Suppose you start with c dollars

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Unformatted text preview: 5 12 11.5 11 10.5 10 9.5 9 0 200000 400000 600000 800000 1e+006 5 UHlity of Money •  U(money) should drop slowly in negaHve region too •  If you’re solvent, losing $1M is prehy bad •  If already $10M in debt, losing another $1M isn’t that bad •  UHlity of money is probably sigmoidal A Sigmoidal Utility Function 1 U($ X ) = 100 1 + 2  ­0.00001X 100 € 100*(1/(1+2**(-(0.00001*x)))) 80 60 40 20 0 -1e+006 -500000 0 500000 1e+006 6 UHlity & Gambling •  Suppose U($X)=X, would you spend $1 for a 1 in a million chance of winning $1M? •  Suppose you start with c dollars: •  EU(gamble)=1/1000000(1000000+(c ­1))+(1 ­1/1000000)(c ­1)=c •  EU(do_nothing)=c •  StarHng amount doesn’t maher •  You have no expected benefit from gambling Sigmoidal UHlity & Gambling •  Suppose: U($ X ) = 100 1 1 + 2  ­0.00001X •  Suppose you start with $1M •  EU(gamble) ­EU(do_nothing)= ­5.7*10 ­7 ...
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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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