Game theory's recognition

When Nobel prizes were started, they were also meant to ease financial constraints for recipients. It wasn't quite anticipated that recipients would have to attain venerable ages, when financial crunches become a non-issue.

Indeed, Peter Doherty, the Australian co-winner of the Medicine Prize in 1996, has a beginner's guide to Nobel prizes, in which he advocates lifestyles that increase life expectancy. That is good advice, because the winners of the 2005 Bank of Sweden prize (not strictly Nobel Prize) in Economics are Robert Aumann and Thomas Schelling. The former was born in 1930, the latter in 1921. Schelling's book The Strategy of Conflict was published in 1960, and there was a subsequent book in 1978. Most of Aumann's significant work was done in the 1970s and the 1980s.

This is not the first time game theory has been recognised. The 1994 awardees (John Harsanyi, John Nash, Reinhard Selten) also worked on game theory, the book and the film A Beautiful Mind, based on Nash's life, having done quite a bit to popularise game theory.

The 2005 citation states that Aumann and Schelling are being recognised "for having enhanced our understanding of conflict and cooperation through game-theory analysis". Game theory is really mathematics, although economics, much more than other social sciences, has adopted and adapted it. By training, Aumann is a mathematician, while Schelling is an economist.

Although the origins of game theory can be traced further back, the substantive origin is accepted to be John von Neumann and Oskar Morgenstern's 1944 book, Theory of Games and Economic Behavior.

Morgenstern was an economist, but von Neumann was a mathematician. All games involve strategic inter-dependence, where one agent's pay-off depends not only on that agent's choice, but also on what others do.

Notwithstanding the name, which originated because of initial analysis of parlour games, there is nothing trivial about game theory. Depending on the number of players, games are divided into 2-person and n-person, 'n' being more than two.

There are cooperative games and non-cooperative ones. There are games with perfect (or complete) information and ones without. There are games against nature. There are one-shot games and repeated ones.

After Neumann-Morgenstern and the Nash extension, there is no further theoretical interest in non-cooperative games, although they are used for modelling. Cooperative games are not only more interesting, they have no unique theory. For instance, the Aumann-Maschler (Michael Maschler) approach is an alternative to Neumann-Morgenstern.

While Aumann is more of a theoretician and Schelling more of a practitioner, both addressed similar questions. When games are played repeatedly, why is there cooperation in some cases and conflict in others?

An obvious application, though not the only one, of Schelling's work is the arms race, where an agent can gain by choosing an apparently inferior option. For instance, uncertain retaliation is more efficient than certain retaliation. Aumann extended the then existing theory by focusing on infinitely repeated games. Repetition, contrasted with one-shot games, often encourages cooperation. Game theory is more of an approach, rather than a unique answer, to any situation involving strategic inter-dependence, firm behaviour, trade theory or reactions of nation states.

Aumann and Schelling never worked together. But other than their common interest in game theory, what unites them is their extension of our understanding of cooperative games. If a lot of game theory has now passed into everyday jargon, that reflects its relevance and Aumann and Schelling have been recognised for making game theory relevant.