Dtheory[1]

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Unformatted text preview: •  Winning is worthless •  Suppose you start with  ­$1M •  EU(gamble) ­EU(do_nothing)=+4.9*10 ­5 •  Gambling is raHonal because losing doesn’t hurt 7 Convexity & Gambling •  Convexity: f (αx + (1 − α ) y ) ≤ αf ( x ) + (1 − α ) f ( y ) 0 ≤ α ≤ 1 •  Suppose x and y are in the convex region of the uHlity funcHon and are possible outcomes of a bet € •  Current cash on hand is x<z<y •  Suppose bet has 0 expected change in monetary value: z = αx + (1 ­α)y •  Will the bet be accepted? •  UHlity of doing nothing: f(z) •  UHlity of accepHng the bet: αf(x)+(1 ­α)f(y) MulHahribute UHlity FuncHons •  So far, we have defined uHlity over states •  As always, there are too many states •...
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This note was uploaded on 02/17/2012 for the course COMPSCI 170 taught by Professor Parr during the Spring '11 term at Duke.

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