12 Decision Theory and Games

The models so far assumed that the data are known. Most decisions are taken without knowing what will happen: how large demand will be, whether a competitor will cut prices, whether a test will succeed. Decision theory chooses among actions whose outcomes depend on an uncertain state of nature, with or without probabilities for the states, and values the information that would reduce the uncertainty. When the uncertainty comes from an opponent who chooses deliberately, the problem becomes a game, and for two-person zero-sum games von Neumann’s minimax theorem, which turns out to be LP duality in another form, gives a complete solution.

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