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

Chapter 7 · Decisions in Time

Rufus Isaacs

1914 – 1981

The problem on the desk

At RAND, Isaacs asked how a pursuer should steer when the evader is also choosing its motion. He sought strategies for continuous conflict, rather than a fixed trajectory computed against an unresponsive target.1

A life in moments

  1. 1914

    New York City

    Born on 11 June.2

  2. 1936

    Massachusetts Institute of Technology · Cambridge, Massachusetts

    Completed his undergraduate degree.2

  3. early 1950s

    RAND Corporation · Santa Monica

    Developed differential games in research seminars and memoranda.3

  4. 1954

    RAND Corporation · Santa Monica

    Issued Differential Games I on 30 November.4

  5. 1965

    Published Differential Games after a long interval following the RAND work.5

  6. 1967–1977

    Johns Hopkins University · Baltimore

    Held a professorship until retirement in December 1977.6

  7. 1981

    Johns Hopkins Hospital · Baltimore

    Died on 18 January.6

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

Here we approach the subject through its applications.

Differential Games I: Introduction, 19547

A story

A delayed book

Isaacs wrote his main RAND reports in 1954–55. Breitner traces the eventual book to a 1963 teaching fellowship that gave him time to assemble the theory.5

Around Isaacs

  • built on the work John von Neumann The first memorandum explicitly begins from von Neumann and Morgenstern’s theory of strategy.7

Recorded as advisor Edward Kasner Recorded as students Richard Worsham Mathematics Genealogy Project record

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

Two desks

Isaacs and Pontryagin Controlling motion when objectives compete. The same problem from two desks → Isaacs and Krasovskii Guaranteed outcomes in continuous pursuit. The same problem from two desks →

The card in the book

Mathematician who received his doctorate from Columbia University. At the RAND Corporation in the early 1950s he founded the theory of differential games and developed it systematically in a series of research memoranda — pursuit and evasion, the Main Equation now read as the Hamilton–Jacobi–Isaacs equation, dominance regions, and worked examples such as the homicidal chauffeur and the guarding of a territory — published a decade later as a book. He later worked in industry and defence analysis and taught at Johns Hopkins University.

Main works Differential Games (1965); the RAND research memoranda Differential Games I–IV (1954–55).

To read further

Sources (7)
  1. Differential Games I: Introduction, Rufus Isaacs, 1954; pp. 1–6
  2. Rufus Isaacs, INFORMS History and Traditions; Biography
  3. Rufus Philip Isaacs and the Early Years of Differential Games, Michael H. Breitner, 2003; §§2–3
  4. Differential Games I: Introduction, Rufus Isaacs, 1954; Title and p. 1
  5. Rufus Philip Isaacs and the Early Years of Differential Games, Michael H. Breitner, 2003; §4, pp. 20–21
  6. Rufus Philip Isaacs and the Early Years of Differential Games, Michael H. Breitner, 2003; §4, p. 21
  7. Differential Games I: Introduction, Rufus Isaacs, 1954; p. 1

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.