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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online