Efficient Combinatorial Auction Mechanisms in Electronic Commerce
Tumpa Banerjee
1
, Dinesh Kumar Pradhan
2
and Prasenjit Choudhury
3
1
Department of Computer Application, Siliguri Institute of Technology, Siliguri, India
2
Department of CSE/IT, Dr. B. C. Roy Engineering College, Durgapur, India
3
Department of Computer Application, National Institute of Technology, Durgapur, India
Keywords:
Resource Allocation, Combinatorial Auction, New FixedPrice, New Combinatorial Auction using LinearPro-
gramming (New CA LP), Combinatorial Auction using Greedy, New Combinatorial Auction using Greedy
Approach ( CAGREEDY-MODIFIED).
Abstract:
Electronic commerce or e-commerce is the trading of products or services via internet. The product with little
demand is generally sold in fixed price. However, when the demand of a product is huge, auction mechanism
can be used to maximize the profit. Selling price of some inevitable products like medicine does not depend
on the demand. Auction is the best method for selling products which provide maximum possible profit to
the sellers and the buyers get the product in reasonable price. Today, a large part of e-commerce uses online
auction for selling their products or to provide any service to the worldwide buyers. Winner determination
and payment value calculation of combinatorial auction is a very complex task. The solution to this problem
demands optimal result to the auctioneer within manageable time and the satisfaction of both the buyers and
sellers in terms of profit. Most simple combinatorial auction already used by many websites for e-procurement
is fixed price auction. Fixed price auction is not truthful and gives more profit to the seller. In this paper we
study different auction mechanisms for item procurement in e-commerce and proposed a new truthful auction
strategy that outperforms the existing approaches in the context of time and truthfulness.
1 INTRODUCTION
Auction is the most important mechanism for dy-
namic pricing in e-commerce (Muller, 2001). The
seller offers a variety of items or service for sale with
the aim of obtaining more profit. Online Auction is
useful to maximize the seller revenue and provides an
opportunity to a buyer to buy the products or services
at fair market value based on selling price and not
asking price. A seller can meet maximum numbers of
customer from different geographic area because of
the location independence of e-commerce. Combina-
torial auctions have been gaining significant interest
as an automated mechanism for selling multiple
products or services to a single buyer (Narahari and
Dayama, 2005). Combinatorial auction is extremely
useful in numerous e-business applications such as e-
selling, e-procurement, e-logistic etc. Combinatorial
auctions are those those in which participants place
bids on combination of products or services, called
packages, rather than individual product (Cramton
et al., 2005). In this case, participants or buyers
either win all the products or services of the package
they have requested to buy or lose. Combinatorial
auctions are useful to a buyer to buy all the related
products or services altogether at one bid at fair
market value and seller also able to sell bundle of
products or services at a time at maximum profit.
Auctions have gained much greater prominence as
the means of determining prices at which goods are
bought and sold as a result of improved commu-
nication and information processing capabilities of
the personal computers and the Internet (Morgan,
2002). At a consumer level, the auction site eBay
and Amazon have transformed the market for buying
and selling collectibles as well as a host of other
products and their sales revenue continue to grow
rapidly by more than 90 percent in last five years
(http://www.marketwatch.com/investing/stock/ebay/
financials).
1.1 Some Applications of Combinatorial
Auctions
Numerous applications have been reported in various
290
Banerjee, T., Pradhan, D. and Choudhury, P.
Efficient Combinatorial Auction Mechanisms in Electronic Commerce.
In Proceedings of the 18th International Conference on Enterprise Information Systems (ICEIS 2016) - Volume 2, pages 290-297
ISBN: 978-989-758-187-8
Copyright
c
2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
research papers for combinatorial auction. We have
only discussed few of the applications areas of com-
binatorial auction.
Spectrum Allocation: Wireless and mobile tech-
nologies are growing very rapidly in recent times.
Service providers need to provide emerging wireless
service and new wireless architecture to fulfill the re-
quirement of huge number of wireless/mobile devices
and applications. In static resource management sys-
tem spectrum is allocated for long term basis. Some
radio spectrum may leave idly where some wireless
systems are unable to work due to spectrum crisis.
Static resource management in wireless system is in-
efficient in modern era since demand and supply may
not always match. Auction is widely used to dy-
namic allocation of spectrum to improve the chan-
nel/spectrum utilization(Zheng et al., 2014). Govern-
ment or authorities use auction mechanism to sell the
spectrum license among telecommunication compa-
nies.
Electricity Distribution: In (Zhongjing and Yingy-
ing, 2014)(Sarlati et al., 2013) hierarchical electricity
distribution retailers distribute electricity using auc-
tion mechanism. The electricity market consists of
one generation provider (owner of whole electricity),
several retailers (different companies) and many con-
sumers. Combinatorial auction mechanisms are used
by electric generation provider to assign electricity to
the retailers.
E-Procurement: Auctions are widely used in E-
procurement (Narahari and Dayama, 2007)(Shikui
et al., 2014)(Gregory and Molson, 2013). Procure-
ment is purchase of goods and services. Buyers look
for sellers who would sell the items and services. Sell-
ers with similar goods and services submit their bids;
Sellers also obtain the information regarding goods
and interest of other sellers which help them to price
negotiation. Buyers continue the bid until one seller
is ready to offer lower price than the one offered in
the last bid or the end of time. More than one round
is required to finalize the winner.
Resource allocation: In cloud computing, cloud
provider rent their various resources to the user for
their use over internet. Users from various location of
the world may hire resource from cloud. Combina-
torial auction mechanism is used by cloud providers
to rent their resources to the users (Zaman and Grosu,
2013a)(Iosifidis and Koutsopoulos, 2010) on pay per
use basis.
1.2 Literature Review and Research
Motivation
There are three basic techniques of combinatorial auc-
tion; i.e. Fixed Price Auction, Combinatorial Auc-
tion Linear Programming (CA-LP) and Combinato-
rial Auction with Greedy approach (CA-GREEDY).
Shikui (Shikui et al., 2014) has proposed the
Fixed Price Auction mechanism which is the sim-
plest combinatorial auction and is used by many cloud
providers. It has been proved that it is not incentive
compatible (Zheng et al., 2014).
Archer (Archer et al., 2005) has proposed one
mechanism CA-LP of combinatorial auction using
linear programming problem and (Shikui et al.,
2014)has given extended version of CA-LP. Though
CA-LP is incentive compatible but it has been solved
by linear programming problem and results non linear
time complexity.
CA-GREEDY is another combinatorial auction
mechanism proposed by Archer (Archer et al., 2005),
Zaman (Zaman and Grosu, 2013b). This mechanism
takes less time to determine the winner and calculat-
ing payment value and it is incentive compatible but
not like CA-LP.
CA-Provision is another approach using greedy
mechanism proposed by (Zaman and Grosu, 2013a).
A plethora of research has been done on combina-
torial auctions. None of the existing literature com-
pares the performance parameter of the existing pop-
ular multi-item auction used in e-commerce. The ob-
jective of this paper is to compare the three auction
techniques and proposed a new mechanism design ap-
proach to improve the performance.
Rest of the paper is organized as follows: section
2 present the comparison of popular auction mech-
anisms in e-commerce. The multiple products sell-
ing is represented as mechanism design problem in
section 3, the new proposed Fixed Price, CA-LP and
CA-GREEDY-MODIFIED mechanism is discussed
in section 4. The simulation of proposed mechanisms
is detailed in section 5; finally we conclude the paper
and discuss future research direction in section 6.
2 COMPARISON OF
COMBINATORIAL AUCTION
MECHANISMS
Basic parameters for measuring performance of any
auction mechanism are truthfulness, execution time
and the value of utility function. Utility of each user
is the difference between the bid values she has asked
Efficient Combinatorial Auction Mechanisms in Electronic Commerce
291
for her requested resources at the bidding time and
the original price she has been charged for using re-
sources. Execution time means total time taken to ex-
ecute the algorithm to determine the winner and for
calculating the payment value. Truthfulness means
that each bidder bids their true value of the resources.
We have implemented all the existing combinatorial
auction mechanisms in MATLAB environment and
tested for various numbers of inputs. For all simula-
tions, inputs are randomly generated within the given
range and the following values of performance param-
eter found.
Table 1: Performance comparison of combinatorial auction
mechanisms.
Truth
fullness
Value of the
utility
function
Time
Complex-
ity
Fixed
Price
No Zero Low
CA-LP Yes High High
CA-
GREEDY
Yes Average Average
The above table shows that Fixed Price auction is
not at all truthful and the value of the utility func-
tion is zero so the seller’s revenue is very high but
its execution time is low. The seller revenue is very
high in this case but not maximum. We have pro-
posed New FixedPrice combinatorial auction where
the seller may earn maximum possible profit. But
CA-LP ensures that truthfulness is the dominant strat-
egy of each user and the value of utility function is too
high compared to other combinatorial auction. But
execution time of CA-LP is very high. So CA-LP
is the best combinatorial auction mechanism for all
performance parameters for small input values. CA-
LP takes longer time to execute a large number of
inputs. But payment method of CA-LP mechanism
is designed in such a way that the user pay zero for
the product with a little demand. But the product
with a little demand is generally sold at the fixed
price. In this paper, we have proposed New CA LP
where we extended the payment part of CA-LP so
that seller’s revenue will not be zero for any prod-
uct, the buyer has to pay minimum fixed price of
the product. CA-GREEDY mechanism also ensures
truthfulness, execution time and value of the util-
ity function at average. CA-GREEDY is very use-
ful for large number of inputs but value of the util-
ity function is not quite bright. In a research pa-
per Zaman (Zaman and Grosu, 2013a) has given one
new method; i.e. CA-PROVISION based on CA-
GREEDY where the value of utility function is bet-
ter than CA-GREEDY but not like CA-LP. In this pa-
per we have modified the CA-GREEDY mechanism
(CA-GREEDY-MODIFIED) to improve the value of
the utility function so that CA-GREEDY-MODIFIED
will be the best choice for combinatorial auction for a
large number of inputs and provides best value for all
performance parameters.
3 MULTIPLE PRODUCT
DISTRIBUTION AS A
MECHANISM DESIGN
PROBLEM
For formulating the multiple product or service sell-
ing process we consider the following notations and
assumptions:
1)Let
I = (u
1
,u
2
,...,u
n
)
be the set of n buyers,
K = (r
1
,r
2
,..., r
m
)
be the set of m available products or services and r
i
is
the total number of available products or resource of
type i and
W = (w
1
,w
2
,...w
m
)
be the set of weights where w
i
is the weight or mini-
mum value per unit of ith product.
2) A set of winners WIN contains list of winners.
3) Each user or buyer precisely knows the value
that he bids but does not know the bid value of the
others. The bidder i submits the bid
(a
i1
,a
i2
,..., a
im
,v
i
)
Where a
i j
denote the number of j
th
resource request
by user i and v
i
is the valuation of total items re-
quested by her. User i can put a
i j
as zero, if she does
not want any number of resource j.
4) Bidders are not aware of the type and number
of requested products and total valuation submitted by
other bidder.
5) Let
P = (p
1
, p
2
,...p
n
)
be the set of payment value paid by the buyer to the
seller.
6) The agents always try to maximize a utility
function. Utility function defines as the difference be-
tween bid value submitted by user and the value actu-
ally paid.
The below mentioned matrix represents the bid
profiles of all the bidders.
bid =
a
11
a
12
... a
1m
v
1
a
21
a
22
... a
2m
v
2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
a
n1
a
n2
... a
nm
v
n
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
292
After collecting all the individual bids, combina-
torial auction mechanism determines the winners and
it also fixes the charge paid by every winning bidder.
4 NEW PROPOSED MECHANISM
In this section, three mechanisms have been presented
to solve the problem of multiple product sale to a sin-
gle buyer in a single bid. The first New FixedPrice
auction, is the extended version of Fixed Price Auc-
tion by Archer (Archer et al., 2005). The next two
mechanisms are the proposed New-CA-LP and CA-
GREEDY-MODIFIED based on linear programming
problem and Greedy mechanism.
4.1 New Fixed Price Auction
(New FixedPrice Auction)
Fixed Price Auction mechanism is the simplest
combinatorial auction and is used by many cloud
providers (Zaman and Grosu, 2013b). The Fixed-
Price auction mechanism defines a fixed price vector
(q
1
,q
2
,...q
m
) where q
i
is the price a buyer has to pay
to buy one instance of i
th
product. Archer (Archer
et al., 2005) explains this mechanism as first come
first serve basis until the products are exhausted. In
this case during the opening of the market there will
be a huge traffic to submit the request first. The fixed
price auction mechanism has been extended by re-
ordering the users in descending order of the respec-
tive bid value. The bidder with the highest bid value
will get the first chance to win the products. Bidders
win the products depending on their bid values, no
need to compete for submitting the bid first and the
auctioneer profits more. It also makes sure that in or-
der to get the requested bundle of products, the valu-
ation vi of buyer u
i
is at least F
i
, where F
i
is the sum
of the fixed prices of each products in her bundle. In
this case the bid value reflects necessity and urgency
of the products. The algorithm for implementing the
fixed price auction is given below(Algorithm-1).
In the our algorithm (Algorithm-1), reordering of
the bids is included and time complexity increases
from O(n) to O(nlogn). But using this method an
auctioneer can avoid one time rush and the resource
providers have a chance to earn more revenue because
resource providers distribute resources from high to
low bid value. Fixed price method is not incentive
compatible (Zheng et al., 2014) resource allocation.
The Winners have to pay the value what they have de-
clared during bid submission. To encourage users to
participate in auction we need to charge less than the
value declared by them.
Algorithm 1. New FixedPrice Auction.
Step 1 : Collect the bid f romthe users.
Step 2 : Arrangethe users in order (u
1
,u
2
,..., u
n
)
so that v
1
>= v
2
>= ...v
n
Step 3 : InitializeW IN = φ
Step 4 : f or i = 1to n
i f v
i
>=
m
j=1
a
i j
q
j
then
i f A
i
<= R
thenW IN = W IN U NION
{
i
}
and R = R A
i
whereA
i
= (a
i1
,a
i2
,..., a
im
)
and R = (r
1
,r
2
,..., r
m
)
[End I f ]
[End I f ]
[End f or]
Step 5 : f or i = 1to n
I f i W IN then p
i
= v
i
Else p
i
= 0
[EndI f ]
[EndFor]
It is assumed that two types of products are offered
by the buyer. Relative weight of the products is W=[2
,1] and fixed prices are 10 and 15 respectively. Total
ten users participate in the bidding process. Numbers
of products of each type are 10 and 15 respectively.
Table 2: Examples of Submitted bids.
No of Prod-
ucts (r1)
No of Prod-
ucts (r2)
Bid Value
2 1 40
1 2 30
2 5 60
3 3 35
2 4 50
3 1 33
2 0 20
0 5 60
1 3 55
4 2 85
Each users(i) bid is 3-tuple (r
i1
,r
i2
,v
i3
) where r
i1
is the number of requested instances of item 1, r
i2
is
the number of requested instances of item 2 and v
i3
is
the bid value that user i wants to pay for the requested
items.
Result: Existing Fixed Price auction and proposed
New Fixed Price auction have been implemented on
the above data set and the result is given below (Table-
3):
4.2 New CA LP
Combinatorial Auction-Linear Programming (CA-
Efficient Combinatorial Auction Mechanisms in Electronic Commerce
293
Table 3: Result of New FixedPrice Auction.
Winner
set
Payment
set
Seller
rev-
enue
Existing
Fixed Price
auction
1, 2, 3, 5,
6
40, 30, 60,
50, 33
213
New Fixed
Price Auction
10, 8, 3, 9,
1
85, 60, 60,
55, 40
300
LP) represents as standard linear programming
problem. Archer (Archer et al., 2005) explained the
combinatorial auction just like the virtual machine
allocation problem in (Zaman and Grosu, 2013b),
the bidder can request maximum one (a
i j
ε {0,1})
resource of each type Where as in (Shikui et al.,
2014) user can request any number of resources (a
i j
ε {0,1,2,3,....}). Archer (Archer et al., 2005) reduced
the number of resources to prohibit oversell of the
products. In our case the total number of products is
not reduced because we consider oversell is impos-
sible. Winners are selected if the requested products
are available. The payment calculation part of the
algorithm (Zaman and Grosu, 2013a) is modified
and as a result of that the price of the less demand
product will be the fixed value. According to (Zaman
and Grosu, 2013b) payment of each winner is the
minimum value to win the bid. In the situation while
demand is less than supplies, one buyer becomes
the winner irrespective of her bid value. The buyer
may become the winner even when the bid value is
zero; then that user pays zero for using resources.
Every seller asks at least fixed price for low demand
products. For example, one seller has two types of
products (r1, r2). Total numbers of available products
are (2, 2). Four buyers submit their bids
bid =
2 3 60
1 3 70
3 2 90
2 0 80
In this situation only the requirements of 4
th
user
matche with the availability. Existing CA-LP calcu-
lates the payment value as the critical value to win and
the payment value of user u
4
is 0.
The existing CA-LP mechanism provides the
buyer with maximum value of utility function but the
sellers may become looser. So in our algorithm an
auctioneer calculates payment value as the minimum
price to win the product but it should not be less than
the fixed price of the product. The algorithm is given
below
Algorithm 2. New CA LP.
Step 1 : Fixed prices o f the products are (y
1
,y
2
,...,y
m
)
Step 2 : Collect the bid f rom the users.
(a)Solvethe f ollowing linear programming problem
Maximize
n
i=1
v
i
x
i
Sub ject to
n
i=1
a
i j
x
i
<= r
j
f or j = 1, 2, ...,m where x
i
>= 0
and the value o f x
i
is the winning
probability o f user u
i
Step 3 : WinnerDetermination
(a)Initialize W IN = φ
(b)For eachuser u
i
taken in descending order o f x
i
I f A
i
<= R
then W IN = W IN UNION
{
i
}
and R = R A
i
where A
i
= (a
i1
,a
i2
,...,a
im
)
and R
i
= (r
1
,r
2
,...,r
m
)
[EndI f ]
[End f or]
Step 4 : Payment Calculation
(a)For eachuser u
i
W IN
Per f orm binary search f or v
i
0
in [0,v
i
]
where v
i
0
is the critical value to win
I f v
i
0
>=
m
j=1
a
i j
y
j
then
set p
i
= v
i
0
Else
set p
i
=
m
j=1
a
i j
y
j
[EndI f ]
[End f or]
(b)Set p
i
= 0 f or i does not belong to W IN
Result:Existing CA-LP auction and our proposed
New CA LP auction mechanisms have been executed
on the above data set where minimum service charges
for the resources are [3,3] and the result is given
below(Table-4):
Table 4: Result of New CA LP.
Winner
set
Payment
set
Value of the
utility
function
CA-LP
9, 10, 8, 1,
7, 2
35, 52, 0,
26, 15, 27
130
New CA
LP
9, 10,
8,1,7,2
35, 52, 15,
26, 15, 27
120
4.3 CA-GREEDY-MODIFIED
The winner determination and payment mechanism
of CA-GREEDY and CA-PROVISION in (Zaman
and Grosu, 2013b)are extended in CA-GREEDY-
MODIFIED. In strategy-proof auction each user
would maximize her utility . CA-GREEDY and CA-
PROVISION provide the seller with more benefit as
their users utility is less in comparison to CA-LP. For
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
294
maximizing the value of the utility function, we have
changed the payment mechanism of greedy method.
We use Vickery-Clark-Groves (VCG) mechanism for
payment value calculation. The algorithm is given be-
low.
Algorithm 3. CA-GREEDY-MODIFIED.
Step 1 : Collect the bid f romthe users.
Step 2 : Winner determination
(a)W IN = φ
[Find out approax valuation based on
the number items requested and weight
o f the items]
(b) f or i = 1 to n
S
i
=
m
j=1
a
i j
W
j
[End f or]
(c)Reorder the users suchthat
v
1
/s
1
>= v
2
/s
2
>= ... >= v
n
/s
n
(d) f or i = 1to n
i f A
i
<= R
thenW IN = W IN U NION
{
i
}
and R = R A
i
where A
i
= (a
i1
,a
i2
,..., a
im
)
and R = (r
1
,r
2
,..., r
m
)
[EndI f ]
[End f or]
Step 3 : Payment Calculation
(a)For each user i W IN
Per f orm binary search in 0to v
i
, such
that we f ind a critical value v
i
0
,
which isthe least value to win.
I f v
i
0
>=
m
j=1
a
i j
W
j
then set p
i
= v
i
0
Else
set p
i
=
m
j=1
a
i j
W
j
[EndI f ]
[End f or]
(b)Set p
i
= 0 f or i does not belong toW IN
The CA-GREEDY-MODIFIED mechanism deter-
mines the winners in accordance with ranking the
buyers in descending order of their unit price (v
i
/s
i
)
(Lehmann et al., 2002) and then they are greedily se-
lected as winners from the list. Before selecting the
winner the mechanism verifies that the new combina-
tion of products does not exceed the number of avail-
able items of each type of products. The payment p
i
a winner u
i
pays is calculated as the minimum price
to win the bid but it should not be less than the fixed
price of the products i.e. the winners pays the critical
value.
Result: We have implemented existing CA-
GREEDY (Narahari and Dayama, 2007), CA-
PROVISION(Zaman and Grosu, 2013a) auctions and
our proposed CA-GREEDY-MODIFIED auction on
the above data set where fixed price for the products
is [3,3] and the result is given below:
Table 5: Result of CA-GREEDY-MODIFIED.
Winner
set
Payment
set
Value of the
utility
function
CA-
GREEDY
10, 9, 8, 1,
5
67, 54, 52,
39, 42
36
CA-
PROVISION
10, 9, 1, 8,
7, 2
83, 53, 36,
50, 20, 0
48
CA-
GREEDY-
MODIFIED
10, 9,
1,8,7
51, 12, 9,
15, 6,9
188
5 RESULTS AND DISCUSSION
We have implemented all the combinatorial auction
mechanisms in MATLAB environment. MATLAB
environment is convenient for matrix operation and
it exhibits the execution time of the entire program or
portion of the program. Input data sets are randomly
generated within a specified range for a given num-
ber of users. Once the data sets are generated, all the
strategies are tested on the same data sets. Execution
time, profit and the values of the utility functions of
all the simulations are collected, to generate compar-
ative graph for the specified algorithms. We compare
the performance of existing Fixed Price auction with
the New Fixed Price auction, existing CA-GREEDY
with CA-GREEDY-MODIFIED and also the perfor-
mance of CA-GREEDY-MODIFIED with the perfor-
mance of other combinatorial auction based mecha-
nisms in respect of execution time and the value of
the utility function.
Fixed price auction that is the most simple auc-
tion mechanism has already been used by many e-
commerce web sites. In this case the users pay the ac-
tual value that she has submitted at the bidding time.
So the value of the utility function is zero. We com-
pare our New FixedPrice auction mechanism with the
existing fixed price auction in respect of execution
time (Figure-1) and seller revenue(Figure-2). In com-
parison with the existing Fixed Price Auction, New
Fixed price Auction mechanism provides the service
provider with more profit. The execution time of New
Fixed price Auction is higher than the existing one but
it is better as it is a polynomial time problem.
The same types of winner determination and pay-
ment method have been used in New CA LP mech-
Efficient Combinatorial Auction Mechanisms in Electronic Commerce
295
Figure 1: Execution time of New FixedPrice Auction vs
Existing Fixed Price Auction.
Figure 2: Seller Revenue of New FixedPrice Auction and
existing Fixed Price Auction.
anism as in the existing CA-LP. Only difference
between New CA LP and existing CA-LP is that
New CA LP charge fixed price for low demand prod-
ucts whereas CA-LP may charge very low price even
if it may be zero. So we are not conferring any com-
parative results of New CA LP and CALP because of
equal execution time and utility functions value.
Figure-(3) and Figure-(4) represent the value of
the utility function and require time of CA-GREEDY,
CA-PROVISION and CA-GREEDY-MODIFIED for
different number of users and resources. Figure-(3)
shows that our CA-GREEDY-MODIFIED takes max-
imum time to execute in comparing to other two auc-
Figure 3: Execution time of CA-GREEDY-MODIFIED,
CA-GREEDY and CA-PROVISION.
Figure 4: Utility function’s value of CA-GREEDY-
MODIFIED, CA-GREEDY and CA-PROVISION.
tion mechanisms but its utility functions value, an-
other performance parameter is also very high in com-
parison with other two. For small input values three
mechanisms perform the same approximately. But for
large inputs the value of the utility function of CA-
GREEDY-MODIFIED is 50 percent more than CA-
GREEDY and CA-PROVISION mechanisms but its
required 60 to 80 percent more execution time.
Figure-(5) and Figure-(6) shows the evaluation
results of all the combinatorial auction mechanisms
when there are different number of bids and dif-
ferent number of products. We can see that CA-
GREEDY-MODIFIED always outperforms the other
three auction mechanism. Figures-(5) and (6) demon-
strates the value of the utility function and execution
time of CA-LP, CA-GREEDY, CA-PROVISION and
CA-GREEDY-MODIFIED mechanisms. It shows the
value of the utility function of CA-LP is much better
than CA-GREEDY and CA-PROVISION but more or
less the same as CA-GREEDY-MODIFIED. But the
execution time is too high comparable to other auction
mechanisms. CA-LP auction mechanism takes more
than one hour for 500 users bidding for 50 differ-
ent items. CA-GREEDY-MODIFIED auction takes
Figure 5: Utility function’s value of CA-GREEDY-
MODIFIED, CA-GREEDY and CA-PROVISION and CA-
LP.
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
296
Figure 6: Execution time of CA-GREEDY-MODIFIED,
CA-GREEDY and CA-PROVISION and CA-LP.
less time and utility functions value is also high. In
CA-GREEDY-MODIFIED auction mechanism users
pay minimum value to win the resources. So truth
telling is the dominant strategy of the CA-GREEDY-
MODIFIED auction.
6 CONCLUSION
The indispensability of combinatorial auction for sell-
ing a group of products has been look over for any
e-commerce application. Extensive simulation exper-
iments have been carried out to concluded that CA-
GREEDY-MODIFIED is clearly a better choice for
selling products or service over Internet. The value
of the utility function of New CA LP is better than
the other auction mechanisms. In CA-GREEDY ap-
proach execution time is less than the other truthful
auction mechanisms but the utility function value is
not so good as CA-LP. Moreover, CA-LP is solved
by linear programming problem which is a NP com-
plete problem. So execution time of CA-LP auc-
tion mechanism is infinite for large number of in-
puts. The utility value of the proposed CA-GREEDY-
MODIFIED is better than CA-GREEDY and is closer
to CA-LP and takes less time than New CA LP. So
CA-GREEDY-MODIFIED is the best auction mech-
anism to sell multiple products via electronic devices.
Further work includes the deployment of the proposed
mechanisms on an experimental e-commerce testbed
and tries to reduce execution time of CA-GREEDY-
MODIFIED.
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