Information Technology Reference
In-Depth Information
Using Bayes' rule we determine the posterior probability:
c i ) P ( c i )
i =1 p (np
p (np
|
P ( c i |
i =1 ,
···
,N
np) =
(2)
|
c i ) P ( c i )
We then define the N-dimensional vector, whose components are the posterior proba-
bilities from the GMM,
η (np) = [ P ( c 1 |
np) ,P ( c 2 |
np) ,...,P ( c N |
np)]
(3)
and for each normalized price np j we compute η (np j ) which is η evaluated at the np j
price. We cluster these collections of vectors using k-means. The center of each cluster
corresponds to regime R k for k =1 ,
,M ,where M is the number of regimes.
Figure 3 shows the cluster centers, which correspond to regimes, for the low market
segment. The figure shows only some of sample points for better visualization.
···
P(c|R 1 )
P(c|R 2 )
P(c|R 3 )
1
0.8
0.6
0.4
0
0.2
0.2
0.4
0
0.6
0
0.2
0.8
0.4
0.6
0.8
P(c 1 |np)
1
1
P(c 2 |np)
Fig. 3. K-means clustering applied to the posterior probability P ( c| np) in the low market segment
We distinguish three regimes, namely over-supply ( R 1 ), balanced ( R 2 ), and scarcity
( R 3 ). Regime R 1 represents a situation where there is a glut in the market, i.e. an over-
supply situation, which depresses prices. Regime R 2 represents a balanced market sit-
uation, where most of the demand is satisfied. In regime R 2 the agent has a range
of options of price vs sales volume. Regime R 3 represents a situation where there is
scarcity of products in the market, which increases prices. In this case the agent should
price close to the customer reserve price - the maximum price a customer is willing to
pay.
The number of regimes was selected a priori, after examining the data and looking
at economic analyses of market situations. Both the computation of the GMM and k-
means clustering were tried with different initial conditions, but consistently converged
Search WWH ::




Custom Search