a game theory–based analysis of search engine non–neutral behavior

7/31/2019 A game theorybased analysis of search engine nonneutral 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
http://find/http://goback/


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Contents

Model and neutral case

Non-neutral model

Neutral vs. non-neutral model

Conclusions
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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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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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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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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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Contents


Non-neutral model


Conclusions

Model and neutral case Non neutral model Neutral vs non neutral model Conclusions
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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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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)



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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)

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Contents


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)

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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

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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

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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)

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Contents


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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a game theory–based analysis of search engine non–neutral behavior

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