What Is Game Theory?

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Melvyn Bragg and his guests discuss game theory, the mathematical study of decision-making. First formulated in the 1940s, the discipline entails devising 'games' to simulate situations of conflict or cooperation. It allows researchers to unravel decision-making strategies, and even to establish why certain types of behaviour emerge. Some of the games studied in game theory have become well known outside academia - they include the Prisoner's Dilemma, an intriguing scenario popularised in novels and films, and which has inspired television game shows. Today game theory is seen as a vital tool in such diverse fields as evolutionary biology, economics, computing and philosophy.

Listen to Melvyn Bragg and guests discuss Game Theory on the In Our Time podcast

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John F. Nash Jr. was best known for advances in game theory, which is essentially the study of how to come up with a winning strategy in the game of life — especially when you do not know what your competitors are doing and the choices do not always look promising.

Dr. Nash did not invent game theory; the mathematician John von Neumann did the pioneering work to establish the field in the first half of the 20th century. But Dr. Nash extended the analysis beyond zero-sum, I-win-you-lose types of games to more complex situations in which all of the players could gain, or all could lose.

The central concept is the Nash equilibrium, roughly defined as a stable state in which no player can gain advantage through a unilateral change of strategy assuming the others do not change what they are doing....

Continue reading Kenneth Chang's short article: Explaining a Cornerstone of Game Theory: John Nash's Equilibrium

Further Reading

Consider the following situation: when two hunters set out to hunt a stag and lose track of each other in the process, each hunter has to make a decision. Either she continues according to plan, hoping that her partner does likewise (because she cannot bag a deer on her own), and together they catch the deer; or she goes for a hare instead, securing a prey that does not require her partner’s cooperation, and thus abandoning the common plan. Each hunter prefers a deer shared between them to a hare for herself alone. But if she decides to hunt for deer, she faces the possibility that her partner abandons her, leaving her without deer or hare. So, what should she do? And, what will she do?

Situations like this, in which the outcome of an agent’s action depends on the actions of all the other agents involved, are called interactive. Two people playing chess is the archetypical example of an interactive situation, but so are elections, wage bargaining, market transactions, the arms race, international negotiations, and many more. Game theory studies these interactive situations. Its fundamental idea is that an agent in an interactive decision should and does take into account the deliberations of her opponents, who, in turn, take into account her deliberations. A rational agent in an interactive situation should therefore not ask: “What can I do, given what is likely to happen?” but rather: “What can I do in response to what they do, given that they have a belief about what I will do?” Based on this perspective, game theory recommends rational choices for these situations, and predicts agents’ behavior in them....

Continue reading the Internet Encyclopedia of Philosophy article on Game Theory by Till Grüne-Yanoff

Related Topics

Economics | Mathematics

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