=Paper=
{{Paper
|id=None
|storemode=property
|title=Dynamic Model of Double Electronic Vickrey Auction
|pdfUrl=https://ceur-ws.org/Vol-1356/paper_100.pdf
|volume=Vol-1356
|dblpUrl=https://dblp.org/rec/conf/icteri/KobetsYP15
}}
==Dynamic Model of Double Electronic Vickrey Auction==
https://ceur-ws.org/Vol-1356/paper_100.pdf
Dynamic Model of Double Electronic Vickrey
Auction
Vitaliy Kobets1, Valeria Yatsenko2 and Maksim Poltoratskiy1
1
Kherson State University, 27, 40 rokiv Zhovtnya st., Kherson, 73000 Ukraine
vkobets@kse.org.ua, max1993poltorackii@gmail.com
2
Taras Shevchenko National University of Kyiv, 90-A, Vasulkivska st., Kiev, 03022 Ukraine
ValeriaYatsenko@rambler.ru
Abstract. The paper deals with different approaches to the definition of e-
commerce, including special mechanisms for the distribution of goods and
payments, such as auction model. Different formats of auctions that change
welfare of their participants are investigated. Software modules were developed
for researching the effectivenes of double electronic Vickrey auction. It is
defined that in double Vickrey auction incentives for most buyers and sellers
are created to reveal their true types. The developed software module of double
Vickrey auction showed the highest efficiency in the terms of social welfare
among alternative formats and disproved the ability of Vickrey auction to
achieve results like market mechanism of perfect competition.
Keywords. e-commerce, online auction, e-auction, Vickrey auction, social
welfare.
Кey Terms. ElectronicAuction, Software, DoubleAuction, SocialWelfare.
1. Introduction
The current phase of civilization development is characterized by drastic
transformations in all spheres of life: from culture and sport to politics and
economics. Taking advantage of new methods, changing subject matter of
investigations, using neologisms such as digital economy, information economy, info-
networks economy, knowledge-based economy, Internet economy, "new" economy,
virtual economy, service economy. The variety of modern categories is typical for the
modern stage of evolutionary development of international economy, placing special
emphasis on the leading role of the triad of determinants of economic growth and
development of today, which includes intellectual capital, creative and innovative
factor as the basis for developing of knowledge-based economy.
Another feature of the modern epoch of human development is asymmetry of
socio-economic development of the international economic system, which is
deepening due to globalization. Most scientists think that essential determinants of
escalation of global asymmetries lie in ICT-sphere: This leads to more considerable
disproportion in international economy and increases social polarization [1]. ‘The
Golden Billion’ are enjoying their successful development due to unequal
relationships with peripheries, as the number of “profitable niches” in global space is
highly limited; therefore the way to the civilized “floor” can be easily made due to
innovation-information achievements by means of integration the market mechanism
into the networked information economy [2].
The technological component of modern economic processes contributes to the
development of the networked economy as the synthesis of information and global
economies [3].
Works of W. Vickrey, E. Daniel, Gr. Dunkan ,G. Karypis, J. Konstan, P. Cotler, B.
Mahadevan, J. Riedl, A. Summer and B Sarwar are devoted to the problems of
establishment and development of global and local e-commerce markets in terms of
globalization processes. National scientists, namely A. Bereza, A. Berko, V.
Vysotska, I. Kozak, F. Levchenko, Y. Lyenshyna, V. Pasichnyk, L. Patramanska, E.
Strelchuk, T. Tardaskina do not stand apart of such scientific research. Theoretical
and statistical investigations of this category are being conducted by some
international organizations such as OECD, UNKTAD, UNISTRAL, WTO аnd ITU,
development projects and strategic programs in regard to e-commerce are being
elaborated by World Bank and EBRD.
The paper goal is to ground the impact of e-commerce on the participants’ welfare
through empirical experiment for electronic auctions, implemented by the means of
the relevant transactions via designed software that is economically desirable
distribution of goods and payments irrespective of strategic behavior of participants.
The paper has the following structure: the second part is devoted to literature
review; the third one determines auction formats; the fourth part constructs the
general model of double electronic Vickrey auction for true type and hidden type
agents; the fifth part concludes.
2. Related Works
Development of information economy has caused formation of e-society with its
integral parts: e-government in politics, e-business in economy, e-education, e-
ecology, e-medicine and others (Table 1). E-trading is deemed to be a part of e-
commerce which in its turn together with document control and business management
makes e-business [4].
In its narrow sense e-commerce is close to e-trading because its main function is
online purchase and sale transactions; in the wide sense the definition of e-commerce
covers any transaction effected using computer networks [5, 6, 7].
So e-commerce is a complex of business operations carried out using computer
networks (Internet, Intranet, Extranet), which are connected with the change of
material rights and all processes that support this process including Electronic Data
Interchange (EDI), Electronic Funds Transfer (EDF), e-trade, e-cash, e-marketing, e-
banking, e-Insurance, e-logistics.
Table 1. Different ways of interpretation the category “e-commerce”
Meaning Original Definition
OECD
(Ogranization
commerce=e-trade)
An e-commerce transaction is the sale or purchase of goods or
for Economic
services over computer mediated networks (broad definition) or
«narrow» (e-
Cooperation
via the Internet (narrow definition) 1.
and
Development)
R. Doernberg, L. E-commerce means the ability to perform transactions involving the
Hinnekens, exchange of goods or services between two or more parties using
W. Hellerstein, electronic tools and techniques.
J. Li
E-commerce means any form of business process in which the
A. Sammer,
interaction between the actors happens by using the Internet –
Gr. Dunkan
(е-comerce = totality of business
technology
E-commerce includes searching for information, contracting,
supply of products, goods or services, making payments, sale or
purchase of goods or services, whether between businesses,
processes)
UN Experts households, individuals, Governments and other public or private
«wide»
organizations, conducted over the Internet. The goods and services
are ordered over the Internet, but the payment and the ultimate
delivery of the good or service may be conducted on- or offline.
E-commerce is a wide array of commercial activities carried out
through the use of computers, including on-line trading of goods and
WTO
services, electronic funds transfers, on-line trading of financial
Specialists
instruments, electronic data exchanges between companies and
electronic data exchanges within a company 2.
Aspects of e-commerce are considered in Table 2 based on [8].
Table 2. Aspects of e-commerce
1. № Aspect Essence
It is a method of delivery via telephone lines, computer networks,
2. 1. Connections
electronic means
3. 2. Process It is a technology to automate business operations.
It is a tool to reduce costs, improve quality of goods and services and
4. 3. Services
accelerate delivery.
5. 4. Time E-commerce allows to carry out operation online (24 hr. per day).
6. 5. Space Open Internet infrastructure makes it a global environment.
According to most experts B2B is the largest segment of e-commerce (Table 3).
For example, according to UNCTAD data, B2B is a dominant segment in the
American market with twice higher volume of sales compared to those of B2C (559
billion dollars against 252 billion dollars).
1
Ecommerce Sales Topped $1 Trillion for First Time in 2012. Available
www.emarketer.com
2
E-commerce and Development Key Trends and Issues Available
www.wto.org/english/tratop_e/devel_e/wkshop_apr13_e/fredriksson_ecommerce_e.pdf
Table 3. Forms of interaction in e-commerce
Abbreviation Denomination Definition
Business-to- businesses make online transactions with other
B2B
Business businesses
Business-to- online transactions are made between businesses and
B2C
Customer individual consumers (social commerce)
Business-to-
B2А administrative document control
Administration
Business-to-
B2G operations between companies and public institutions
Government
e-commerce model in which a government entity buys
electronic
e-government or provides goods, services, or information to
government
businesses or individual citizens.
It is also confirmed by the structure of the e-commerce market in South Korea
based on open sources3. (Fig. 1).
Fig. 1. The structure of e-commerce in South Korea in 2013, %
Internet-shops make an essential part of e-commerce in Ukraine - sector B2C, but
B2B segment has great opportunities. For example, International center for electronic
trading B2B-center has been successfully functioning for three years in Ukraine, and
according to newsb2b.blogspot.com has made it possible to reduce procurement
prices for Ukrainian enterprises by 20% on the average as well as procurement labor
costs by 70%. The system allows to hold 43 kinds of tender, including more than 172
thousand companies from 110 countries of the world, among them 3500 companies
from Ukraine: Group of companies Privat, Ukreksimbank, PUMB, AZOT, Antonov,
Ergopak, Rubizhne cardboard mill, Volnogorsk glass, Kolos, Ukrrosmetal, Ukrolia,
and international group of companies – JTI, SoftServe, МТС, Allianz. The number of
tenders held by Ukrainian segment of the B2B-center system annually increases by
60%. As of today there are two B2B trading sites functioning in Ukraine - b2b-
center.ua and b2b-center.uspp.ua, the latter was created by mutual efforts of B2B-
center and the Ukrainian Union of Industrialists and Entrepreneurs (UUIE), which
allowed it to make online purchases.
The main determinants of insufficient development of e-business and e-commerce
are undeveloped technical and technological base. Asymmetric levels of ICT-
infrastructure development cause disproportional global development of e-commerce
with its traditional key centers in Old and New World – Western Europe and North
America, and Asia-Pacific Region (Table 4).
At the same time the growth rates of B2C sales in the developing countries are
essentially falling. The highest level is traditionally demonstrated by China (63.8%)4.
(Fig. 2).
3
The Statistics Portal. Available www.statista.com
Table 4. Comparative analysis of the development of B2C e-commerce segment all over the
world in 2013 4
Sales, Growth Level of Share of sales,
Regions bln. dol. rates, % coverage, % %
Deviation %
North America 419,53 12,5 72 28,3 31,2 2
Asia Pacific 388,75 23,1 44,6 2,1 2,3 2,9
Western Europe 291,47 14 72,3 26,4 25,4 1
Central and Eastern
48,56 20,9 41,6 4,1 4 0,1
Europe
Latin America 45,98 22,1 33 34,9 32,9 0,1
Middle East and Africa 27 31 31,3 4,2 4,3 0,2
Total 1,22129 17,1 40,4 - - - -
Fig. 2. Growth rates of B2C sales from 2012 to 2014, %
High growth rate at the level of 20.9% is demonstrated by Central and Eastern
Europe, but it is lower than in Asia and North America (Fig. 3).
Analysis of commodity composition of e-commerce markets in Ukraine, Russia,
Switzerland and the U.S. in 2013 showed disproportional distribution of sales
according to segments: e-commerce market in the U.S. is well-balanced and offers a
wider range of products than Ukrainian market (Fig. 4). The range of goods in Swiss
e-commerce market is not wide but it is well-balanced in contrast to Ukrainian market
where 90% of all orders are distributed between two main sectors.
Despite the development of e-commerce business in Ukraine, online-orders do not
gain a great popularity with the population, the anticipated level in 2014 was about
3% comparing to 90% in the leading country – the U.S. What makes Ukrainian
4
Internet business in Ukraine. Available http://ain.ua
market special is that people here mostly use the Internet to learn about the goods, to
know about technical specifications of the products, to read other customers’
feedbacks, to compare prices and so on, and only a limited number of users place
orders, that is why the level of online-shopping and the number of online buyers
remain low.
Fig. 3. Dynamics of growth rate of B2C e-commerce sales in regions from 2012 to 2014, % 3
Fig. 4. The commodity structure of sales in B2C e-commerce segment in selected countries 5.
The results of the research showed the tendency typical for the national markets of
all countries – one leading company being in dominant position well ahead of its
nearest competitors. Ukrainian e-commerce market is entering the phase of growth
because of relatively low volumes of sales of Ukrainian companies (Fig. 5).
In spite of rapid development of e-commerce and e-business in Ukraine there are
still some certain difficulties and obstacles that reduce the growth rates of online
business as a whole (Table 5).
Fig. 5. Comparative analysis of the B2C e-commerce sales volumes in different countries
according to investigation in 2013, mln. dollars
Table 5 Problems and prospects of e-business in Ukraine 5
Factor Essence
insufficient development of IT;
Factors limited using of IT;
impeding the conservatism and distrust of innovations;
development of low purchasing power of the population;
e-business in lack of specialists;
Ukraine contractor’s mistrust of the banking system;
lack of legal regulation
Prospects for e- creating jobs for skilled workers;
business in access to Western capital investment;
Ukraine increasing in tax revenues from the use of electronic payments
Factors development of electronic payment systems on the Internet;
accelerating legislative regulation of the e-commerce, the legal recognition of
development of electronic records and electronic signatures;
e-business in protecting commercial information during network transmission
Ukraine
One of the main impacts of e-commerce activity is the formation of certain triad of
consequences: product price cutting; speeding up the time and transformation of space
(elimination of borders); creation of horizontal links between players and direct
contact [4] (Fig. 6).
price
а
time direct contact
Fig. 6. The triad of e-commerce components
3. Auctions Formats
In most real markets sellers have no perfect information about the market demand,
and know only about its statistical distribution. Only buyers know exactly how much
product they want to buy at a definite price. Self-regulating market mechanism is not
always able to disclose all information about the buyers’ solvency and sellers’ costs.
The research of decentralized market mechanisms allows us to determine how and
why real markets collect and transmit information. Then special mechanisms for the
distribution of goods are created, such as auction models.
Auctions can implement the mechanisms of transformation of private information
about the value of goods for buyers into common knowledge. In turn, the rules of the
auction can stimulate sellers to disclose private information about their cost of goods.
Maximum purchasing capacities of the buyer and seller costs are called agents types.
5
Ukraine overview. Available www.ebrd.com/where-we-are/ukraine/overview.html
Designing economic mechanisms for auctions allows building a model of relevant
institutions that determine the conditions and means of achieving the goal of the
designer [Kobets, 2014]. This model is effective if it allows the planner to create
incentives for the disclosure of information held by others to achieve private or public
purpose.
To solve these problems auctions mechanisms are designed which motivate the
agents to truthfully reveal their private information. Auctions are important for goods
that have no natural market, such as bankrupt firms, mobile and radio frequencies.
Here accurate information about the number of regular buyers is missing, variance of
buyers’ values can be very large, and pre-sale valuation and transaction costs are
significant.
Operating of Internet-auction is a necessary condition for the development of e-
commerce segment and its further growth grounded on [4, 12] (Fig.7).
Effective use of electronic auctions has been confirmed empirically by the most
famous giants of global e-commerce such as eBay.com, Sothbys.Amazon.com
Yahoo!Auctions and DigiBid.com, which actively use a similar mechanism to
promote and sell products and services. Westernbid.com, lotok.com.ua, eTorg.com
auctions are gaining their popularity in Ukraine. There are several types of auctions
with specific methods of pricing (Table 6):
If a product is sold to the individual who values it most, the auction is efficient.
Auction yielding maximum revenue to the seller is optimal [13-14].
Vickrey auction
Agents convey their true type only if it gives them maximum (expected) payoff.
Revealing the type means the seller’s payoff maximization and efficient allocation of
resources (the buyer who values the product most receives it). Vickrey auction (sealed
bid second price auction) best of existing auctions formats reveals the types of
participants. True strategy is a dominant for Vickrey auction format (as opposed to
the first price auction) [15]. The winner receives a payoff as the difference between
his own purchase capacity and second price. So when one of the agents has a greater
solvency than others, he gets a discount equal to the difference between the first and
second largest bids. If Vickrey auction has several winners, then it will select one of
them with equal probability.
Then there were 2 extensions of this approach: the revelation principle, which
showed that direct mechanisms are similar to indirect ones and implementation theory
that helps to built mechanism so that all its equilibria were optimal ones [16].
Double auction
Theory shows that double auctions, where traders (buyers and sellers) charge their
prices can be effective trade institutions, where each agent has private information
about his own values of goods.
With the increasing number of traders, the double auction will more effectively
generalize personal information so that eventually all information is reflected in
equilibrium prices (as argued Wilson). These results are consistent with F.Hayek’s
argument that markets efficiently summarize relevant private information.
Vickrey auction theory gained wide support from the economists; some elements
of the theory have been used in the US in B2G(A) type of e-commerce in organizing
the trade licenses to use national radio frequencies. The US State Treasury asked FTC
to use this type of auction for revenues maximization.
Internet- auction
Requirements: Characteristics of Rules of
simple client
software; the goods in the functioning
obligatory
Goods
ensuring an auction:
appropriate level of New high-tech registration of
confidentiality by using products; participants;
the protocol that quickly collectible product must
eliminates customer products, rarities, always be paid for;
information; artifacts; offer to sell can
the complexity of the not be removed
communication protocol substandard before deadline;
depends on the volume products
Income goods for sale
and number of messages; commission on the are only an
flexibility of rules - intermediary
each item must have its transaction Characteristics:
between
buyers andof
the possibility
own mathematical tools sellers.
Results:
to find the optimal a significant
costsmethod;
pricing are directed for concentration of
resource supporting;
asynchronous supply and demand;
receiving firstmodelhand Web- site
communication interaction of
information about the Internet- shop parties 24 hours a
demand for goods and day:
services; Internet-
providing
the formation a auction detailed descriptions
permanent audience and images of
Fig. 7. The mechanisms of pricing in Internet- auctions
products
Table 6. Diversity of Іnternet - auctions
Type Subspecies Essence
Descending Next bid is lower than the previous.
Order
Growing Next bid must be higher than the previous.
sealed bid first- This auction does not disclose the participants’ offers. The
According to the degree of openness
price auction buyer who offers and pays the maximum price will win.
Closed
sealed bid Vickrey auction means the participants don’t disclose their
second price proposals. The winner, who has offered the maximum price,
auction pays the second after it.
The main characteristic of the auction is that buyers know
English auction about competitor’s offers. The price starts from a certain
minimum level mark. The winner pays the highest price.
The main characteristic of the auction is that buyers disclose
Open
Dutch auction their bids. The maximum price is fixed and reduced until a
buyer agrees to accept it.
The main characteristic of the auction is that buyers and sellers
disclose their bids and asks respectively. The seller and the
Double auction
buyer interact the same time - as a result, the equilibrium
market price is fixed.
The challenges of the market mechanism require creating rules of interaction for
bidders, realized by means of transactions on computer platforms with appropriately
developed software and leading to economically desirable distribution of goods and
payments deprived of collusion or dishonest behavior of participants.
4. Double Electronic Vickrey Auction Model
To construct the auction model, we introduce the following assumptions. Seller
offers one indivisible good to N buyers, who are risk neutral. Buyer i has purchase
capacity vi , i 1,..., N . Evaluation of solvency of buyer i is obtained from the
interval [1;100] in accordance with the distribution function Fi (vi ) and distribution
density fi (vi ) . Buyers’ values of good are mutually independent. Every buyer knows
his/her own value and does not know the values of other buyers. However, density
distribution functions f1 ,…, f N are common knowledge and are known to both
buyers and the seller. Although the seller is uninformed about the exact solvency
value of the buyer, he knows the distribution from which each value is received. If the
solvency of the buyer who wins the product is vi , and he pays the price p , his
consumer surplus equals CSi vi pi . The seller’s short-run profit will change when
the auction format changes.
Sealed bid first-price auction
Buyers make sealed bids bi that depend on their ability to pay vi . Buyers’ bids are
considered as a strategy in the form of functions mapping their solvency in non-
negative bid: bi R . Expected payoff of buyer i will be:
CS (r; v) F N 1 (r ) (v b (r )) , (1)
N 1
where r - buyer bid, v - buyer reservation price, F (r ) - the probability that the
buyer bid on the goods is the highest among all applicants. After first order condition
for function maximization (1) and for conditions F (v) v and f (v) 1 we get size
of equilibrium bid for sealed bid first-price auction:
v
b (v ) v . (2)
N
So in this auction format, each buyer conceals his true solvency, relying on a lower
bid level than its reservation price.
Double electronic Vickrey auction for true type’s agents
Buyers will behave differently in sealed bid first price auction and Vickrey auction.
First price auction offers 2 motives for buyer: (i) an incentive to rise his stake to
increase his chance of winning; (ii) an incentive to reduce his bid to reduce the price
he pays when winning. For Vickrey auction the second motive is not valid, because
the winner pays the price which does not depend on his bid. This allows to expect
aggressive competition for the good at Vickrey auction. Let B be the second largest
bid at the auction, then a winner disclosing his reservation price will win payoff
CS (v) v B .
Suppose that M risk neutral sellers operate in the market. The cost distributions for
sellers are obtained from the interval [1;100] in accordance with the known
distribution functions. Sellers make sealed asks ai that depend on their costs ci . If
the seller’s cost is ci , and he gets the price p , his producer surplus (profit) is
PSi pi ci .
Consider our software module for electronic Vickrey auction in Fig. 8.
Fig. 8. Double electronic Vickrey auction for true type’s agents
In general the number of buyers and sellers may differ N M . The buyers’ ability
to pay is ordered from maximum to minimum and for sellers it is from minimum to
maximum.
The agreement between agents (deal = 1) occurs when a price offered by buyer is
not below the price set by the seller ( b(vi ) a(ci ) ), otherwise the agents refuse the
transaction (deal = 0). The price for each transaction for each pair of buyer and seller
is set at the average level:
v c
Pi i 1 i 1 , (3)
2
The auction continues until the highest price offered by a buyer will be lower than
the minimum price charged by the seller: b(vi ) a(ci ) (Fig. 9). After each transaction
the benefits of buyers are defined in the form of consumer surplus CS and sellers
gains – as producer surplus PS . The sum of consumer and producer surplus forms
social welfare SW as efficiency indicator of Vickrey auction format (Fig. 10).
Fig. 9. Bids and asks distribution at double electronic Vickrey auction for true type’s agents
Fig. 10. Dynamics of consumer and producer surplus, social welfare at double electronic
Vickrey auction for true type’s agents
Fig. 10 shows that functions CS , PS and SW are decreasing in the number of
transactions, because during each round of the auction buyers with the highest ability
to pay and sellers with lowest cost will benefit. In each round of double Vickrey
auction the price of good at first increases and then remains constant, then begins to
decrease until it reaches zero (Fig. 11).
Fig. 11. Price dynamics in double electronic Vickrey auction for true type’s agents
Vickrey auction agents’ underestimating their ability to pay or overestimating their
costs will result in reducing consumer surplus, producer surplus and social welfare.
As soon as agents with larger ability to pay and lower cost can not deal in auction,
they will discover during few periods that revealing their true type will allow them to
maximize their own surplus.
Proposed model of double electronic Vickrey auction for true type’s agents is
described by the following algorithm by the means of C#:
publicvoid Deal(Auction auction)
{intcount_take = 0;
intcount_not_take = 0;
stringpattern_one="The transaction took place (1)";
stringpatter_second="The transaction did not take place
(0)";
for(inti=0;i=
auction.Seller_auction[i].Ask)
{count_take += 1;
richTextBox5.Text +=+i+1+pattern_one + "\n";}
else
{count_not_take += 1;
richTextBox5.Text +=+i+1+patter_second + "\n";}}}
publicList Price(Auction auction)
{intprice_did_not = 0;
float average = 0f;
for(inti=0;i=
auction.Seller_auction[i].Ask)
{average = (float)(auction.Customer_auction[i+1].Bit +
auction.Seller_auction[i+1].Ask) / 2;
averageList.Add(average);
this.richTextBox3.Text += average.ToString()+"\n";}
else if (auction.Customer_auction[i].Bit <=
auction.Seller_auction[i].Ask)
this.richTextBox3.Text += price_did_not.ToString()+"\n";
if (i + 1 == auction.Customer_auction.Count)
break;}
returnaverageList;}
Double electronic Vickrey auction for hidden type’s agents
During the sale of goods through the auction mechanism a buyer tends to
undercharge his own ability, while the sellers tend to overvalue their own costs. So
electronic Vickrey auction for true type’s agents is less likely than e-auction for
hidden type’s agents. In theory double Vickrey auction motivates participants to fully
disclose their types, because they pay the second largest cost. However, the proposed
here new model of double Vickrey auction for hidden type’s agents demonstrated that
some of agents can hide their true type, despite the existing incentives for disclosure.
According to traditional models of double Vickrey auction agent type is disclosed
completely.
Consider software module ‘Vickrey auction’ for double electronic Vickrey auction
for hidden type’s agents (Fig. 12).
Fig. 12. Double electronic Vickrey auction for hidden type’s agents
In this module first we enter Numbers of buyers and Numbers of sellers. Consider
equal numbers of buyers (15) and sellers (15). After entering the data into the
appropriate field (Fig. 12), we obtain buyers’ real ability to pay real bid (as a random
number between 1 and 100) and deviation bias for bid (as a random number in the
interval (0, 1)), which reduces percent of real solvency and gives us actual ability to
pay actual bid. Therefore the relationship between indicators for buyers looks like:
actual bid = real bid * (1- bias for bid). Similarly, we obtain the real costs of seller
real ask and deviation bias for ask, percent of which overstates the actual costs, and
reported expenses actual ask are received. Thus, the relationship between indicators
for sellers is as follows: actual ask = real ask*(1+bias for ask).
After that reported solvency actual bid is arranged in descending order, and
reported costs actual ask is arranged in ascending order. Then pair-wise comparison
takes place between the buyer with the highest ability to pay and seller with lowest
cost. If bi ai then there is an agreement (deal=1) between buyer i and seller i at
the price of Pi (bi 1 ai 1 ) / 2 . For deal i consumer surplus of buyer is
CSi bi Pi , producer surplus is PSi Pi ai , social welfare is SWi CSi PSi .
Otherwise, the agreement between the buyer and the seller does not take place
(deal=0). Buyers and sellers who do not deal have the incentive to reveal their true
types (solvencies or costs).
Proposed model of double electronic Vickrey auction for hidden type’s agents is
described by the following algorithm by the means of C#:
publicList Deal(Auctionauct, ListDealList)
{intcountdeal = 0;
intcountnodeal = 0;
for (inti = 0; i=auct.Seller_auction[
i].ActualSell)
{DealList.Add(true);
countdeal++;}
else
{DealList.Add(false);
countnodeal++;}}
returnDealList;}
publicList PS(Auctionauc, ListListPs,
ListListPrice)
{float temp;
floatps;
for (inti = 0; i0 &&
auc.Customer_auction[i].ACtualBid>auc.Seller_auction[i].A
ctualSell)
{ps = ListPrice[i] - auc.Seller_auction[i].Ask;
ListPs.Add(ps);}
else
{ps = 0;
ListPs.Add(ps);}}
returnListPs;}
But the agreement between buyers and sellers is not completed. Those buyers and
sellers who have no deals may revise their bids, that is to reveal their real types. They
have an incentive to do so because they haven’t got the desired unit of good. After
revealing their true type their deviation will be zero: bias for ask = 0, bias for bid = 0.
Further agreements will be revised to reflect the new bids. Then those agents who in
the first round were able to buy (sell) goods at their bid and concealed their true type
in the second round may lose this opportunity. Then they will get an incentive to
disclose their true types. This procedure continues until the final round yields no
changes in the redistribution of goods compared to the previous round. It means that
the double Vickrey auction for hidden type’s agents is completed.
Fig. 12 demonstrates that the buyers’ solvency of 2, 6 and 14 remains hidden while
the remaining buyers fully reveal their types. Similarly, sellers 1, 4, 8 and 12 did not
disclose their true costs, while the rest of the sellers do it. Thus our Vickrey auction
model compared with other auctions formats reveals some true types of agents, but
this auction format does not motivate all to do as stated in classical Vickrey auction
model. In proposed auction model low cost sellers and high solvency buyers can
conceal their true types.
For our example 80% of buyers and 73% of sellers reveal their types (i.e. 76% of
all traders). 20% of buyers and 27% of sellers conceal their types (i.e. 24% of all
traders).
5. Conclusions
To improve e-commerce efficiency there are special mechanisms for distribution of
goods and payments such as auctions models that are designed to convert private
information about the value of goods for buyers and sellers into common knowledge.
Vickrey auction (sealed bid second price auction) best of the existing auction
formats reveals the types of participants. Software modules for dynamic double
electronic Vickrey auction were first developed to generalize this auction format. It is
determined that in double electronic Vickrey auction incentives are created for most
buyers and sellers to reveal their true solvencies and costs. But for some buyers and
sellers these incentives are not enough to disclose their types, which reduces the
efficiency of the auction format. The designed program of dynamic double electronic
Vickrey auction is closest to perfect competition market and in terms of social welfare
ahead of alternative auction formats such as first price auction, English and Dutch
auctions, in which the vast majority of agents are hiding and not revealing their types.
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