Editing Auction (section)

===Participants=== <!-- a link to here exists-->

{| class="wikitable"
|-
! scope="col" | [[Forward auction]]
! scope="col" | [[Reverse auction]]
! scope="col" | [[Double auction]]
|-
|[[File:Purchaseauction.svg|frameless|none]]
|[[File:Supplyauction.svg|frameless|none]]
|[[File:Doubleauction.svg|frameless|none]]
|-
! colspan="3"| <math> \operatorname{v}_{1..m} </math> stand for sellers and <math> \operatorname{c}_{1..n} </math> for buyers
|}

Auctions can differ in the number and type of participants. There are two types of participants: a [[buyer]] and a [[Sales|seller]]. A buyer pays to acquire a certain good or service, while a seller offers goods or services for money or barter exchange. There can be single or multiple buyers and single or multiple sellers in an auction. If just one seller and one buyer are participating, the process is not considered to be an auction.<ref>{{cite book |last1=Ganguly |first1=D. |last2=Chakraborty |first2=Samit |title=2008 Ninth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing |chapter=E Commerce - Forward and Reverse Auction - A Managerial Tool to Succeed over Business Competitiveness |s2cid=7466904 |pages=447–452 |date=2008 |doi=10.1109/SNPD.2008.51|isbn=978-0-7695-3263-9 }}</ref><ref>{{cite book |last1=Preist |first1=Chris |last2=Bartolini |first2=Claudio |last3=Byde |first3=Andrew |title=Proceedings of the 4th ACM conference on Electronic commerce |chapter=Agent-based service composition through simultaneous negotiation in forward and reverse auctions |s2cid=1868153 |pages=55–63 |date=2003 |doi=10.1145/779928.779936|isbn=1-58113-679-X |citeseerx=10.1.1.1.1755 }}</ref><ref name="priceneg">{{cite journal |last1=Friedrich |first1=Michael |last2=Ignatov |first2=Dmitry |title=General Game Playing B-to-B Price Negotiations |journal=CEUR Workshop Proceedings |date=2019 |volume=2479 |pages=89–99 |url=http://ceur-ws.org/Vol-2479/project2.pdf}}</ref> 
{| class="wikitable"
|-
!  
! Single Seller
! Multiple Sellers
|-
! Single Buyer
| [[Trade]]
| [[Reverse auction]]
|-
! Multiple Buyers
| [[Forward auction]]
| [[Double auction]]
|}
The forward auction is the most common type of auction — a seller offers item(s) for sale and expects the highest price. A reverse auction is a type of auction in which the roles of the buyer and the seller are reversed, with the primary objective to drive purchase prices downward.<ref name="Reverse">{{citation
| last1 = Schoenherr
| first1 = Tobias
| last2 = Mabert
| first2 = Vincent A.
| title = Online reverse auctions: Common myths versus evolving reality
| journal = Business Horizons
| volume = 50
| issue = 5
| pages = 373–384
| date = September–October 2007
| doi = 10.1016/j.bushor.2007.03.003
}}</ref> While ordinary auctions provide suppliers the opportunity to find the best price among interested buyers, reverse auctions and [[buyer-determined auction]]s give buyers a chance to find the lowest-price supplier. During a reverse auction, suppliers may submit multiple offers, usually as a response to competing suppliers' offers, bidding down the price of a good or service to the lowest price they are willing to receive. A reverse price auction is not necessarily 'descending-price' —  the reverse [[Dutch auction]] is an ascending-price auction because forward Dutch auctions are descending.<ref>{{Cite web|url=https://www.procurehere.com/the-benefits-of-a-reverse-dutch-auction/|title=The Benefits of a Reverse Dutch Auction|work=Procurehere Blog|language=en-US|date=2018-01-15|access-date=2019-04-30|archive-url=https://web.archive.org/web/20190430125251/https://www.procurehere.com/the-benefits-of-a-reverse-dutch-auction/|archive-date=2019-04-30}}</ref> By revealing the competing bids in real-time to every participating supplier, reverse auctions promote "information transparency". This, coupled with the dynamic bidding process, improves the chances of reaching the fair market value of the item.<ref>{{cite journal
| url = https://www.scribd.com/doc/39032383/Electronic-Reverse-Auction-and-the-Public-Sector-Factors-of-Success-Moshe-E-Shalev-Stee-Asbjorensenf
| first1 = Shalev | last1 = Moshe
| first2 = Asbjornsen | last2 = Stee
| title = Electronic reverse auctions and the public sector – factors of success
| journal = J. Public Procurement
| volume = 10
| issue = 3
| date = Fall 2010
| access-date = 19 January 2014
| pages = 428–452
}}</ref>

A double auction is a combination of both forward and reverse auctions. A [[Walrasian auction]] or ''Walrasian tâtonnement'' is a double auction in which the auctioneer takes bids from both buyers and sellers in a market of multiple goods.<ref name="Milgrom p267">[[#Milgrom2004|Milgrom, 2004: p267]]</ref> The auctioneer progressively either raises or drops the current proposed price depending on the bids of both buyers and sellers, the auction concluding when supply and demand exactly balance.<ref>[[#Milgrom2004|Milgrom, 2004: pp. 267-268]]</ref> As a high price tends to dampen demand while a low price tends to increase demand, in theory there is a particular price somewhere in the middle where supply and demand will match.<ref name="Milgrom p267" /> A '''Barter double auction''' is an auction where every participant has a demand and an offer consisting of multiple attributes and no money is involved.<ref>{{cite arXiv |last1=Tagiew |first1=Rustam |title=Towards Barter Double Auction as Model for Bilateral Social Cooperations |date=22 May 2009 |eprint=0905.3709 |class=cs.GT }}</ref> For the mathematical modelling of satisfaction level, [[Euclidean distance]] is used, where the offer and demand are treated as vectors.