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
Leon A. Petrosyan, 2007

Chapter 3 · Bargaining, Commitment, and Repeated Cooperation

Leon A. Petrosyan

born 1940

Photograph: Leon petrosyan, Robert Aumann and Leon Petrosyan, 2007, Wikimedia Commons, CC BY-SA 4.0. Shown toned and cropped. File and licence

The problem on the desk

A cooperative agreement may look attractive initially yet unravel as a dynamic game proceeds. Petrosyan’s question was how to distribute its benefits so that continuing cooperation remains acceptable at later decision points.R1

A life in moments

  1. 1940

    Leningrad

    Born on 18 December.2

  2. 1957

    Yerevan State University · Yerevan

    Began university study before transferring to Leningrad.2

  3. 1965

    Leningrad State University · Leningrad

    Defended a candidate dissertation on a class of pursuit games.3

  4. 1972

    Leningrad State University · Leningrad

    Defended his doctoral dissertation.4

  5. 1975

    Leningrad State University · Leningrad

    Was first elected dean of the applied mathematics and control faculty.4

  6. 1993

    His monograph on differential pursuit games appeared in English.4

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

Unfortunately the classical cooperative game theory considers cooperation as one-shot interaction between the decision makers

Time-consistency of cooperative solutions, 2006 (Nikolay A. Zenkevich and Leon A. Petrosjan)5

A story

From pursuit to cooperation over time

His early research, guided by Nikolai Vorobyev, concerned pursuit games. Later he investigated why cooperative solutions taken from static games could lose their stability during a continuing interaction.3

Around Petrosyan

  • co-author Nikolay Zenkevich Co-authored the 2006 working paper on time-consistent cooperative solutions.1

Recorded as advisor Nikolai Nikolaevich Vorobiev Recorded as students Vladimir Mazalov, Nikolai Zenkevich, Elena Parilina 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 at Leningrad, later Saint Petersburg, State University, where he long led the Faculty of Applied Mathematics and Control Processes and its department of game theory and statistical decisions. He worked on differential games of pursuit and on dynamic cooperative games, and introduced the requirement that a cooperative solution be time-consistent, together with the imputation distribution procedure that implements it.

Main works “Stability of solutions in differential games with many participants” (in Russian, Vestnik Leningrad University, 1977); Differential Games of Pursuit (1993); Cooperative Stochastic Differential Games, with D. W. K. Yeung (2006).

To read further

Sources (5)
  1. Time-consistency of cooperative solutions, Nikolay A. Zenkevich and Leon A. Petrosjan, 2006; Authors’ abstract; working paper 815, Saint Petersburg State University
  2. Leon Aganesovich Petrosyan: seventieth birthday, Vestnik of Saint Petersburg University, editorial anniversary article, 2011; p. 147
  3. Leon Aganesovich Petrosyan: seventieth birthday, Vestnik of Saint Petersburg University, editorial anniversary article, 2011; pp. 147–148
  4. Leon Aganesovich Petrosyan: seventieth birthday, Vestnik of Saint Petersburg University, editorial anniversary article, 2011; p. 148
  5. Time-consistency of cooperative solutions, Nikolay A. Zenkevich and Leon A. Petrosjan, 2006; Abstract, second sentence; excerpt; co-authored with Nikolay Zenkevich

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.