Signal Processing - January 2016 - 48

400
200
0

0.6
20

0.8
Signal Quality (p)

1 40

High-Quality Restaurant's Customers

Low-Quality Restaurant's Customers

600

Deal Price (c)

600
400
200
0

0.6

Signal Quality (p)

× 104
6
4
2
0
40

0.6

Deal Price (c)

0.8
0 1

1 40

Deal Price (c)

(b)
High-Quality Restaurant's Revenue

Low-Quality Restaurant's Revenue

(a)

0.8

× 104
6
4
2
0
40

0.6
20

Signal Quality (p)
Deal Price (c)

(c)

0.8
0 1
(d)

Signal Quality (p)

[FIG13] a new restaurant's strategy: the number of customers choosing the restaurant with (a) low quality and (b) high quality and the
result of the revenue of the (a) low-quality and (b) high-quality restaurants.

average utility, which is the average review rating customers
can obtain. A comparison was made between the decision-learning method, denoted as learning with negative network externality, and that which does not consider negative network
externality, denoted as learning without negative network
externality. Note that the former considers the interplay
between the learning and decision making, while the latter only
considers the learning of system state but totally ignores the
influence among customers' decision making. The results are
shown in Figure 12(b). One can see that by combing learning
with negative network externality, the proposed method can
achieve much better utility for customers.
We further study the best pricing and promotion strategy of
a new restaurant under the Chinese-restaurant-game framework. Let us consider two restaurants. One is always of high
quality, and the other is a new restaurant, which could be of low
or high quality. The same utility function trained from the real
data in the above experiment is used to infer the strategy. The
results are shown in Figure 13. One can see that if the new restaurant is of low quality, then the number of customers

choosing the new restaurant decreases as signal quality
increases and vice versa. One can also see that the optimal deal
price of the high-quality restaurant is higher than that of the
low-quality restaurant. Therefore, the high-quality restaurant
should make every effort to increase the signal quality, while the
low-quality restaurant should hide the quality information and
use a low deal price to attract customers to increase the revenue. This offers a vivid example of using data to learn and come
out with an optimal strategy.
EXTENSION TO THE CHINESE-RESTAuRANT-GAME FAMILy
We have discussed the Chinese-restaurant game under a fixed
population setting, i.e., there are a finite number of customers
choosing the tables sequentially. However, in some applications,
customers may arrive and leave the restaurant at any time,
which results in the dynamic population setting. Examples
include cloud storage service selection, deal selection on Groupon, and Wi-Fi access point selection in a conference hall [35].
In such a case, the utilities of customers will change from time
to time because of the dynamic number of customers on each

IEEE SIGNAL PROCESSING MAGAZINE [48] jANuARy 2016

Table of Contents for the Digital Edition of Signal Processing - January 2016