A game theory–based analysis of search engine non–neutral behavior
Transcript of A game theory–based analysis of search engine non–neutral behavior
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
A game theorybased analysis of searchengine nonneutral behavior
Luis Guijarro
1
Vicent Pla
1
Bruno Tuffin
2
PatrickMaille3 Pierre Coucheney2
1Universitat Politecnica de Valencia, Spain
2INRIA, France
3Telecom Bretagne, France
NGI 2012, Karlskrona, June 2012
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
Contents
Model and neutral case
Non-neutral model
Neutral vs. non-neutral model
Conclusions
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
General model
Users who access content
by using the search engine
One content provider,
which provides paidcontent to the users
The search engine, which
helps the users in locating
the content at the contentprovider
UsersSearch
Engine
Content
Provider
p
q
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
Neutral case
There is no side payment from the CP to the SE
Users D(p) = 0(D0 d p)
D represents the number of users subscribing
to the CP p is the flat-rate price charged by the CP d represents the user sensitivity to the price 0 is the probability that the content is located
by the SE and therefore accessed by the user D0 is the maximum potential level of demand
C
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
Neutral case
Content provider c = D p
the CP does not incur costs
Search engine SE
= D
the SE does not charge any usage-based
price to the CP additional revenue from sponsored links,
assumed proportional to Di.e., satisfied
users more willing to use the SE again
M d l d t l N t l d l N t l t l d l C l i
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
Solution
Given parameters D0, 0, d and , the CP is the only agent in
the model. It will charge a price p(n)
so as to maximize itsprofits c. The FOC
cp
= 0
will yield:
p(n) =D02d
D(n) =0D02
(n)c =
02
D204d
(n)SE
=0D02
Model and neutral case Non neutral model Neutral vs non neutral model Conclusions
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
Contents
Model and neutral case
Non-neutral model
Neutral vs. non-neutral model
Conclusions
Model and neutral case Non neutral model Neutral vs non neutral model Conclusions
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
Model
The effect of the side payment will be two-fold: Paying q to the SE will increase the chances that the
content is located and accessed by the users. We model
this effect through an increasing 1(q).
The more the SE charges to the CP, the less the userstrust the search results and the less likely they will use the
SE. We model this reputation effect through a decreasing
2(q).
Thus, we need a probability (q) = 1(q)2(q).
We will assume that (0) = 0
if CP does not pay any charge to the SE, then the model
comes down to the neutral case.
Model and neutral case Non-neutral model Neutral vs non-neutral model Conclusions
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Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
General solution
D(p,q) =(q)(D0 d p)
c =D (p q)
SE =Dq+ D.
Given () and parameters D0, d, and , the CP and the SEinteract strategically and non-cooperatively in order to
maximize their respective profits. The FOCs are
cp =(q)(D0 2dp+ dq) = 0
SEq
=(D0 dp)
(q+ )
(q)
q+ (q) 1
= 0
Model and neutral case Non-neutral model Neutral vs non-neutral model Conclusions
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Model and neutral case Non neutral model Neutral vs. non neutral model Conclusions
General solution
CP profit maximization yields p(nn) = D0/2d+ q/2.
SE profit maximization at q put the following constraints on
(q)
(q) +
q(q+ ) =
> 0 if 0 < q< q,
0 if q= q,
< 0 if q> q,
and(q) (0)
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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Model and neutral case Non neutral model Neutral vs. non neutral model Conclusions
Particular solution
We propose
1(q) =
1
1 0q+ 1
2(q) =1
q+ 1
Note that:
(0) = 0 1
the maximum is reached at
q= 1 20. Therefore,the restriction (q) (0)imposes that 0 < 1/2
1 0.5 0 0.5 1 1.5 2 2.5 33
2.5
2
1.5
1
0.5
0
0.5
1
0=0.33
q
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Particular solution
The solution to the game is
q =0 + (1 20)
2 + 0.
The constraint (q) > 0 imposes that
> 2 + 0
1 20
and from q and p(nn)
D(nn) =(q)(D0 d p(nn))
(nn)c =D
(nn) (p(nn) q)
(nn)SE
=D(nn)q + D(nn)
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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Contents
Model and neutral case
Non-neutral model
Neutral vs. non-neutral model
Conclusions
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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Profits
(nn)c >
(n)c iff C2
D0d
>q
1
0
,
(nn)SE
> (n)SE
iff C3 D0
d> q
1 +q0
.
We have that
(nn)c > (n)c (nn)SE > (n)SE
(1)
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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User welfare
For given values of qand pwe compute the (average) benefit
that users make by finding and subscribing to the serviceoffered by the CP, as the product of D0 times (q) times theaverage user benefit from using the service given its price p
UW(p, q) = D0(q)D0/dw=0 d/D0[w p]
+
dw
=1
2d
D2(p,q)
(q)
where x+
= max(0, x). The above expression is applicable toboth the neutral and non-neutral cases. It is easy to check that
UW(nn) > UW(n) (nn)c >
(n)c
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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On the conditions C2 and C3
C2 is the most
constraining condition
There is a wide range of
values for D0/d and suchthat C3 holds but C2 does
not, i.e., where the SE is
better off but both the CP
and the users are harmedwith a non-neutral SE
2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
D0
/d>*
C2(0= 0.1)
C3(0= 0.1)
C2(0= 0.2)
C3(0= 0.2)
C2(0= 0.35)
C3(0= 0.35)
Thresholds for conditions C2 and C3
to hold, for 0 = 0.1, 0.2, 0.35
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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On the values of c, SE and UW
For low values of 0, all
stakeholders are better offin the non-neutral case
As 0 increases, the firststakeholders to be harmed
are the users and the CP 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450
10
20
30
40
50
60
0
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0
2
4
6
8
10
12
c
n
c
nn
SE
n
SE
nn
UWn
UWnn
c, SE and UW for neutral and
non-neutral cases (D0/d= 6, = 8)
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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Contents
Model and neutral case
Non-neutral model
Neutral vs. non-neutral model
Conclusions
Model and neutral case Non-neutral model Neutral vs. non-neutral model Conclusions
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Conclusions
Under certain conditions, a side payment by the contentprovider to the search engine is beneficial for all stakeholders,
since:
the users are better off, which means that the improvement
achieved by the increase in the likeliness to find thecontent compensates for the increase in the content price;
the CP benefits from a better visibility, allowing it to
increase the subscription price to cover the payments to
the SE;
and the SE benefits from the increase in either the demand
or the side payment, or in both.
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