Game Theory :: The mathematics of games

Game theory is a distinct and interdisciplinary approach to the study of human behavior. The disciplines most involved in game theory are mathematics, economics and the other social and behavioral sciences. Game theory (like computational theory and so many other contributions) was founded by the great mathematician John von Neumann. The first important book was The Theory of Games and Economic Behavior, which von Neumann wrote in collaboration with the great mathematical economist, Oskar Morgenstern. Certainly Morgenstern brought ideas from neoclassical economics into the partnership, but von Neumann, too, was well aware of them and had made other contributions to neoclassical economics.

A Scientific Metaphor

Since the work of John von Neumann, “games” have been a scientific metaphor for a much wider range of human interactions in which the outcomes depend on the interactive strategies of two or more persons, who have opposed or at best mixed motives. Among the issues discussed in game theory are

1) What does it mean to choose strategies “rationally” when outcomes depend on the strategies chosen by others and when information is incomplete?

2) In “games” that allow mutual gain (or mutual loss) is it “rational” to cooperate to realize the mutual gain (or avoid the mutual loss) or is it “rational” to act aggressively in seeking individual gain regardless of mutual gain or loss?

3) If the answers to 2) are “sometimes,” in what circumstances is aggression rational and in what circumstances is cooperation rational?

4) In particular, do ongoing relationships differ from one-off encounters in this connection?

5) Can moral rules of cooperation emerge spontaneously from the interactions of rational egoists?

6) How does real human behavior correspond to “rational” behavior in these cases?

7) If it differs, in what direction? Are people more cooperative than would be “rational?” More aggressive? Both?

Thus, among the “games” studied by game theory are

Bankruptcy
Barbarians at the Gate
Battle of the Networks
Caveat Emptor
Conscription
Coordination
Escape and Evasion
Frogs Call for Mates
Hawk versus Dove
Mutually Assured Destruction
Majority Rule
Market Niche
Mutual Defense
Prisoner’s Dilemma
Subsidized Small Business
Tragedy of the Commons
Ultimatum
Video System Coordination

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