Agent Technology for e-Commerce. Appendix A: Introduction to Decision Theory Maria Fasli http://cswww.essex.ac.uk/staff/mfasli/ATe-Commerce.htm. Decision theory. Decision theory is the study of making decisions that have a significant impact Decision-making is distinguished into:
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Agent Technology for e-Commerce
Appendix A: Introduction to Decision Theory
Maria Fasli
http://cswww.essex.ac.uk/staff/mfasli/ATe-Commerce.htm
Decision theory is the study of making decisions that have a significant impact
Decision-making is distinguished into:
Probability space
Axioms
L=[p1,o1;p2,o2;…;pn,on]
P(ab)=P(a|b)P(b)
P(a|b)=P(a) and P(b|a)=P(b) or P(ab)=P(a)P(b)
The product rule can be written as:
P(ab)=P(a|b)P(b)
P(ab)=P(b|a)P(a)
By equating the right-hand sides:
This is known as Bayes’ rule
Simple example: to take or not my umbrella on my way out
The consequences of decisions can be expressed in terms of payoffs
Payoff table
Loss table
An alternative representation of payoffs – tree diagram
Payoff table
Payoff table
Loss table
If P(rain)=0.7 and P(not rain)=0.3 then:
ER(carry umbrella) = 0.7(-£1)+0.3(-£1)=-£1
ER(not carry umbrella) = 0.7(-£50)+0.3(-£0)=-£35
EL(carry umbrella) = 0.7(£0)+0.3(£1)=£0.3
EL(not carry umbrella) = 0.7(£49)+0.3(£0)=£34.3
(a) outcome o for certain and
(b) taking a bet or lottery in which it receives o’ with probability p and o’’ with probability 1-p
then u(o)=(p)u(o’)+(1-p)u(o’’)
How can an agent assess a utility function?
u(R+)=1 and u(R-)=0
u(R+) u(R) u(R-) or 1 u(R) 0
u(job-offer) = u(salary) + u(location) +
u(pension package) + u(career opportunities)
u(job-offer) = 0.4u(salary) + 0.1u(location) +
0.3u(pension package) + 0.2u(career opportunities)
But if there are interdependencies between attributes, then additive utility functions do not suffice. Multi-linear expressions:
u(x,y)=wxu(x)+wyu(y)+(1-wx-wy)u(x)u(y)