- Person
- Robert Aumann
- Lived
- b. 1930
- Field
- Game theory
- From
- Israeli-American
The story
The Nash equilibrium, named after the mathematician John Nash, describes a situation in which each player's strategy is the best response to the others', with each player choosing independently. It became the central idea of non-cooperative game theory. Robert Aumann, who had first heard about game theory from Nash himself as a graduate student at MIT, asked what happens when players do not choose in isolation, but can condition their choices on a shared random signal, such as a traffic light, or on private recommendations from a trusted mediator.
In 1974 he answered with a new solution concept, the correlated equilibrium. In a correlated equilibrium, an outside device draws a recommended action for each player and tells each player only their own recommendation. The arrangement is an equilibrium if no player can do better by ignoring the suggestion, given that the others follow theirs. Aumann was the first to define the idea, which includes every Nash equilibrium as a special case and is more flexible.
A classic illustration is the game of chicken, in which two drivers each choose whether to dare or to back down. Each wants to dare only if the other backs down, and if both dare, both lose badly. A neutral third party who randomly tells each driver what to do, without revealing the other's instruction, can give both players a higher expected payoff than they could reach with any of the game's Nash equilibria, in which they act on their own.
Correlated equilibria have another practical advantage. They are much easier to compute than Nash equilibria, since finding one only requires solving a linear program. And players who simply adjust their behaviour in response to each other's past play can end up converging to a correlated equilibrium, which made the concept important in later research on learning in games.
The idea helps explain why impartial mediators, giving each side different information, can help adversaries settle disputes, and why simple shared signals can prevent collisions and conflicts. It was one of the contributions that made Aumann a leading figure in game theory, and in 2005 he shared the Nobel Memorial Prize in Economic Sciences with Thomas Schelling for enhancing the understanding of conflict and cooperation.
Why it matters
Correlated equilibrium is now a standard tool in economics and computer science, used in the design of mediation, traffic systems and algorithms for learning in games.
About Robert Aumann
German-born Orthodox Jewish mathematician in Jerusalem whose theory of repeated games showed how cooperation can last between rivals; Nobel Prize in Economics 2005.
More about Robert Aumann
- Robert Aumann co-founded Jerusalem's Center for RationalityAround 1990–91 Robert Aumann helped found the Center for Rationality at the Hebrew University of Jerusalem, a game theory centre drawing members from more than a dozen departments.
- Robert Aumann proved rational people can't agree to disagreeIn his 1976 paper Agreeing to Disagree, Robert Aumann gave the first formal definition of common knowledge and proved that rational people sharing the same starting beliefs cannot agree to disagree.
- A nuclear defence puzzle drew Robert Aumann to game theoryRobert Aumann, trained in pure mathematics, turned to game theory in the 1950s to solve a practical problem: how to defend a city against bombers when most of them are decoys.
- Robert Aumann showed mathematically why cooperation lastsRobert Aumann proved that repeated encounters can make cooperation between rivals rational, work on conflict and cooperation that earned him the 2005 Nobel Prize in Economic Sciences.
- Robert Aumann's game theory served nuclear arms controlIn the mid-1960s Robert Aumann and Michael Maschler developed the theory of repeated games with incomplete information for a US agency preparing arms control talks with the Soviet Union.
- Robert Aumann and Lloyd Shapley analysed games of the manyWith Lloyd Shapley, Robert Aumann wrote Values of Non-Atomic Games in 1974, extending game theory to markets and elections with huge numbers of players and giving rise to the Aumann–Shapley value.
- Robert Aumann trained a generation of game theoristsRobert Aumann's doctoral students at the Hebrew University include Sergiu Hart, Abraham Neyman, David Schmeidler and Yair Tauman, each a leading figure in game theory.
Sources
- Robert Aumann Wikipedia
- Correlated equilibrium Wikipedia
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