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
Reinhard Selten, 2001

Chapter 13 · Where the Mathematics Stops

Reinhard Selten

1930 – 2016

Photograph: Tohma, Reinhard Selten at CJD Christophorusschule Königswinter (7 March 2001, uploader’s date), CC BY-SA 4.0, via Wikimedia Commons. Shown toned. File and licence

The problem on the desk

An equilibrium may prescribe implausible behaviour in parts of a game that are never reached. Selten first required equilibrium in every subgame, then introduced a stronger refinement based on the possibility of small mistakes.1

A life in moments

  1. 1930

    Breslau

    Born on 5 October.2

  2. 1957–1967

    Johann Wolfgang Goethe University · Frankfurt am Main

    Worked as Heinz Sauermann’s research assistant.3

  3. 1961

    Johann Wolfgang Goethe University · Frankfurt am Main

    Completed his mathematics doctorate.3

  4. 1965

    Johann Wolfgang Goethe University · Frankfurt am Main

    Published his two-part oligopoly study introducing subgame perfection.4

  5. 1975

    University of Bielefeld · Bielefeld

    Published the reexamination of perfectness.5

  6. 1984

    University of Bonn · Bonn

    Joined Bonn and founded its experimental economics laboratory.6

  7. 1994

    Shared the economics prize with Harsanyi and Nash.7

  8. 2016

    Poznań

    Died on 23 August.2

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

In retrospect the earlier use of the word “perfect” was premature.

Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, 19759

A story

Renaming his earlier concept

Selten’s 1975 opening calls the older concept subgame perfect and reserves perfect for a stronger notion. A footnote credits Harsanyi with the idea of modelling slight mistakes.8

Around Selten

  • built on the work John C. Harsanyi Selten credits Harsanyi’s influence on the slight-mistakes model.10
  • shared a prize John F. Nash Jr. Selten, Nash and Harsanyi shared the 1994 economics prize.7

Recorded as advisors Ewald Burger, Wolfgang Franz Recorded as students Benny Moldovanu, Rosemarie Nagel, Bettina Rockenbach 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

Born in Breslau, he studied mathematics at the University of Frankfurt, where he took his master's degree in 1957 and his doctorate in mathematics in 1961, and worked for about a decade as assistant to the economist Heinz Sauermann, with whom he ran early laboratory experiments on oligopoly. After a visiting professorship at Berkeley (1967–68) he was professor at the Free University of Berlin (1969–72), at Bielefeld (1972–84) and at Bonn from 1984. In a 1965 paper on an oligopoly model with demand inertia he defined subgame perfectness, and in 1975 the refinement now called trembling-hand perfectness; with John Harsanyi he wrote a general theory of equilibrium selection. He shared the 1994 Nobel Memorial Prize in Economic Sciences with Harsanyi and John Nash.

Main works “Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit” (Zeitschrift für die gesamte Staatswissenschaft 121, 1965); “Reexamination of the perfectness concept for equilibrium points in extensive games” (International Journal of Game Theory 4, 1975); A General Theory of Equilibrium Selection in Games, with J. C. Harsanyi (1988).

To read further

Sources (10)
  1. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, Reinhard Selten, 1975; p. 25 and §7
  2. Reinhard Selten: academic work and curriculum vitae, University of Bonn, BonnEconLab; Biography
  3. Reinhard Selten: academic work and curriculum vitae, University of Bonn, BonnEconLab; Academic Career
  4. Reinhard Selten: academic work and curriculum vitae, University of Bonn, BonnEconLab; Publications: 1965
  5. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, Reinhard Selten, 1975; p. 25, affiliation
  6. Reinhard Selten: academic work and curriculum vitae, University of Bonn, BonnEconLab; Opening and Academic Career
  7. Reinhard Selten: academic work and curriculum vitae, University of Bonn, BonnEconLab; Memberships and Honors
  8. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, Reinhard Selten, 1975; p. 25 and footnote 2
  9. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, Reinhard Selten, 1975; p. 25
  10. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, Reinhard Selten, 1975; p. 25, footnote 2

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.