# John Harsanyi

## (1920 - 2000)

John Harsanyi was born on May 29, 1920, in Budapest, Hungary. After high school, Harsanyi attended the University of Budapest (today: Eötvös Loránd University). In 1944, Harsanyi was taken captive by the Nazis due to his Jewish origins. On his way to the railway station to be deported to an Austrian concentration camp, Harsanyi escaped and was kept hidden by a Jesuit priest in the cellar of their monestary.

After the war, in 1946, Harsanyi re-enrolled at the University of Budapest to obtain his Ph.D. in philosophy with minors in sociology and psychology. From September 1947 to June 1948, he worked as a faculty member at the University Institute of Sociology, but had to leave because of his anti-Communist views.

On December 30, 1950, Harsanyi escaped from Eastern Europe and the spread of Communism and moved to Sydney, Australia. However, his degrees from Hungary were not acknowledged in Australia, so he attended school at the University of Sydney. In 1953, Harsanyi received his M.A. in economics. He was appointed Lecturer of Economics at the University of Queensland in 1954, but moved in 1956 to Stanford after receiving a Rockefeller Fellowship. It was at Stanford that Harsanyi received his Ph.D. in economics, under the guidance of Kenneth Arrow (Nobel Prize recipient for economics in 1972).

Harsanyi returned to Australia to work at the Australian National University in Canberra. His interest in game theory, however, was not welcomed in Australia and Harsanyi soon came back to the United States to teach economics at Wayne State University in Detroit. Then, in 1964, Harsanyi was appointed Professor at the Business School of the University of California, Berkeley (later extended to the Department of Economics), where he remained until retirement.

Harsanyi published four books on his research of game theory: *Rational Behavior and Bargaining Equilibrium in Games and Social Situations* (1977), *Essays on Ethics, Social Behavior, and Scientific Explanation* (1976), *Papers in Game Theory* (1982), and *A General Theory of Equilibrium Selection in Games* (1988).

He was a member of the National Academy of Science, a Fellow of the American Economic Association, and a Distinguished Fellow of the American Economic Association.

He was awarded the Nobel Prize for Economics in 1994 for his work in game theory. Game theory is the mathematical analysis of human behavoir in competitive situations. Harsanyi contributed to the study of game theory in mathematics by developing the analysis of games of incomplete information. Harsanyi had hoped that game theory would produce more peaceful political institutions and a higher standard of living.

John Harsanyi died on August 9, 2000, at the age of 80.

The following press release from the Royal Swedish Academy of Sciences describes Harsanyi's work:

In games with complete information, all of the players know the other players' preferences, whereas they wholly or partially lack this knowledge in games with incomplete information. Since the rationalistic interpretation of Nash equilibrium is based on the assumption that the players know each others' preferences, no methods had been available for analyzing games with incomplete information, despite the fact that such games best reflect many strategic interactions in the real world.

This situation changed radically in 1967-68 when John Harsanyi published three articles entitled Games with Incomplete Information Played by Bayesian Players, (Management Science 14, 159-82, 320-34 and 486-502). Harsanyi's approach to games with incomplete information may be viewed as the foundation for nearly all economic analysis involving information, regardless of whether it is asymmetric, completely private or public.

Harsanyi postulated that every player is one of several "types", where each type corresponds to a set of possible preferences for the player and a (subjective) probability distribution over the other players' types. Every player in a game with incomplete information chooses a strategy for each of his types. Under a consistency requirement on the players' probability distributions, Harsanyi showed that for every game with incomplete information, there is an equivalent game with complete information. In the jargon of game theory, he thereby transformed games with incomplete information into games with imperfect information. Such games can be handled with standard methods.

An example of a situation with incomplete information is when private firms and financial markets do not exactly know the preferences of the central bank regarding the tradeoff between inflation and unemployment. The central bank's policy for future interest rates is therefore unknown. The interactions between the formation of expectations and the policy of the central bank can be analyzed using the technique introduced by Harsanyi. In the most simple case, the central bank can be of two types, with adherent probabilities: Either it is oriented towards fighting inflation and thus prepared to pursue a restrictive policy with high rates, or it will try to combat unemployment by means of lower rates. Another example where similar methods can be applied is regulation of a monopoly firm. What regulatory or contractual solution will produce a desirable outcome when the regulator does not have perfect knowledge about the firm's costs?

Strategic InteractionGame theory is a mathematical method for analyzing strategic interaction. Many classical analyses in economics presuppose such a large number of agents that each of them can disregard the others' reactions to their own decision. In many cases, this assumption is a good description of reality, but in other cases it is misleading. When a few firms dominate a market, when countries have to make an agreement on trade policy or environmental policy, when parties on the labor market negotiate about wages, and when a government deregulates a market, privatizes companies or pursues economic policy, each agent in question has to consider other agents' reactions and expectations regarding their own decisions, i.e., strategic interaction.

As far back as the early nineteenth century, beginning with Auguste Cournot in 1838, economists have developed methods for studying strategic interaction. But these methods focused on specific situations and, for a long time, no overall method existed. The game-theoretic approach now offers a general toolbox for analyzing strategic interaction.

Game TheoryWhereas mathematical probability theory ensued from the study of pure gambling without strategic interaction, games such as chess, cards, etc. became the basis of game theory. The latter are characterized by strategic interaction in the sense that the players are individuals who think rationally. In the early 1900s, mathematicians such as Zermelo, Borel and von Neumann had already begun to study mathematical formulations of games. It was not until the economist Oskar Morgenstern met the mathematician John von Neumann in 1939 that a plan originated to develop game theory so that it could be used in economic analysis.

The most important ideas set forth by von Neumann and Morgenstern in the present context may be found in their analysis of two-person zero-sum games. In a zero-sum game, the gains of one player are equal to the losses of the other player. As early as 1928, von Neumann introduced the minimax solution for a two-person zero-sum game. According to the minimax solution, each player tries to maximize his gain in the outcome which is most disadvantageous to him (where the worst outcome is determined by his opponent's choice of strategy). By means of such a strategy, each player can guarantee himself a minimum gain. Of course, it is not certain that the players' choices of strategy will be consistent with each other. von Neumann was able to show, however, that there is always a minimax solution, i.e., a consistent solution, if so-called mixed strategies are introduced. A mixed strategy is a probability distribution of a player's available strategies, whereby a player is assumed to choose a certain "pure" strategy with some probability.

**Sources:** Wikipedia; "John Harsanyi Autobiography"; HaasNews; Press Release