Signal Processing - January 2016 - 47

3.65
3.6
Yelp Rating

Significant Discount
nt

Limited Offers

Social Network
Tools

3.55
3.5
3.45
3.4

6
2
4
Months After Sucessful Groupon Deal

0

8

EXPERIMENTS WITH REAL DATA
FROM SOCIAL SySTEMS
We use deal selection on Groupon as an example to illustrate
the Chinese-restaurant-game framework. Many have the experiences that some deals on Groupon look good but eventually
turn out to have poor quality because of the overwhelming
number of customers showing up at the same time, i.e., the
negative network externality is at work. By collecting the data
on Groupon and Yelp around the Washington, D.C., area for
eight months, we indeed observe the decline of Yelp review ratings after some successful Groupon deals, as depicted in
Figure 11. One can see a nonlinear decline function in review
ratings. Let us use the real Yelp rating data to train the utility
function of customers by approximating it as a linear model, as
shown in Figure 12(a). Then, based on (8), we evaluate the

3
2.98
2.96
2.94
2.92
2.9
2.88
2.86
2.84
2.82
2.8
2.78

Utility Function Trained from Data
Real Data
Linear Modeling

0

50

200
100
150
Number of Sold Deals
(a)

250

300

3.95
Average Review
Rating of Customer 1~50

With the best-response function, a customer's optimal decision is purely determined by the received signal given the grouping, i.e., the number of customers at each table and the
information revealed by other customers. Therefore, we can partition the signal space into subspaces where within each subspace
the customer will choose a specific table. By integrating the signal over each subspace, we can derive a recursive form of the
probability mass function for the final grouping, i.e., the final
number of customers at each table. With the recursive form of
the final grouping, the expected utility of each customer can be
computed, and the best response of all customers using backward
induction can be derived.
From previous discussions, we can see that the learning and
decision making in the Chinese-restaurant-game framework are
interweaved. On one hand, customers learn the system state from
the information revealed by previous customers for better decision making. On the other hand, the decisions and information
revealed by the customers will affect subsequent customers'
learning and decision-making processes. Moreover, before any
decision making, the utility function in (8) needs to be learned
from the real data.

Average Review Rating

[FIG11] yelp star rating declines after a successful Groupon deal.

3.9
3.85
3.8
3.75
3.7
3.65

2

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6
Lower Restaurant Quality
Learning with Negative Network Externality
Learning Without Negative Network Externality
(b)

[FIG12] (a) utility function modeling using real data from
Groupon and yelp and (b) the performance comparison of our
method with the learning method without negative network
externality.

IEEE SIGNAL PROCESSING MAGAZINE [47] jANuARy 2016
Table of Contents for the Digital Edition of Signal Processing - January 2016
