Page 174 - Artificial Intelligence for the Internet of Everything

160 Artificial Intelligence for the Internet of Everything

E (V | b)

0.25

0.20

0.15

0.10

0.05
b
0.5 1.0 1.5 2.0
Fig. 9.6 EðVjbÞ 0 when the company knows the cost, L¼ U½0,2Š and C¼ U½0,1Š.

We note with interest that EðVjbÞ is a (once) differentiable function on
[0, 2] (Fig. 9.6).
In Example 9.2, EðVjbÞ has a maximum value of 9/32 when b ¼ 5/4,
which is the same as Howard’s base example.
We see that when the company knows the cost C,the distribution
and not just the mean, it affects the behavior of EðVjbÞ.Wealsosee that
knowledge of C guarantees that EðVjbÞ 0. That is, the company never
loses money.

9.6 CLAIRVOYANCE ABOUT L

Now we are in the situation where the company knows the competitor’s
lowest bid, which is represented by L.Asbeforeweassumethatifthe
company’s bid b ties with the competition’s lowest bid l that the company
wins the contract. If we know l we bid l; this bid is placed to win the
contract and maximize profit. Note, if one finds this result disturbing,
we can always make the bid b a tiny amount less than l.Nonetheless,
we therefore see that B and L must be thesame. Thecompany will
always win the bidding, but it may lose money depending on the value
of c.Therefore,

(9.25)
EðVjbÞ¼ EðVjlÞ