Matching Markets & Auctions

Bence Gábor
Microeconomics
BBCI 2015 (Summer Semester)
Instructor: Prof. (FH) Mag. Dr. Ferry Stocker

Table of Contents Table of Contents 2 Introduction 3 Matching Markets 3 Finding the best match 3 Auctions 4 Auction formats: 4 Private values vs Common values: 5 Bidding strategies: 5 Glossary 6 Bibliography 7 Books: 7 Websites: 7 Graphs: 7

Introduction
The aim of this report is to introduce matching markets and auctions in microeconomic level. These two might sound unfamiliar to many people, although they appear in our life almost on daily basis, we just do not usually recognize them.
Matching Markets
Markets can be thought as a prime example of network structured interaction between people (usually sellers and buyers) who interact with each other.
A few of the basic examples of matchmaking from everyday life are marriage, applicants and colleges, students and dormitory rooms, students and universities, doctors and hospitals, and so on. Of course normally there are some constrains, otherwise there would be no need for any kind of market. For instance an organ donor’s blood type must be compatible with the patient’s, or a student has some expectations toward the available dormitories.
Finding the best match
The procedure of finding the best match is relatively easy when only one side of the market has preferences over its matches, like in the mentioned student-dorm example. In that case each student apply for the most desired room. However, real life is not in an ideal world, it often happens that not all or none of them gets the desired place, which indicates unstable pairing. We can help on this (staying at this example) by letting swapping the rooms among them. This process can be repeated until all rooms are allocated, and then stability – Pareto efficiency – can be achieved. On the other hand this state is not always likely to be equal or fair, if one is not lucky enough to be in one of the early rounds of swapping cycles, it can easily happen that the person will not receive the best of his or her choice.
Things are getting complicated and a little bit exciting, when both sides have preferences over their matches. The matching procedure for these occasions is devised by Gale and Shapley, called the deferred acceptance algorithm. An understandable demonstration would be the case of four students (a,b,c, and d) who apply for colleges (A,B,C, and D). The following image shows the preferences:

Figure 1
Let’s choose colleges’ side. On the left column each college makes an offer to the student it ranks highest (so for example college ‘A’ prefers student ‘a’ the most and student ‘c’ the least). In the first round in this example student ‘d’ gets offers from ‘B’ and ‘D’, so he or she chooses college ‘B’, according to his or her ranking. Regarding to others, both student ‘a’ and ‘b’ have one offer, which they accept, so student ‘c’ is only left behind in the first round. In the second round college ‘D’ (the one which was rejected by student ‘d’) offers a place to its next preference, namely student ‘c’. Now that each student has an offer, the procedure stops.
It is provable that this method produce stable outcomes, although it is manipulable: one can get better results, by misrepresenting its preferences.
Auctions
Auctions are well known to everyone in the decade of World Wide Web, it would be hard to find someone among the Internet users who has never heard of eBay for example. In many cases auctions are more beneficial for both buyers and sellers, than the negotiated prices, because it bring the potential buyers together and competition arises.
Auction formats:
First-price Sealed-bid auctions:
Each bidder submits a bid without knowing the other bidders’ offer. The highest bidder gets the item, and pays the price he or she offered.
Second-price Sealed-bid auctions:
Procedure is the same as the previous, except this time the winner has to pay the second highest bid, instead of what he or she offered.

Open ascending-bid auctions (English auction):
This is the classic form, which can be often seen in films. Each participant make increasingly higher bids, until no one would like to make a higher bid. The highest bidder wins and pays the amount he or she offered. In this type of auction the seller is allowed to set a reserve price, which means it can only be sold, if the winner bid exceeds this amount.
Open descending-bid auctions (Dutch auction):
This is exactly the opposite of the previous, the seller sets an unrealistic high price, and it is lowered until one bidder offers the current price.
Private values vs Common values:
Auctions can also be classified as involving private values or common values.
Private values:
A situation in which each bidder in an auction has his or her own personalized valuation of the object.
Common values:
A situation in which an item being sold in an auction has the same intrinsic value to all buyers, but no buyer knows exactly what that value is.
Bidding strategies:
From the bidder’s perspective, in a first-price auction giving a bid equal to his valuation of the object will not get him any profit or surplus even if he wins. On the other hand, if the bid is far below the valuation, chances of winning are dramatically reduced. Therefore the bid should be somewhere near below the valuation.
In a second-price auction it is a bit different, since the winner pays the second highest bid which is outside his control. Here probably the best choice is to maximize the probability of winning, meaning that the bid should be equal to the full valuation.
From the seller perspective, the auction format in general does not matter because of the revenue equivalence theorem: when participants in an auction have private values, on average any auction format will generate the same revenue for the seller. However, when bidders have common values, a complication arises that does not occur when bidders have private values, the winner’s curse: A phenomenon whereby the winning bidder in a common values auction might bid an amount that exceeds the item’s real market value.

Glossary

* Pareto efficiency: is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off. * Bid: a certain amount of money offered in an auction * Bidder: the person who offers that amount of money * Reserve price: the minimum price set by the seller, which must be exceeded by the winner bid, otherwise the item will not be sold * Intrinsic value: is a set value, without reference to its actual market value

Bibliography
Books:
* Avinash Dixit, 2014. Microeconomics: A Very Short Introduction (Very Short Introductions). 1 Edition. Oxford University Press. * David Besanko, Ronald R. Braeutigam, 2010. MICROECONOMICS 4th Edition
Websites:
* From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World. By David Easley and Jon Kleinberg. Cambridge University Press, 2010. [Accessed 14th May, 2015] http://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch10.pdf * Auction theory – Wikipedia [Accessed 14th May, 2015] http://en.wikipedia.org/wiki/Auction_theory * Pareto Efficiency – Wikipedia [Accessed 14th May, 2015] http://en.wikipedia.org/wiki/Pareto_efficiency Graphs: * Figure 1:
Avinash Dixit, 2014. Microeconomics: A Very Short Introduction (Very Short Introductions). 1 Edition. Oxford University Press. (p 109)