you will get immediate feedback. You can work on these extra questions to get more routine for your exam. Points scored in this quiz don't contribute to your final grade.

Prerequisites:

Some game theory (e.g. as covered in BW24.2), basic calculus (here are some basic differentiation rules)

Literature:

• Kalai, E. & M. Smorodinsky (1975): “Other Solutions to Nash`s Bargaining Problem”, Econometrica, 43, 513-518.Jstor
• Muthoo, A. (1999): Bargaining theory with applications. Cambridge Univ. Press, Cambridge
• Osborne, M. J. & A. Rubinstein (1990): Bargaining and markets. Academic Press, San Diego.
• Roth, A. E. (1995): Bargaining Experiments , ch. 4 in The Handbook of Experimental Economics, ed. by J. H. Kagel & A. E. Roth.
• Shaked, A. and J. Sutton (1984), Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model , Econometrica 52, 1351 1364 Jstor

Outline:

Topic	Lecture	Exercise
1. Introduction, von Neumann-Morgenstern Utility, Nash's axioms.	07.04.2025	14.04.2025
2. Nash's theorem, applications.	14.04.2025	21.04.2025
3. Risk aversion, applications (bribery, asset ownership).	21.04.2025	28.04.2025
4. Discussion of Nash's axioms.	28.04.2025	05.05.2025
5. Applications (moral hazard in teams).	05.05.2025	12.05.2025
6. The strategic approach: Rubinstein's model.	12.05.2025	19.05.2025
7. Strategies in bargaining in the alternating offers model. Nash equilibrium.	19.05.2025	26.05.2025
8. Subgame perfect equilibrium.	26.05.2025	02.06.2025
9. Constant discount rates, fixed bargaining cost, finitely divisible pies.	02.06.2025	09.06.2025
10. Outside options	09.06.2025	16.06.2025
11. More than two players, comparison Rubinstein/Nash	16.06.2025	23.06.2025
12. Incomplete information.	23.06.2025	30.06.2025
13. Markets and decentralised trade.	30.06.2025	07.07.2025
14. Summary, exercises, discussion board, Q+A.	07.07.2025	14.07.2025

Motivation:

Consider a situation where two agents obtain gains from cooperation. This could be an exchange that is mutually beneficial or a cooperation in a political or social environment. How should the agents divide the proceeds from their joint project? How is the ratio of goods in an exchange, how the result of a political or personal settlement determined? Market equilibria assume a large number of agents and the presence of a Walrasian auctioneer — assumptions that are not always fulfilled. Bargaining theory attempts to address this issue, studying a situation where a small number of players find a settlement in a distributive conflict. Is the settlement always efficient or is it found only after time consuming and costly negotiations? Who is the winner and who the looser of a settlement? How is bargaining power determined? How, finally, can we compare such a bargaining solution with market equilibria?

Learning aims:

Students should understand the main paradigms of axiomatic bargaining theory (Nash, Kalai-Smorodinsky) and of strategic bargaining theory (Rubinstein's alternating offer game).