Saddle Point
Back to the cover

Part I · Foundations

  1. 0 Mathematical Foundations
  2. 1 Observation, Beliefs, and Decision

Part II · Engines

  1. 2 Competing for Allocation: The Blotto Game
  2. 3 Bargaining, Commitment, and Repeated Cooperation
  3. 4 Signals, Disclosure, and Persuasion
  4. 5 Different Models of One Game
  5. 6 Leadership and Rules: Inspection
  6. 7 Decisions in Time
  7. 8 Many Agents
  8. 9 Networks, Dependence, and Resilience
  9. 10 Aggregating Information

Part III · Systems

  1. 11 Architecture of Decision Support
  2. 12 Simulation and Wargaming with AI Agents

Part IV · Limits

  1. 13 Where the Mathematics Stops
Robert J. Aumann, 2006

Chapter 3 · Bargaining, Commitment, and Repeated Cooperation

Robert J. Aumann

born 1930

Photograph: Rama, Robert Aumann, 2006, Wikimedia Commons, CC BY-SA 2.0 France (https://creativecommons.org/licenses/by-sa/2.0/fr/). Shown toned. File and licence

The problem on the desk

Can people with a common prior retain different posterior beliefs when those posteriors are common knowledge? Aumann supplied a precise information framework in which the answer is no. The assumptions, not merely shared facts, do the work.1

A life in moments

  1. 1930

    Frankfurt am Main

    Born on 8 June.2

  2. 1950

    City College of New York · New York

    Completed his bachelor’s degree.3

  3. 1955

    Massachusetts Institute of Technology · Cambridge

    Completed his doctorate in mathematics.3

  4. 1956

    Hebrew University of Jerusalem · Jerusalem

    Joined the mathematics faculty.3

  5. 1965

    Hebrew University of Jerusalem · Jerusalem

    Organised an international game-theory workshop with Maschler.3

  6. 1976

    Published Agreeing to Disagree.1

  7. 2005

    Shared the economics prize with Schelling.4

Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.

In their own words

people with the same priors cannot agree to disagree.

Agreeing to Disagree, 19766

A story

A short theorem about an infinite-looking condition

The 1976 paper begins with everyone knowing, knowing that others know, and further iterations. Aumann turns that condition into common knowledge and obtains the equality of the two posteriors.5

Around Aumann

  • same institution Michael Maschler Co-organised the 1965 Jerusalem game-theory workshop with Maschler.3
  • shared a prize Thomas C. Schelling Shared the 2005 economics prize with Schelling.4

Recorded as advisor George William Whitehead Jr. Recorded as students Sergiu Hart, Abraham Neyman, Shmuel Zamir, David Schmeidler Mathematics Genealogy Project record

The genealogy lists only what the database records; a missing name is not a missing teacher.

The card in the book

Mathematician who received his doctorate from the Massachusetts Institute of Technology in 1955 and has worked since 1956 at the Hebrew University of Jerusalem, where he was a founding member of the Center for the Study of Rationality. He developed the theory of repeated games, including games with incomplete information with Michael Maschler, introduced correlated equilibrium, and formalised common knowledge. He shared the 2005 Nobel Memorial Prize in Economic Sciences with Thomas Schelling.

Main works “Subjectivity and correlation in randomized strategies” (Journal of Mathematical Economics 1, 1974); “Agreeing to disagree” (Annals of Statistics 4, 1976); Repeated Games with Incomplete Information, with M. Maschler (1995).

To read further

Sources (6)
  1. Agreeing to Disagree, Robert J. Aumann, 1976; Annals of Statistics 4(6), p. 1236, abstract and opening paragraphs
  2. Brief Biography, Robert J. Aumann; Birth, education and Hebrew University; indexed institutional biography
  3. Curriculum Vitae, Robert J. Aumann; Education; positions; honours; organisation of the 1965 workshop
  4. In Memoriam: Thomas C. Schelling, 1921–2016, Weatherhead Center, Harvard University, 2016; 21 December; Yale, Harvard, Maryland and award paragraphs
  5. Agreeing to Disagree, Robert J. Aumann, 1976; p. 1236
  6. Agreeing to Disagree, Robert J. Aumann, 1976; p. 1236, abstract; clause beginning after “In brief”

The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.