REPRESENTATION OF E-COMMERCE INTERACTIONS BY

MEANS OF A GAME THEORY MODEL

Adoption of the Trust

Cosimo Birtolo, Giuseppina Russo and Davide Ronca

Poste Italiane S.p.A. – Tecnologie dell’Informazione, RS - Centro Ricerca e Sviluppo, 80133 Napoli, Italy

Keywords:

Trust, e-Commerce, Game Theory, Recommendation System, Collaborative Filtering.

Abstract:

In this paper, we investigated the application of trust in an e-Commerce system. In a B2C scenario of an

e-Commerce system, a game model is proposed in order to investigate the best strategies for merchants and

customers. Preliminary investigation outlines the beneﬁts of trust information in the proposed game and

preliminary results, conducted on a transactional database, shows an increased value of sensitivity of provided

recommendations to the customers, entailing an higher customer loyalty. Future works are aimed at validating

this ﬁndings by means of a larger real dataset.

1 INTRODUCTION

The concept of trust is related to the research in many

ﬁelds, including computer science, cognitive science,

economics, sociology and psychology. Trust is a com-

plex concept, and different deﬁnitions of trust there

exist.

In general, trust is a directional relationship be-

tween two parties that can be called trustor and

trustee. In the e-Commerce domain, trust is applied

to a speciﬁc purpose, such as mutual trust between

the customers and the sellers or in a customer-based

perspective if the seller is trustworthy. In particular,

according to the customer’s point of view, it is pos-

sible to distinguish two scenarios: (i) if the customer

can rely on the seller suggestions when he does not

know exactly what product to buy or (ii) if the cus-

tomer can consider seller trustworthy when he wants

to buy a speciﬁc item.

Webs of trust are networks through which a trust-

aware system can ask a user to evaluate other users

already known. For example, Epinions suggests to

put in a user’s web of trust “those reviewers whose

reviews and ratings resulted to be extremely useful”.

Online interpersonal relations are becoming one of

the major characteristics of the Web 2.0, and are

also useful for social aspects (MySpace, Msn, Face-

book), working connections (LinkedIn) and informa-

tion (Slashdot.org, Epinions.com) besides, obviously,

commercial purposes (eBay.com, Amazon.Com).

This paper proposes a game theoretic trust-based

recommendation system. The proposed approach is

based on the adoption of trust information in rec-

ommendation system in order to improve the qual-

ity of suggestions, entailing a more faith on the e-

Commerce platform.

Game theory provides a formal mathematical

framework for modeling and deﬁning strategies for

a set of common problems and has been proposed

by different recent studies as a foundation for quan-

titative and theoretical analysis of different problems

(Oza, 2006; Shiva et al., 2010).

The remainder of this paper is organized as fol-

lows: Section 2 introduces trust and social norms,

Section 3 describes the strategy for suggesting prod-

ucts to the customers, Section 4 models the problem

by means of game theory, Section 5 describes the pro-

posed strategy, Section 6 provides preliminary results,

and Section 7 outlines conclusions and future direc-

tions.

2 TRUST AND SOCIAL NORMS

Do online trust systems contribute to trade goods?

This question is answered by several research anal-

ysis of existing systems. Among the different studies,

Resnick and Zeckhauser (Resnick and Zeckhauser,

2002) have analyzed the feedback rating system used

in eBay as a reputation system. They deﬁned that a

trust system must meet three challenges: (i) provide

577

Birtolo C., Russo G. and Ronca D..

REPRESENTATION OF E-COMMERCE INTERACTIONS BY MEANS OF A GAME THEORY MODEL - Adoption of the Trust.

DOI: 10.5220/0003962605770582

In Proceedings of the 8th International Conference on Web Information Systems and Technologies (WEBIST-2012), pages 577-582

ISBN: 978-989-8565-08-2

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

information that allows buyers to distinguish between

trustworthy and non-trustworthy sellers (ii) encourage

sellers to be trustworthy, and (iii) discourage partici-

pation of those who are not.

According to Liu (Liu and Shi, 2010) trust and

reputation management research is highly interdisci-

plinary, involving researchers from networking and

communication, data management and information

systems, e-commerce and service computing, artiﬁ-

cial intelligence, and game theory, as well as the so-

cial sciences and evolutionary biology.

2.1 Social NBorms

According to a common deﬁnition: “a norm exists in a

given social setting to the extent that individuals usu-

ally act in a certain way and are often punished when

seen not to be acting in this way” (Lim et al., 2008).

Recent studies have proven how homogeneous so-

cial norms may arise in heterogeneous societies con-

sisting of groups with competing interests.

An important norm that has been found to per-

vade human societies for repeated interactions is reci-

procity norm. Indeed, people use reciprocity norms

even in very short time-horizon interactions (Mui

et al., 2002). Reciprocity norms refer to social strate-

gies consisting in reacting to the positive actions of

others with positives responses and in reacting to the

negative actions of others with negative responses.

Several reciprocity strategies have been proposed

in literature, the most famous of which is the tit-for-tat

strategy which has been studied within the Prisonerss

Dilemma game. This strategy entails a cooperation if

the other participants have cooperated and a defection

if the other players have defected. To sum up, reci-

procity is viewed as a social norm shared by agents in

a society.

This social norm could be very useful in the e-

Commerce domain where among different elements

that characterize customer-behavior, past actions of

other customers and feedback of stranger users are

also taken into account.

In an environment such as Web, where individu-

als “regularly” perform reciprocity norms, there is an

incentive to acquire a reputation for repeated actions.

3 RECOMMENDATION SYSTEM

Recommendation systems are aimed at helping users

in the search of interesting items among a large set of

items within a speciﬁc domain by using knowledge

about user’s preferences in the domain.

So that, based on users interests, preferences,

hobbies and online behaviors, recommender systems

model the relationship between users and items and

help customers to select items from a set of choices,

deciding what products to buy, in order to ﬁt their

tastes. Typically recommendations can be generated

on the basis of user interaction history or on the his-

tory of related users.

In other words, Recommendation System is a way

for improving personalization by giving personalized

suggestions.

Recently, recommendation systems have largely

been adopted in different domains: almost every

e-Commerce site (e.g., Amazon) has its own rec-

ommendation engine; different Web site are focus-

ing on suggesting a personalized content such as a

movie (e.g., MovieLens and Netﬂix) or a song (Ya-

hoo!Music). Therefore, different kinds of recom-

mender systems are implemented, from simple ones,

that only recommend items according to statistics, to

complex ones, that use several different approaches

and recommendation techniques.

Recommendation systems were introduced in

1992 by means of the Tapestry project (Goldberg

et al., 1992). Several different approaches have re-

cently been proposed in order to increase the accu-

racy of the predicted values, thus minimizing the pre-

diction error and improving the quality of the rec-

ommendation while taking into account performance

issues. However, some issues related to the qual-

ity of recommendations and to computational aspects

still arise because collaborative systems rely solely on

users preferences to make recommendations. Among

recommendation techniques, Collaborative Filtering

has gained great success in the practical application

of e-Commerce (Adomavicius and Tuzhilin, 2005)

and has been proven to be one of the most suc-

cessful techniques. CF algorithms are divided into

two categories: Memory-Based Collaborative Filter-

ing and Model-Based Collaborative Filtering. In gen-

eral, Memory-based algorithms are aimed at ﬁnding a

group of users with similar tastes and producinga pre-

diction for the active user by means of the entire user-

item database. In contrast, model-based algorithms

use the user-item database to infer a model which is

then applied for predictions.

Model-based CF algorithms, such as Clustering

CF, address this problem by providing more accurate

predictions for sparse data as conﬁrmed by (Huang

and Yin, 2010) and by (Birtolo et al., 2011) who

proved with their experimentation the beneﬁts of

clustering-based CF algorithms.

Once it is deﬁned what items to consider, a predic-

tion p

(u) for the active user u is generally evaluated

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by:

(u) = ¯r

∑

j∈W

sim(i, j) · (r

(u) − ¯r

)

∑

j∈W

|sim(i, j)|

(1)

where r

(u) is the rating given to item j by the user

u, ¯r

is the average rating given to item i, sim(i, j) is

a similarity function between item i and item j, and

is the set of items belonging to the same cluster of

item i.

Recent works proved some beneﬁts in terms of an

increased quality of suggestions, by including trust in-

formation in recommendation systems (Liu and Yuan,

2010). These arising systems are called Trust-based

Recommendation Systems (TRS) (Massa and Avesani,

2007; Zarghami et al., 2009) and combine the poten-

tialities of a traditional recommendation system with

a trust-aware system. The major problems of a TRS

are the time necessary to explicitly deﬁne the on-

line relations among users and, ﬁrst and foremost, the

small number of social links deﬁned by users them-

selves, aspect that leads to a scarce quality of rec-

ommendations. The second problem, instead, is cur-

rently investigated and enhancing user trust seems to

be a challenging task. Different cultures, different

habits and different preferences complicate this prob-

lem and data are often unavailable (Huberman et al.,

2005).

4 MODELING E-COMMERCE

INTERACTIONS BY MEANS OF

GAME THEORY

In this paper, in order to study the trust in the e-

Commerce system, a model of relationship between

a customer and a merchant is proposed.

Observing the dynamics of user behavior when he

interacts with e-Commerce platform or when he looks

for an item to buy, a model of this problem according

to game theory is outlined.

The studied game is depicted in Fig.1. At the be-

ginning of the game, the merchant M selects an item i

within a given catalogue and he proposes this item to

the customer C.

If the customer decides not to buy the proposed

item, the game ends. In this case, the merchants pay-

off is 0 and the customers payoff is a.

On the other hand, if the customer chooses to

buy the product, this choice yields a merchants pay-

off equals to a, while the customers payoff b can

range within the interval b

..b

, assuming b

as the

Figure 1: The game model.

worst case (i.e., the item does not satisfy the cus-

tomer), while b

as the best case (i.e., the item sat-

isﬁes the customer). Throughout we shall assume

1 ≤ b

≤ a ≤ b

Assuming a 1-to-5 scale of user feedback (n = 5),

we have 5 different payoffs for a customer who buys

the proposed item. Tab.1 illustrates the payoff ma-

trix for the different possible outcomes, the couple

(x,y) represents the payoff of customer and merchant

respectively, while e

..e

are the customer’s possi-

ble strategies (e

: “the customer buy the proposed

item” and e

: “the customer do not buy the proposed

item”) and f

.. f

are the merchant’s possible strate-

gies (f

: “the merchant proposes an item which the

customer consider strongly unsatisfactory”... f

: “the

merchant proposes an item which the customer con-

sider strongly satisfactory”).

Table 1: The payoff matrix of the proposed game model.

Merchant

Customer f

,a) (b

,a)

(a,0) (a,0) (a,0) (a,0) (a, 0)

The proposed game is non-cooperative because

each player chooses a strategy independently and

non-zero-sum (see Tab.1), indeed a merchant’s gain

does not necessarily imply customer’s loss.

The best strategy for both customer and merchant

is investigated above, proving the beneﬁts if trust is

taken into account.

4.1 Parameters of the Proposed Model

The merchant’s payoff a, according to cost of the

suggested item ranges from 1 (“very low cost”) to 5

(“very high cost”). While the customer’s payoff b is

equal to r, which is the rating expressed by the cus-

tomer after his evaluation of the purchased item.

REPRESENTATIONOFE-COMMERCEINTERACTIONSBYMEANSOFAGAMETHEORYMODEL-Adoptionof

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The ratings r are integer numbers on a 1(“bad”)-

to-5(“excellent”) scale. In other words, the cus-

tomer’s payoff ranges from [1,5], 1 being the worst

result and 5 the best.

Extending this model, it is possible to consider

also a different deﬁnition of the customer’s payoff.

For instance, b could be deﬁned as a convex combi-

nation of a and r, in order to take into account the

intrinsical value of item that decreases its initial value

once it is bought; so that the customer’s payoff is de-

ﬁned as:

b = σ· a/2+ (1− σ) ·r (2)

where σ ∈ [0,1], while a is divided by 2 because we

assume that an item decreases its initial value of 50%

once it was bought. In this study, we assume b = r.

4.2 Best Strategies

Values of a and b inﬂuence the best strategies. In any

case, the best strategy for merchant is to sell his item

(obtaining a payoff a), while for customer is to buy if

a = b

and not to buy if a = b

. In other cases, two

main factors inﬂuence customer’s decision: (i) value

of a, (ii) expectation to obtain an item which complies

with his preferences.

Assuming that a user has a positive payoff if the

bought goods satisfy his taste, we have 0 < b

< b

< a < b

< b

. Looking at the payoff matrix

(see Tab.1), the strategy proﬁles (e

, f

) and (e

, f

)

are Nash Equilibrium pairs and (e

, f

) is Pareto-

dominant.

If the game is played once, the merchant can select

an item without taking into account customer’s pref-

erences, while repeating the game different times, dif-

ferent strategies occur. Customer can change his strat-

egy according to his past experience. For instance he

can adopt a reciprocity strategy. While merchant must

take into account user feedback in order to ensure a

positive interaction and to increase the customer loy-

alty.

5 ASSISTING THE SELECTION

OF THE STRATEGY BY MEANS

OF TRUST MEASURE

Best strategies are based on the products’ sale and on

user satisfaction, so that two main problems have to

be addressed:

• Improving the quality of merchants’ suggestions

by taking into account user preferences

• Enhancing user trust on the willingness of a par-

ticular merchant and on the quality of personal-

ized suggestions

In literature, the selection of personalized item in

order to guarantee user satisfaction is addressed by

means of recommendationsystems. Even if these sys-

tems are widely adopted on the web, some issues re-

lated to the quality of recommendation and to compu-

tational aspects still arise, so that in the last ten years

several approaches have been proposed.

Trust can considered as a remarkable element in-

ﬂuencing a user’s decision making. It represents the

level of trust that a user has toward the recommen-

dation source. The concept of trust includes both the

cognitive and the emotional dimensions. Trust-based

Recommendation System uses the social ties estab-

lished among online users. Even though these online

ties are not established with the explicit aim of fa-

voring the advice taking, recommender systems can

use them to connect a user with a source of relevant

information. In order to take into account trust in-

formation in suggestions, we proposed the following

approaches:

1. Deﬁning an index of homophily

between users in

order to promote some suggestions and penalize

other ones.

2. Promoting suggestion by analyzing experience of

users close to the active one, not only by taking

into account similar rating but also considering

their demographical information such as cultural

background and nationality (customer closeness

metric). This information is useful in order to take

into account similar habits.

The ﬁrst proposed approach introduce and index

of homophily h(u,v) between item u and item v in

order to emphasize trustworthy information which

come from a subset of trusted users. This index is

calculated according to the Eq. 3.

h(u,v) =

max(α,k)

min(β,k)

·t (3)

where t is the trust component and α and β are two

parameters (α < β), so that when k > β, h(u,v) = k/α

greater than 1 (positive homophily) and when k < α,

h(u,v) = k/β lesser than 1 (penalty of correlation

between items or a negative homophily because few

users have evaluated in the same way the two items).

For instance assuming α = 2 and β = 5, when k < 2

we have:

h(u,v) =

max(2,k)

min(5,k)

·t < t

Homophily can be deﬁned as similarity in knowledge

and preferences between two users

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when k > 5 we have:

h(u,v) =

max(2,k)

min(5,k)

·t > t

Adopting the index of homophily means to mod-

ify prediction function of a standard recommender

system, so that the prediction of a rating p of item

i for the user u is expressed by Eq. 4.

(u) = ¯r(u) +

∑

v=1

h(u,v) · sim(u,v) · (r

(v) − ¯r(v))

∑

v=1

|h(u,v) · sim(u,v)|

(4)

where r

(u) is the rating given to item i by the user u,

¯r(u) is the average rating given by the user u, sim(u, v)

is a similarity function between user u and user v, V

is the set of users with proﬁle of interest similar to the

target user u.

While according to the second approach, close-

ness information is adopted, this means to restrict the

cluster of user to those very close to the active one,

so that prediction of a rating p of item i for the active

user u expressed by Eq. 1 is updated by:

(u) = ¯r

∑

j∈T

sim(i, j) · (r

(u) − ¯r

)

∑

j∈T

|sim(i, j)|

(5)

where T

⊆ W

because T

is a selection of users ac-

cording to the customer closeness metric.

From merchant point of view, by adopting trust-

based recommendation system the quality of rec-

ommendation should increase, while from customer

point of view, by understanding the motivation of sug-

gestion and by incorporating trustworthy information

the customer loyalty should increase and so the buy-

ing or a repeated buying of items should be encour-

aged.

6 EXPERIMENTAL RESULTS

In our experimentation we consider a transactional

database of a real e-Commerce platform of Poste Ital-

iane. The dataset consists of 2,406 ratings for 477

items rated by 1,878 users; we assume equals to 5

the rating of a repeat customer purchase, while equals

to 4 a single purchase. According to related litera-

ture (Herlocker et al., 2004) we consider as interest-

ing item

i for the user u , an item which user u have

rated by 4 or 5, while not interesting the other ones.

For the experimentation we consider a subset en-

suring at least a ﬁxed number s of ratings per user

(s = 5). The resulting subset is made of 107 items and

is randomly divided into a training set (80% of the rat-

ings per user) and a testing set (20% of the ratings per

user). Starting with the training set recommendation

algorithms predict unknown ratings, while the testing

set is used to evaluate the accuracy of the predictions.

Different methods can be adopted to calculate the

similarity of items or users. Generally, sim(i, j) = 1

when i = j, while in other cases sim(i, j) indicates the

similarity between item i and item j. According to the

literature (Birtolo et al., 2011; Jeong et al., 2010), we

adopt Pearson correlation similarity between items i

and j deﬁned as:

sim(i, j) =

∑

u∈U

(u) − ¯r

)(r

(u) − ¯r

)

∑

u∈U

(u) − ¯r

)

∑

u∈U

(u) − ¯r

)

(6)

where ¯r

is the average rating of item i (m is the num-

ber of users):

¯r

∑

l=1

(l)

In order to evaluate the predicted rating we con-

sider the Eq.5. We measure the true positive rate or

sensitivity deﬁned as the probability that an item will

be interesting for users when he wishes to buy it.

The adoption of trust in recommendation sys-

tem rather than the standard recommendation system

(memory-based collaborative ﬁltering) improve the

number of predicted interesting items. Sensitivity of

the proposed trust-based recommendation system is

equals to 77,876%, while for a traditional item-based

collaborative ﬁltering is equals to 43.363%. The val-

ues are justiﬁed by the cold-start issues related to the

low number of users who rated a signiﬁcative number

of products. Indeed, in order to make accurate recom-

mendations, the system must ﬁrst learn the users pref-

erences from their ratings, so that if the users rated

few items the recommendation could be unsuitable.

Moreover, new items or items not rated by a substan-

tial number of users (cold-start items) could rarely or

never be recommended.

7 CONCLUSIONS AND FUTURE

WORKS

Trust as a multidisciplinary ﬁeld can beneﬁt from

careful integration and exploitation of advances in

artiﬁcial intelligence, game theory, distributed com-

puting, information systems, knowledge discovery,

knowledge modeling, engineering, social sciences,

and economics. The more Internet applications in-

crease the more trust systems could play an important

REPRESENTATIONOFE-COMMERCEINTERACTIONSBYMEANSOFAGAMETHEORYMODEL-Adoptionof

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581

role in establishing effective cooperation among dis-

tributed Internet application participants.

In this paper we presented a game theoretic trust-

based recommendation system. Our approach is

based on the adoption of trust information in recom-

mendation system in order to improve the quality of

suggestions, thus identifying the best strategy for the

game model proposed. To sum up, the main con-

tributions of this paper are: (i) the representation of

e-Commerce interactions by means of a game the-

ory model, (ii) the proposal of the best strategy by

means of the adoption of trust information, and (iii)

the modeling of a trust-aware recommendation sys-

tem by means of an integration between similarity,

which is evaluated according the customer proﬁle of

interest, and the proposed trust metrics.

In future, we aim at investigating two main direc-

tions. The ﬁrst is to extend the approach presented

here in order to ﬁnd the experimentalevidencethat the

proposed model can provide beneﬁts (e.g., increased

proﬁts for merchants or increase customer surplus) in

a large real dataset of Poste Italiane. Furthermore,

user information regarding age, sex, occupation, and

geographical information with the provided feedback

related to some products are available so that exper-

imenting deeper the different trust model could con-

ﬁrm the beneﬁts of the proposed approach.

The second direction will examine how to ﬁnd

out multi-player scenario, indeed in e-Commerce do-

main online shopping is becoming more and more

widespread and represents an everyday activity for

many. In this actual scenario, we will analyze the pro-

posed game model when it is executed with different

players, several customers and several merchants at

the same time. Moreover, we will highlight new aris-

ing issues and investigate the best strategy.

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