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
Thomas L. Saaty

Chapter 12 · Simulation and Wargaming with AI Agents

Thomas L. Saaty

1926 – 2017

Photograph: Rozann W. Saaty / Saaty family archives, Thomas L. Saaty, date uncertain, CC BY-SA 3.0, via Wikimedia Commons. Shown toned. File and licence

The problem on the desk

How can a decision-maker compare alternatives when both measurable quantities and qualitative judgments matter? Saaty’s hierarchy decomposes the question, elicits pairwise comparisons and combines the resulting priorities.1

A life in moments

  1. 1926

    Mosul

    Born on 18 July.2

  2. 1953

    Yale University · New Haven

    Completed his doctorate in mathematics.3

  3. 1954

    Operations Evaluation Group

    Joined the group and studied naval-message processing.2

  4. 1969

    Wharton School, University of Pennsylvania · Philadelphia

    Began his university teaching career.2

  5. 1977

    Published on hierarchical priority scaling and an application to transport planning.4

  6. 1979

    University of Pittsburgh · Pittsburgh

    Joined the university.2

  7. 1980

    Published The Analytic Hierarchy Process.4

  8. 2017

    Died on 14 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

Decisions involve many intangibles that need to be traded off.

Decision Making with the Analytic Hierarchy Process, 20086

A story

Beginning with sensitivity

As a student, Saaty spent two summers with Project SCOOP, examining how changes in input data affect linear-programming solutions. His later decision methods grew from a wider operations-research career.5

Around Saaty

Recorded as advisor C. Einar Hille Recorded as students Luis Vargas, David Berman, Peter Blair 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 worked on operations research at the Operations Evaluation Group from 1954, then at the Office of Naval Research from 1959 and, in the 1960s, as a scientific analyst at the Arms Control and Disarmament Agency; his 1968 book set out mathematical models of arms control and disarmament. He taught at the Wharton School from 1969 and at the University of Pittsburgh from 1979, and created the analytic hierarchy process, a method that decomposes a decision problem, compares its elements and synthesises the results into priorities.

Main works Mathematical Methods of Operations Research (1959); Mathematical Models of Arms Control and Disarmament (1968); The Analytic Hierarchy Process (1980).

To read further

Sources (6)
  1. Decision Making with the Analytic Hierarchy Process, Thomas L. Saaty, 2008; International Journal of Services Sciences 1(1), pp. 83–98; author abstract
  2. Thomas L. Saaty, INFORMS History and Traditions; Brief biography and education
  3. Thomas L. Saaty, INFORMS History and Traditions; Education
  4. Thomas L. Saaty: 2008 Impact Prize citation, INFORMS, 2008; 2008 award citation; origins and 1977 applications
  5. Thomas L. Saaty, INFORMS History and Traditions; Early-career paragraph
  6. Decision Making with the Analytic Hierarchy Process, Thomas L. Saaty, 2008; Abstract, first sentence

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.