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 Axelrod, 2019

Chapter 12 · Simulation and Wargaming with AI Agents

Robert Axelrod

born 1943

Photograph: Ford School, retirement celebration for Robert Axelrod (12 October 2019), cropped video still, CC BY 3.0, via Wikimedia Commons. Shown toned. File and licence

The problem on the desk

Which repeated-game rules sustain cooperation among self-interested players? Axelrod invited programs to play an iterated prisoner’s-dilemma tournament, then examined what the results did and did not imply beyond that particular field of opponents.1

A life in moments

  1. 1964

    University of Chicago · Chicago

    Completed a mathematics degree.2

  2. 1969

    Yale University · New Haven

    Completed a doctorate in political science.2

  3. 1974

    University of Michigan · Ann Arbor

    Joined the university.3

  4. 1980

    University of Michigan · Ann Arbor

    Reported the two computer tournaments.4

  5. 1984

    Published The Evolution of Cooperation.5

  6. 2012

    University of Michigan · Ann Arbor

    Published a retrospective examining origins, noise and the collaboration with Hamilton.6

  7. 2014

    Received the National Medal of Science.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

Of course, there is no one “best” strategy for the iterated Prisoner’s Dilemma.

Launching The Evolution of Cooperation, 20128

A story

The problem of mistakes

In retrospect, Axelrod stressed how misperceived or misimplemented moves can trigger retaliation between reciprocal players. He discussed generous and contrite variants as responses to different kinds of noise.7

Around Axelrod

  • co-author William D. Hamilton Axelrod and Hamilton combined game-theoretic and evolutionary perspectives in their 1981 paper.9

Recorded as advisor Hayward Rose Alker Recorded as students Bear Braumoeller, Lars-Erik Cederman, Dan Reiter 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

Political scientist at the University of Michigan since 1974, with a doctorate from Yale (1969). He ran two computer tournaments of the repeated prisoner's dilemma, the first a round robin among the submitted decision rules and a random rule, the second with 62 entries, and reported them in the Journal of Conflict Resolution in 1980; an evolutionary analysis with the biologist William Hamilton followed in 1981 and the book The Evolution of Cooperation in 1984. Both rounds were won by TIT FOR TAT, the rule that cooperates on the first move and then repeats the other player's previous move.

Main works “Effective choice in the prisoner's dilemma” and “More effective choice in the prisoner's dilemma” (Journal of Conflict Resolution 24, 1980); “The evolution of cooperation”, with W. D. Hamilton (Science 211, 1981); The Evolution of Cooperation (1984).

To read further

Sources (9)
  1. Launching The Evolution of Cooperation, Robert Axelrod, 2012; §1 and footnote 2
  2. Robert Axelrod: professional homepage, Robert Axelrod; University of Michigan; Professional biography and selected publications
  3. Robert Axelrod to receive National Medal of Science, University of Michigan, Ford School, 2014; 3 October 2014; appointment since 1974 and award announcement
  4. Launching The Evolution of Cooperation, Robert Axelrod, 2012; §1; references to the two 1980 articles
  5. Robert Axelrod: professional homepage, Robert Axelrod; University of Michigan; Selected publications
  6. Launching The Evolution of Cooperation, Robert Axelrod, 2012; Journal issue date; online publication was in 2011
  7. Launching The Evolution of Cooperation, Robert Axelrod, 2012; §2
  8. Launching The Evolution of Cooperation, Robert Axelrod, 2012; p. 22, footnote 2
  9. Launching The Evolution of Cooperation, Robert Axelrod, 2012; §3

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.