ut fn examples

# ut fn examples - ORIE 4350 Game Theory March 13, 2012 Two...

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1 ORIE 4350 Game Theory March 13, 2012 Two examples of lotteries and utility functions. Example 1 illustrates the 4 axioms (Binmore calls them postulates ) for von Neumann- Morgenstern utility functions from pp. 121-123: Axiom 1: A rational player prefers whichever of two win-or-lose lotteries offers the larger probability of winning. Axiom 2: For a rational player each prize between the best prize W and the worst prize L is equivalent to some lottery involving only W and L. Axiom 3: Rational players don’t care if a prize in a lottery is replaced by another prize that they regard as equivalent to the prize it replaces. Axiom 4: R ational players care only about the total probability with which they get each prize in a compound lottery. (Essentially, this axiom allows us to replace compound lotteries by simple lotteries.) Example 1: (cf. Exercise 4.11 from Binmore) A rational person’s preferences satisfy L < D 1 < D 2 < W . In accordance with Axiom 2 the person regards each of D 1 and D 2 to be equivalent to lotteries whose only prizes are W or L . The appropriate lotteries in this case are given below (we probably found them by

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## ut fn examples - ORIE 4350 Game Theory March 13, 2012 Two...

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