Anatol Rapoport

Anatol Rapoport

Introduction

Anatol Rapoport (May 22, 1911 to January 20, 2007) was a Russian-born American mathematical psychologist who moved between mathematics, biology, psychology and political science without ever settling in one of them. He is best known for two things that pull in opposite directions: he supplied the Tit for Tat program that won Robert Axelrod's celebrated prisoner's dilemma tournaments, and he spent much of his career arguing that game theory was a poor guide to real conflicts. Alongside that he was a founder of general systems theory, a pioneer of mathematical biology, and after 1970 one of the most prominent academic peace researchers in North America.

Rapoport trained first as a concert pianist and conductor, took a doctorate in pure mathematics, and only then drifted into psychology. That sequence is unusual even by the standards of mid-century interdisciplinary science, and it shaped a working style built on formal models that he was always willing to abandon when they failed to describe what people actually did.

Early Life and Education

Rapoport was born in Lozova, then in Kharkov Governorate of the Russian Empire and now in Kharkiv Oblast, Ukraine, into a secular Jewish family. The family emigrated to the United States in 1922 and settled in Chicago; he became a naturalized citizen in 1928.

He began studying music in Chicago and continued with piano, conducting and composition at the Vienna Hochschule für Musik from 1929 to 1934, earning a diploma in piano, composition and conducting from what the University of Toronto archives record as the Staatsakademie für Musik und darstellende Kunst. He performed in Austria, Poland, Hungary and Italy and wrote for the journal Musical Courier. The rise of Nazism closed off a performing career in Europe, and he later concluded that he could not make a living as a pianist in North America either.

He switched to mathematics at the University of Chicago, the home of Nicholas Rashevsky's mathematical biology group. Sources differ on his formal supervision: the University of Chicago record and Wikipedia credit the algebraists Otto Schilling and Abraham Adrian Albert, while the University of Toronto finding aid places him with Rashevsky. He received his Ph.D. in 1941 with a dissertation titled Construction of Non-Abelian Fields with Prescribed Arithmetic — abstract algebra with no obvious connection to anything he later became known for.

According to The Globe and Mail, he was a member of the American Communist Party for about three years and quit before enlisting in the U.S. Army Air Forces in 1941, serving in Alaska and India during the Second World War. He was never caught up in McCarthy-era purges, an outcome that surprised many of his Chicago colleagues.

Academic and Professional Career

After demobilization in 1946 he taught mathematics at the Illinois Institute of Technology, then joined the Committee on Mathematical Biology at the University of Chicago in 1947, where he stayed until 1954. His first scientific papers, on mathematical models of parasitism and symbiosis, appeared in the Bulletin of Mathematical Biophysics in 1947, and his first book, Science and the Goals of Man, written with the semanticist S. I. Hayakawa, followed in 1950.

A year at the Center for Advanced Study in the Behavioral Sciences at Stanford in 1954 was the turning point. There he was introduced to the prisoner's dilemma, and there the Society for General Systems Research was organized; Rapoport co-founded it in 1954 with Ludwig von Bertalanffy, Ralph Gerard and Kenneth Boulding, and served as its president in 1965. He edited the yearbook General Systems from 1956 to 1977.

From 1955 to 1970 he was professor of mathematical biology and senior research mathematician at the University of Michigan and a founding member, in 1955, of its Mental Health Research Institute. The Michigan years produced Fights, Games, and Debates (1960), Strategy and Conscience (1964), Prisoner's Dilemma (1965, with A. M. Chammah), Two-Person Game Theory (1966) and N-Person Game Theory (1970).

In 1970 he moved to the University of Toronto during the Vietnam War, explaining that he wanted to live in a country that was not committed to a messianic role. He was appointed professor of mathematics and psychology, a post he held until 1979 (the Toronto archives give his retirement as 1976, followed by visiting posts at the Institute for Advanced Studies in Vienna, the Wissenschaftszentrum in Berlin, Hiroshima and Louisville). Toronto named him professor emeritus in 1980, after which he directed the Institute for Advanced Studies in Vienna until 1983, and then appointed him professor of peace studies in 1984, a position he held until 1996 while continuing to teach until 2000. In 1984 he co-founded Science for Peace and served as its president, remaining on its executive until 1998. He died of pneumonia in Toronto at 95.

Major Contributions to Psychology

Experimental games and Tit for Tat

Rapoport was among the first researchers to use experimental games as instruments rather than as illustrations. Working with Chammah, he ran long series of iterated prisoner's dilemma sessions with human pairs and documented something the theory said should not happen: people cooperate, at rates far above zero, and they learn to do so conditionally. Prisoner's Dilemma (1965) reported that behaviour in detail at a time when most game theorists worked purely axiomatically.

His best-known result came in 1980, when he entered Axelrod's first computer tournament with a four-line program. Tit for Tat cooperates on the first move and thereafter copies whatever the opponent did on the previous move. It won both of Axelrod's tournaments and became, through Axelrod's The Evolution of Cooperation, the standard illustration of how cooperation can get started among self-interested agents.

The critique of strategic rationality

What is less often remembered is that Rapoport thought game theory had been put to dangerous use. Strategy and Conscience (1964) was a direct answer to Herman Kahn and to Thomas Schelling's The Strategy of Conflict. His argument was that rationality in a non-zero-sum game is not unique: what is rational for one player considered alone is not rational for the pair considered together, and the formal apparatus cannot adjudicate between the two standpoints. Applied to nuclear strategy, he held that the framework's empirical requirements simply could not be met and that strategic enterprises built on it were largely ritual.

Schelling replied that Rapoport wanted to redefine rationality so that cooperation came out as rational even when individual incentives ran the other way, and that it would be foolish to assume others will act from conscience. Rapoport's counter was narrower and harder to dismiss: game theory, taught as a description of rational conduct, instructs people that acting with moral scruples is irrational.

Systems theory, contagion and peace research

Before game theory, Rapoport built stochastic models of contagion — of disease, of information, of rumour — and worked on the mathematics of social networks and of parasitism. In peace research he argued that the nuclear arms race could not be modelled as a two-person game at all, and he developed what he called debates as a distinct category from fights and games: interactions aimed at changing an opponent's mind rather than defeating them.

Major Publications

  • Science and the Goals of Man (with S. I. Hayakawa), 1950
  • Fights, Games, and Debates, 1960
  • Strategy and Conscience, 1964
  • Prisoner's Dilemma (with A. M. Chammah), 1965
  • Two-Person Game Theory, 1966
  • N-Person Game Theory, 1970
  • The Big Two, 1971
  • Conflict in Man-made Environment, 1974
  • Semantics, 1975
  • Mathematical Methods in the Social and Behavioral Sciences, 1984
  • The Origins of Violence, 1989
  • Peace: An Idea Whose Time Has Come, 1993
  • Certainties and Doubts: A Philosophy of Life, 2001

He published roughly twenty books. Article counts diverge by source: the University of Toronto finding aid says more than 400 published articles, while Wikipedia and encyclopedic entries say over 300.

Impact and Legacy

Tit for Tat travelled well beyond psychology, into economics, evolutionary biology, political science and animal behaviour, and Rapoport's insistence on testing game-theoretic predictions with real subjects helped create experimental economics. His peace research gave the University of Toronto one of the first degree programs in the field, and Science for Peace remains active. The philosopher Mario Bunge called him a polymath who used mathematics to attack real problems rather than to obscure them.

His legacy also carries a substantial body of criticism, much of it aimed at the simplified version of Tit for Tat that circulates in textbooks. Tit for Tat is brittle: in a noisy environment a single misread move triggers an unbroken echo of mutual defection, which is why later work in Axelrod's own framework and after it favoured contrite or win-stay-lose-shift variants. The tournament itself is routinely over-interpreted — Tit for Tat did not beat most of its opponents head to head, it accumulated the highest average score across a field of fourteen entries, and a single round-robin among submitted programs is not evidence about how cooperation evolves.

There is a second line of criticism, and it comes from Rapoport's own side of the argument. Strategists answered Strategy and Conscience by pointing out that they used many tools besides game theory and that the critique of a formal model lands only weakly on the practice it supposedly underwrites. Within peace studies he was sometimes dismissed as a moralist: his own allies note that his opposition to deterrence was attacked as moral repugnance rather than engaged as an argument about non-unique rationality.

Finally, his constructive proposal for intellectual disagreement has outlived the disputes that prompted it. Daniel Dennett popularized "Rapoport's rules" for criticizing an opponent: restate the other position so clearly that its holder thanks you, list the points of agreement, acknowledge what you learned, and only then rebut.

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Last updated: 2026-10-20

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