7.5 Bayesian decision theory
7.5.1 The elements of game theory
Only a very brief account of this important topic is included here; readers who want to know more should begin by consulting Berger (1985) and Ferguson (1967).
The elements of decision theory are very similar to those of the mathematical theory of games as developed by von Neumann and Morgenstern (1953), although for statistical purposes one of the players is nature (in some sense) rather than another player. Only those aspects of the theory of games which are strictly necessary are given here; an entertaining popular account is given by Williams (1966). A two-person zero-sum game has the following three basic elements:
A statistical decision problem or a statistical game is a game coupled with an experiment whose result x lies in a sample space and is randomly distributed with a density ...
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