A few words in grateful remembrance of Reinhard Selten
Reinhard Selten has passed away. The mathematician and economist, who was born in 1930 in Breslau (now part of Poland) and expelled to Western Germany towards the end of the Second World War, was not an obvious candidate for the Nobel prize. Although he went to good German schools, he did not attend one of the top US universities, but studied and taught for many years at the University of Frankfurt, before subsequently teaching in Berkeley (briefly), Berlin, Bielefeld and Bonn. He graduated in mathematics in Frankfurt in 1957 and became an assistant to Heinz Sauermann. In 1961 he completed his PhD on cooperative game theory, an unusual topic at that time, and received his habilitation (a second degree similar to a PhD required in Germany to apply for a professorship) in 1968 with a monography on multiproduct pricing policy.
The work for which Selten won the Nobel Prize in 1994 first appeared in German in two parts in a political economics journal published by Sauermann, which was a renowned journal for political sciences at the time. It bore a rather unwieldy title: "Spieltheoretische Behandlung eines Olbigopolmodells mit Nachfrageträgheit," which can be translated as: "A game theory treatment of an oligopoly model with demand inertia." In his work Selten developed the idea of sub-game perfection, which subsequently revolutionised game theory and economic policy. The basic idea draws on the Bellman principle, the maximum principle of Pontryagin and, in a sense, even the Euler equations, whereby intertemporal planning results in an optimal sequence of conditional decisions that are re-optimization proof: if a previously considered constellation of conditions does actually occur, then the decision maker takes exactly the decision that he had planned for this constellation, although he has no commitment to do so. Selten was the first person to apply this basic principle of rational decision-making to interactions between several decision-makers, who all react rationally to each other. All act according to mutually credible strategies that are re-negotiation proof. Today there are thousands of articles on game theory that are based on this principle.
In economic policy these principles are respected more or less intuitively by good and strategically-thinking politicians. They were applied formally in a theoretical model of optimal intertemporal policy making in 1977, twelve years after Selten, by Finn Kydland and Edward Prescott in their research into the time consistency of economic policy, for which they also received the Nobel prize.
Sub-game perfect decision-making rules have the advantage that they are credible because they are not subsequently called into question. They do not, however, lead to optimal results for participants, as they can only be achieved via binding intertemporal contracts. Every mutual insurance contract, every contract based on reciprocity such as a marriage under old law, or even the EU Treaty, signifies a violation of the rules of sub-game perfection in the sense that it creates a strong incentive to break the rules. An insurer is averse to paying out when damages occur; many marriages end in divorce because a partner no longer seems attractive; and when states are headed towards insolvency, the no bail-out clause of the Maastricht Treaty is violated. A legal system’s effectiveness is shown by the fact that it is in a position to overcome the disadvantages of short-term renegotiations.
Over the years Selten himself moved on from his original idea because he felt that the mathematical requirements for sub-game perfect solutions were too great to correctly mirror real decisions by humans. He increasingly returned to the idea of mankind's restricted rationality from his years with Sauermann, with whom he conducted the first experiments on this topic in Europe. Selten subsequently founded the first so-called "laboratory" on the systematic experimental review of human behaviour. Today many researchers are following in his footsteps in this area too.
Selten spent several years studying the interactive behaviour of animals, chiefly bees, which he described in models and experimentally tested using similar tools to those he applied to humans.
Throughout his life he remained a mathematician far removed from concrete questions of economic policy
Selten was a member of the CESifo network for many years and also used it to publish work based on experiments on human route planning and auction behaviour.
Personally, I had the honour of meeting Selten on several occasions: our first meeting took place decades ago in Bielefeld, where he was the keenest participant in a seminar where I presented an intertemporal equilibrium model that could explain the persistence of vacant land in urban development. Over the years, our exchanges were always fruitful and thought-provoking.
Reinhard Selten advanced economics worldwide and with his passing we have all lost an honourable colleague, a tireless researcher and an inspiring mentor.
Hans-Werner Sinn
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