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CSCI 100
Think Like Computers
Lecture 6
Fall 2008
Is there a winning strategy?
•Bet $1 in the beginning.
•If lose, double the amount next time.
•Does this work?
Exercise: A Decision Problem
•You consider buying a program to manage
your finances that costs $100. There is a
prior probability of 0.7 that the program is
suitable in which case it will have a
positive effect on your work worth $500.
There is a probability of 0.3 that the
program is not suitable in which case it will
have no effect.
Value of information
•Sometimes, an agent must actively gather
information before making a decision
•Using utility theory, an agent can figure out
how much it would be willing to pay for a
piece of information
•Called information value theory
Example
•What is the value of knowing whether the
program is suitable before buying it?
•[0.7*(500-100)+0.3(0)] –
[0.7(500-100)+0.3(0-100)] = 280 - 250
= 30
Another example
•Suppose an oil company is hoping to buy one of
n blocks of ocean drilling rights.
•Exactly one block contains oil worth C dollars.
•The price of each block is C/n dollars.
•If the company is risk-neutral, it will be indifferent
between buying a block or not.
•A seismologist offers the company a survey
indicating whether block #3 contains oil.
•How much should the company be willing to pay
for the information?
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