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 5 · Different Models of One Game

Jean-François Mertens

1946 – 2012

The problem on the desk

What mathematical object can contain a player’s beliefs about the world, beliefs about other players’ beliefs, and further levels? Mertens and Zamir sought a formal space in which these hierarchies close into a Bayesian game.1

A life in moments

  1. 1946

    Born in 1946.2

  2. 1970

    Université catholique de Louvain · Louvain

    Completed his doctorate.3

  3. 1985

    Published the belief-hierarchy construction with Shmuel Zamir.1

  4. 2010

    Louvain-la-Neuve

    Recorded a research interview with Françoise Forges on 6 July.4

  5. 2012

    Died on 17 July.5

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

A formal model is given of Harsanyi’s infinite hierarchies of beliefs.

Formulation of Bayesian analysis for games with incomplete information, 19857

A story

Questions at a CORE workshopS

Eilon Solan recounted a story he had heard: during a 1978–1979 CORE workshop, Abraham Neyman proposed routes beyond the Big Match while Mertens explained their obstacles. Their later collaboration established a general stochastic-game result.6

Not an eyewitness account. The dialogue and precise workshop date remain unconfirmed.

Around Mertens

  • built on the work John C. Harsanyi The Mertens–Zamir abstract explicitly describes its object as Harsanyi’s infinite hierarchies.1
  • co-author Shmuel Zamir Co-authored the 1985 paper on Bayesian analysis of incomplete-information games.1

Advisors in the record José Paris, Jacques Neveu Students in the record Françoise Forges, Srihari Govindan 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 and economist at CORE, the Center for Operations Research and Econometrics in Louvain-la-Neuve, Belgium. With Shmuel Zamir he constructed the universal space of belief hierarchies — foundations for Harsanyi's types under stated assumptions, used in Chapter 0 — and he made fundamental contributions to repeated games and to the theory of equilibrium selection through stable sets.

Main works “Formulation of Bayesian analysis for games with incomplete information”, with S. Zamir (International Journal of Game Theory 14, 1985); “Stable equilibria — a reformulation” (Mathematics of Operations Research, 1989, 1991); Repeated Games, with S. Sorin and S. Zamir (2015).

To read further

Sources (7)
  1. Formulation of Bayesian analysis for games with incomplete information, Jean-François Mertens and Shmuel Zamir, 1985; Authors’ abstract; IJGT 14(1), pp. 1–29
  2. Interview with Jean-François Mertens (1946–2012), Françoise Forges, 2014; Title and editorial introduction
  3. Mathematics Genealogy Project: 199848, Mathematics Genealogy Project; Degree, advisor and student table
  4. Interview with Jean-François Mertens (1946–2012), Françoise Forges, 2014; pp. 1832–1833
  5. Jean-Francois Mertens, 1946–2012, Eilon Solan, 2012; Closing paragraph
  6. Jean-Francois Mertens, 1946–2012, Eilon Solan, 2012; Paragraphs beginning “The story I heard” and “For Abraham Neyman”
  7. Formulation of Bayesian analysis for games with incomplete information, Jean-François Mertens and Shmuel Zamir, 1985; Abstract, first sentence; co-authored with Shmuel Zamir

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.