Lecture Bargaining Theory

In this 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 others more reluctant to compromise. Understanding the negotiation and decision-making processes that shape sustainable outcomes supports the understanding of topics such as climate negotiations, the management of shared resources, stakeholder participation, and the balancing of diverse interests.

Motivation:

Consider a situation where two agents gain from cooperation. This could be an exchange that is mutually beneficial or a cooperation in a political or social setting. How should the agents divide the proceeds from their joint project? How is the ratio of goods in an exchange, or 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 met. Bargaining theory attempts to address this issue by studying a situation where a small number of players reach 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 is the loser of a settlement? How is bargaining power determined? Finally, how 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).

Online-teaching:

The module will be offered online.

This course covers a more technical topic. For this course, the online format offers learning benefits that are absent in a traditional lecture room. Online videos allow you to learn at your own pace. You can (and you should) pause, slow down, or fast forward according to your individual learning speed. Weekly online homework assignments provide regular feedback and help you to engage with the material. Online discussions and exercises provide and enhance interaction.

Consequently, the online format offers a significantly better learning experience and more opportunities to interact. For this course, students are demonstrably more successful with online teaching than students with traditional teaching. In the past, with traditional classroom teaching, approximately 25% of the students failed the course. Now, with online teaching, fewer than 5% of the students fail.

Lecture + Exercises:

Throughout the term, you will receive a new set of videos each week. You can choose when (and how) you watch these videos. These videos will remain available until the end of the term. I recommend that you establish a routine: watch the weekly videos on the same day and at the same time every week. Each week, you will also complete a short homework assignment.

Weekly Digital Homework:

Each week, you will submit a short homework assignment via Moodle. Although different students will work on different problems, discussing your homework within your study group will be beneficial. Use the discussion board in Moodle to ask questions and to keep in touch with the other course members.

You can obtain one-third of the total points (130 points) with the homework.

At the end of the term, you will find extra (optional) problem sets in Moodle. These extra problem sets are similar in style to the exam. You may attempt these problem sets as often as you wish. For each attempt, you will receive a new collection of problems. When you submit your answers to these extra questions, you will receive immediate feedback and some comments. You can use these extra questions to become more accustomed to the exam. Points scored with these extra questions do not contribute to your final grade.

Digital Exam:

• You can obtain up to two-thirds of the total points (260 points) in the digital exam (on Moodle) on 03.08.2026 at 10:30. The style of the questions in the digital exam on 03.08.2026 at 10:30, will be similar to the questions in the weekly homework. If you have a reliable internet connection, you can write the digital exam from home. If you prefer to write at FSU Jena and require a room, please let us know.

  The sum of the points from the digital homework and the digital exam (up to 390 points) determines your grade.

• Date of the digital exam: 03.08.2026 at 10:30 (on Moodle).
• Resit of the digital exam: 11.11.2026 at 16:30 (on Moodle).

  Students who wish to take the resit of the digital exam must register in time with the examination office.

• Instructions for the Digital Exam
• If you wish to obtain credits for the course, please do not forget to register for the exam!

Discussion Board and Online Meeting:

Use the discussion board in Moodle to ask questions and to discuss issues related to the lecture. I will endeavour to answer your questions as soon as possible, usually within one working day.

The access code for the online meeting can be found in Moodle. I recommend that, before joining the meeting, you watch the videos and attempt to solve the homework. Please arrive on time, and if possible, activate your camera. I do not plan to introduce new material in the discussion board or during the online meeting.

Prerequisites:

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

Outline:

Topic	Lecture/Exercise
1. Introduction, von Neumann-Morgenstern Utility, Nash's axioms.	06.04.2026 - 12.04.2026
2. Nash's theorem, applications.	13.04.2026 - 19.04.2026
3. Risk aversion, applications (bribery, asset ownership).	20.04.2026 - 26.04.2026
4. Discussion of Nash's axioms.	27.04.2026 - 03.05.2026
5. Applications (moral hazard in teams).	04.05.2026 - 10.05.2026
6. The strategic approach: Rubinstein's model.	11.05.2026 - 17.05.2026
7. Strategies in bargaining in the alternating offers model. Nash equilibrium.	18.05.2026 - 24.05.2026
8. Subgame perfect equilibrium.	25.05.2026 - 31.05.2026
9. Constant discount rates, fixed bargaining cost, finitely divisible pies.	01.06.2026 - 07.06.2026
10. Outside options	08.06.2026 - 14.06.2026
11. More than two players, comparison Rubinstein/Nash	15.06.2026 - 21.06.2026
12. Incomplete information.	22.06.2026 - 28.06.2026
13. Markets and decentralised trade.	29.06.2026 - 05.07.2026
14. Summary, exercises, discussion board, Q+A.	06.07.2026 - 12.07.2026

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

FAQ:

• I have a question regarding the lecture?
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