Reinhard Selten was born in Breslau, Germany (now Wroclaw, Poland) in 1930. His childhood cannot have been easy: his father’s Jewish origins meant that the family business had to be sold in the mid-1930s and his father passed away a few years later. He had to leave school at 14 and the family became refugees at the end of the Second World War before settling in what was to become West Germany. Selten was then able to complete his school education, developing a pronounced taste for mathematics. He remembers first reading about game theory while still at school. Selten attributes a youthful interest in politics and consequently economics to his experiences ‘as a member of an officially despised minority’ before and during the war (Nobel Foundation, 2004). Selten enrolled as a student of mathematics at the Johann-Wolfgang-Goethe University of Frankfurt in 1951, and was awarded an MA by the university in 1957. He obtained his PhD, also in mathematics, from the same institution in 1961.

After completing his master’s degree, Selten took up a post as research assistant at Frankfurt until 1967 when he moved for a year to the United States as visiting professor at the University of California, Berkeley. He returned to Frankfurt in 1968 where his Habilitation thesis in economics gave him the permission required to teach in German universities (the thesis was published as a book – Selten, 1970). Since then he has held posts in three institutions. From 1969 to 1972 he was professor at the Free University of Berlin, and from 1972 to 1984 professor at the University of Bielefeld. In 1984 he became Professor of Economics at the Rheinische Friedrich- Wilhelms University of Bonn. Since 1996 he has been head of the Laboratorium für experimentelle Wirtschaftsforschung at the University of Bonn.

Selten is a fellow of the Econometric Society and was president of the European Economic Association in 1997. He is a member of the Nordrhein-Westfalische Akademie der Wissenschaften, an honorary member of the American Economic Association and a foreign honorary member of the American Academy of Arts and Sciences. He holds honorary degrees from a number of universities and in 2000 he won the Prize of the State of North-Rhine Westfalia. In 1994 Selten was awarded the Nobel Memorial Prize in Economics, together with John Harsanyi and John Nash, ‘for their pioneering analysis of equilibria in the theory of non-cooperative games’ (Nobel Foundation, 2004).

As noted in the entries in this volume for John Harsanyi and John Nash, game theory is concerned with analysing interactions between individuals where decision making by each party takes into account the choices made by others. This kind of interaction is common in economics and other branches of social science. The first modern treatment of game theory in economics was John von Neumann and Oskar Morgenstern’s Theory of Games and Economic Behaviour (1944). This study focused on cooperative zero-sum twoperson games. Subsequently, John Nash introduced the more widely applicable concept of a non-cooperative finite game where there is no communication between players, and identified what has become known as Nash equilibrium – a set of optimal strategies for all parties from which, accordingly, no participant has an incentive to deviate.

Although Nash equilibrium is probably the most innovative concept in game theory (we noted in the entry for Harsanyi his and Selten’s acknowledgement of their debt to Nash – see Kuhn et al., 1996), it raised some interesting new problems, one of which was solved by Selten. This is the issue of superfluous or ‘unreasonable’ Nash equilibria that Selten demonstrated could be removed by the application of more stringent equilibrium conditions (Royal Swedish Academy of Sciences, 1995). His approach here was to emphasise the significance of games in extensive form; that is, where attention is explicitly paid to the timing of moves and to the knowledge of players when they move (Gul, 1997). Before Selten’s initial interventions (Selten, 1965a; 1965b), games in extensive and strategic or normal form (where players select their actions simultaneously given expectations about the strategies of others) were thought to be equivalent; Selten suggested that they were not (van Damme and Weibull, 1995). His argument turned on the principle that only credible threats should be taken into account as a game in extensive form unfolds. For example, a threat by a large country to engage in unilateralist protectionist trade policy in the face of rising import penetration might not be credible if the costs of such protection in the form of possible retaliatory action by those smaller countries it discriminates against are potentially high. This may constitute a Nash equilibrium as the emptiness of the threat is perceived by all players and it is not carried out. However, if the threat is credible then, as the large country’s optimal strategy is to protect and the small countries perhaps perceive that it is in their interests to tolerate the protection, this too is a Nash equilibrium. Selten’s point is that relevance of equilibria turns on the credibility of threats and the solution is always ‘self-enforcing’ (van Damme and Weibull, 1995, p. 24).

Selten (1975) labels such equilibria ‘subgame perfect’, where subgame refers to a stage in a game that is a game in itself. The Royal Swedish Academy of Sciences (1995, p. 5) called Selten’s innovation ‘the most fundamental refinement of Nash equilibrium’ and notes its application to the analysis of economic policy, oligopoly and the economics of information. Selten (1975) further refined the criteria for Nash equilibria by introducing the concept of ‘trembling-hand’ perfection. This allows for the possibility that players may make small mistakes in extensive form games. In our example, the credible threat of protection by the large country remains its optimal choice only if the smaller countries tolerate it. If they were to (mistakenly) retaliate, the large country’s protection strategy would no longer be optimal. A Nash equilibrium is trembling-hand perfect if it is able to accommodate the probability of such small mistakes. This work has been applied in industrial organisation theory and macroeconomics (Royal Swedish Academy of Sciences, 1995).

Selten’s Nobel citation also acknowledges his work in evolutionary games (with Peter Hammerstein), see Selten and Hammerstein (1984; 1994), as well as experimental game theory, see, for example, Selten (1990), Selten and Stoecker (1986); Selten et al. (1997). Selten (1978) is a noted paper on entry deterrence. His books include one on equilibrium selection with his fellow Nobel Laureate, John Harsanyi (Harsanyi and Selten, 1988a); Selten (1988b) addresses the notion of bounded rationality. Many of Selten’s most important papers have been collected together in two volumes in Selten (1999).

**Main Published Works**

(1965a), ‘Spieltheoretishe Behandlung eines Oligopolmodells mit Nachfragetragheit – Teil I Bestimmung des dynamischen Preisglieichgewichts’, Zeitschrift für die gesamte Staatswissenschaft, 121, pp. 301–24. (1965b), ‘Spieltheoretishe Behandlung eines Oligopolmodells mit Nachfragetragheit – Teil II Eigenschaften des dynamischen Preisglieichgewichts’, Zeitschrift für die gesamte Staatswissenschaft, 121, pp. 667–89. (1970), Preispolitik der Mehrprodukttenunternehmung in der statischen Theorie, Berlin: Springer- Verlag. (1975), ‘Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games’, International Journal of Game Theory, 4, pp. 25–55.

(1978), ‘The Chain Store Paradox’, Theory and Decision, 9, April, pp. 127–59.

(1984), ‘Gaps in Harley’s Argument on Evolutionary Stable Learning Rules and in the Logic of “Tit for Tat”’ (with P. Hammerstein), The Behavioural and Brain Sciences, 7 (1), pp. 115– 16.

(1986), ‘End Behaviour in Sequences of Finite Prisoners’ Dilemma Supergames’ (with R. Stoecker), Journal of Economic Behavior and Organization, 7 (1), pp. 47–70.

(1988a), A General Theory of Equilibrium Selection in Games (with J.C. Harsanyi), Cambridge, MA: MIT Press.

(1988b), Models of Strategic Rationality, Theory and Decision Library, Series C: Game Theory, Mathematical Programming and Operations Research, Dordrecht: Kluwer.

(1990), ‘Bounded Rationality’, Journal of Institutional and Theoretical Economics, 146, December, pp. 649–58.

(1994), ‘Game Theory and Evolutionary Biology’ (with P. Hammerstein), in R.J. Aumann and S. Hart (eds) Handbook of Game Theory, Vol. 2, Amsterdam: Elsevier Science, pp. 929– 93.

(1997), ‘Duopoly Strategies Programmed by Experienced Players’ (with M. Mitzkewitz and G.R. Uhlich), Econometrica, 65, May, pp. 517–55.

(1999), Game Theory and Economic Behaviour: Selected Essays, 2 vols, Cheltenham, UK and Northampton, MA, USA: Edward Elgar.

**Secondary Literature**

Gul, F. (1997), ‘A Nobel Prize for Game Theorists: The Contributions of Harsanyi, Nash and Selten’, Journal of Economic Perspectives, 11, Summer, pp. 159–74.

Kuhn, H.W., J.C. Harsanyi, R. Selten, J.W. Weibull, E. van Damme, J.F. Nash Jr and P. Hammerstein (1996), ‘The Work of John Nash in Game Theory’, (Nobel Seminar, 8 December 1994), Journal of Economic Theory, 69, April, pp. 153–85.

Royal Swedish Academy of Sciences (1995), ‘The Nobel Memorial Prize in Economics 1994’, Scandinavian Journal of Economics, 97 (1), pp. 1–7.

van Damme, E. and J.W. Weibull (1995), ‘Equilibrium in Strategic Interaction: The Contributions of John C. Harsanyi, John F. Nash and Reinhard Selten’, Scandinavian Journal of Economics, 97 (1), pp. 15–40.