The same problem, two schools
Two desks
The book's thesis is that the schools of game theory are different approaches to the same problems. Here are seven pairs who met one problem at different desks. Each desk is dated and sourced. What each knew of the other is stated only as far as the record goes, and the comparison of approaches is a reading, marked as such.
Kantorovich and Koopmans
1938–1939 · Leningrad · Leningrad University / plywood production problem
Studied production allocation and resolving multipliers.
Leonid Vital’evich Kantorovich (on his seventieth birthday), p. 232
1942 · Washington, D.C. · British Merchant Shipping Mission
Studied cargo routing and its cost.
Tjalling Charles Koopmans, Biographical Memoirs 67, p. 275; pp. 280–282
What is documented
Correspondence is documented from 1956; earlier awareness remains unestablished here.
Still open. No dated record of their first knowledge of each other’s work has been found.
Leonid V. Kantorovich, Brief Biography, paragraph on correspondence with Koopmans in 1956
How the approaches differ Factory allocation and multipliers contrast with shipping routes and associated prices. R
Leonid Vital’evich Kantorovich (on his seventieth birthday), 37(3), pp. 229–238; Tjalling Charles Koopmans, Biographical Memoirs 67, p. 275; pp. 280–282
Different starting problems do not by themselves prove independent discovery.
Isaacs and Pontryagin
1954 · Santa Monica · RAND
Published the first Differential Games research memorandum.
Differential Games I: Introduction, RM-1391, 30 November 1954; pp. 1–6
mid-1950s · Moscow · Steklov Mathematical Institute
Developed the maximum principle with his collaborators.
On the history of discovery of the maximum principle, Abstract; pp. 1–7
What is documented
Isaacs later described an independent start and learning of control theory while completing his book. Pontryagin discusses and cites Isaacs’s 1965 book in a paper received on 8 April 1966: awareness on his side by 1966, not its first date.
Still open. The first date of awareness on Pontryagin’s side is not established.
Rufus Philip Isaacs and the Early Years of Differential Games, pp. 20–22; retrospective statement by Isaacs; К теории дифференциальных игр [On the theory of differential games], Uspekhi Matematicheskikh Nauk 21:4(130), pp. 219–274: introduction p. 219 explicitly discusses Isaacs’s 1965 book, which is reference 2 on p. 274
How the approaches differ Isaacs studied opposing controls; the maximum principle first supplied necessary conditions for optimal control. R
Differential Games I: Introduction, RM-1391, 30 November 1954; pp. 1–6; On the history of discovery of the maximum principle, Abstract; pp. 1–7
Isaacs’s recollection is evidence about his account, not proof of permanent mutual ignorance; the mathematical results are not identical.
Isaacs and Krasovskii
1954 · Santa Monica · RAND
Formulated pursuit games through the Main Equation.
Differential Games I: Introduction, RM-1391, 30 November 1954; pp. 1–6
late 1960s–early 1970s · Sverdlovsk · Ural State University / Institute of Mathematics and Mechanics
Developed positional strategies and guaranteed outcomes.
Nikolai Nikolaevich Krasovskii: on his eightieth birthday, p. 5
What is documented
Krasovskii cites the 1967 Russian translation of Isaacs’s Differential Games in a paper received on 6 April 1970: awareness on his side by 1970, not its first date.
Still open. The earliest awareness in either direction, and any awareness of Krasovskii on Isaacs’s side, are not established by the cited record.
О дифференциальной игре сближения [On a differential game of approach], Doklady Akademii Nauk SSSR 193(2), pp. 284–287; p. 287, reference 3 cites R. Isaacs, Differential Games, Moscow, 1967 (Russian translation)
How the approaches differ The comparison contrasts worked pursuit equations with feedback guarantees using stable sets and extremal aiming. R
Differential Games I: Introduction, RM-1391, 30 November 1954; pp. 1–6; Nikolai Nikolaevich Krasovskii: on his eightieth birthday, Trudy IMM 10(2), pp. 3–19; biography pp. 3–5
This describes emphases, not mutually exclusive methods or a proven independent-discovery claim.
Wald and Stratonovich
1941 · New York · Columbia University
Reported his statistical decision-function research.
Columbia: Promotions and Memorial Minute for Abraham Wald, Annex B to the letter of 26 November 1941
1963–1965 · Moscow · Moscow State University
Lectured on information theory and its value.
Theory of Information and its Value: Foreword and Preface, Foreword, pp. vi–ix
Not established
The record cited here does not establish when either first knew of the other’s work.
How the approaches differ Statistical decision rules contrast with bounds on loss reduction under information constraints. R
Columbia: Promotions and Memorial Minute for Abraham Wald, Annex B to 26 November 1941 letter; Memorial Minute for Professor A. Wald; Theory of Information and its Value: Foreword and Preface, Foreword pp. v–xi; Preface p. xiii
This is a conceptual comparison, not a priority claim.
Brier and Savage
1950 · Washington, D.C. · US Weather Bureau
Published a score for probability forecasts.
Verification of Forecasts Expressed in Terms of Probability, Monthly Weather Review 78(1), pp. 1–3; bibliographic record; The First International Statistical Climatology Achievement Award: Glenn W. Brier, Award remarks; 1958 recollection, 1950 scoring paper and 1955 cost/loss paper
1971 · New Haven · Yale University
Published Elicitation of Personal Probabilities and Expectations.
Elicitation of Personal Probabilities and Expectations, JASA 66(336), pp. 783–801; §§1.1–1.2, §2 and §6; Leonard Jimmie Savage Papers, MS 695, Guide compiled January 1974; biography p. 4; drafts p. 56 (current export)
What is documented
Savage reported initial unawareness of predecessors in 1960, but explicitly cited Brier in 1971.
Elicitation of Personal Probabilities and Expectations, p. 783, §1.1
How the approaches differ A quadratic forecast score contrasts with a broader analysis of truthful elicitation. R
Verification of Forecasts Expressed in Terms of Probability, Monthly Weather Review 78(1), pp. 1–3; bibliographic record; Elicitation of Personal Probabilities and Expectations, JASA 66(336), pp. 783–801; §§1.1–1.2, §2 and §6
The 1971 date is publication; it is not the date Savage first conceived elicitation.
Lefebvre and Harsanyi
1967 · Moscow
Published Conflicting Structures.
Vladimir Aleksandrovich Lefebvre, Dated biographical paragraphs and list of publications
1967 · Berkeley · University of California, Berkeley
Published Part I of his Bayesian-games series.
Games with Incomplete Information Played by Bayesian Players, I–III. Part I: The Basic Model, Management Science 14(3), pp. 159–160 and §1
Not established
The record cited here does not establish when either first knew of the other’s work.
How the approaches differ Algebraic self-and-other representations contrast with probabilistic types for games with incomplete information. R
The Cosmism of Lefebvre’s Reflection: a conversation with V. A. Lefebvre, Psychology; Games with Incomplete Information Played by Bayesian Players, I–III. Part I: The Basic Model, Management Science 14(3), pp. 159–160 and §1
Moscow is the book’s publication place, not a verified physical writing desk. Similar questions do not establish an identical theory or influence.
Borel and von Neumann
1921 · Paris · Académie des sciences
Published his first game note.
John von Neumann’s Conception of the Minimax Theorem: A Journey Through Different Mathematical Contexts, Archive for History of Exact Sciences 56, pp. 61–65, sections 6.1–6.2
December 1926 · Göttingen · Mathematical Institute
Presented game-theoretic work.
A History of the Minimax Theorem: von Neumann’s Conception of the Minimax Theorem, IMFUFA 387, §2; von Neumann’s 1928 footnote discussed there
What is documented
Von Neumann’s 1928 footnote dates his awareness of Borel to proofreading.
Still open. Borel’s first awareness date is not established here.
A History of the Minimax Theorem: von Neumann’s Conception of the Minimax Theorem, IMFUFA 387, §2; von Neumann’s 1928 footnote discussed there
How the approaches differ Small symmetric cases contrast with a general finite zero-sum minimax theorem. R
John von Neumann’s Conception of the Minimax Theorem: A Journey Through Different Mathematical Contexts, Archive for History of Exact Sciences 56, pp. 61–65, sections 6.1–6.2
A retrospective priority statement is not independent evidence of complete mutual ignorance.