Chamberlin vs. Smith in Roth (1995)

I found very interesting description in The Handbook of Experimental Economics, Chapter 1: Introduction to Experimental Economics by Prof. Alvin Roth. He refers two pioneering papers on experimental economics, Chamberlin (1948) and Smith (1962), which investigate commodity markets under different trading rules and check whether competitive equilibrium could be established.

[T]he basic design of Chamberlin (1948) for inducing individual reservation prices and aggregate supply and demand curves has become one of the most widely used techniques in experimental economics.

Interestingly, Chamberlin (1948) reports systematic gap between his experimental results and the competitive equilibrium. The experimental design and its results are summarized as follows.

Chamberlin created an experimental market by informing each buyer and seller of his reservation price for a single unit of an indivisible commodity, and he reported the transactions that resulted when buyers and sellers were then free to negotiate with one another in a decentralized market.
<...>
The experiment he reported involved 46 markets, with slightly varying equilibrium prices. He observed that the number of units transacted was greater than the competitive volume in 42 of these markets and equal to the competitive volume in the remaining 4 markets, while the average price was below the competitive price in 39 of these markets and higher in the rest.

By contrast, (repeated) double auctions experimented by Smith (1962) result in convergence to the equilibrium.

One important form of market organization is the double auction market, first experimentally studied by Smith (1962), who observed rapid convergence to competitive equilibrium when the market was repeated several times with stationary parameters.

One might be puzzled why the number of transaction in ALL experiments in Chamberlin (1948) exceed or equal to the competitive volume: none falls below it. My recent article, Equal Market Design I: Competitive Market Achieves the Greatest Happiness of the Minimum Number, provides a theoretical account on this puzzle. This short paper (only 8 pages!) shows that the number of agents who engage in trades under any market equilibrium is MINIMUM among all Pareto efficient and individually rational allocations in the environment where redistribution by the third party is infeasible, i.e., no monetary transfers beyond buyer-seller pairs are prohibited. So, if buyers and sellers in Chamberlin's experiments somehow manage to reach the PE and IR allocations (it is likely although I have to check the original data if available), the number of transaction must be weakly larger than that of competitive equilibrium.


Acknowledgment
I would like to thank Prof. Morimitsu Kurino who pointed out the possible connection between experimental studies and my research, explicitly mentioning the above two papers, i.e., Chamberlin (1948) and Smith (1962).

References
Chamberlin, E. H. (1948). An experimental imperfect market. The Journal of Political Economy, 95-108.
Kagel, J. H. and Roth, A. E. (1995). The handbook of experimental economics. Princeton, NJ: Princeton university press.
Smith, V. L. (1962). An experimental study of competitive market behavior. The Journal of Political Economy, 111-137.
Yasuda, Y. (2016). Equal Market Design I: Competitive Market Achieves the Greatest Happiness of the Minimum Number, mimeo. SSRN#2755893

What is an Auction?

I found a nice introductory description of auction from the viewpoint of economics or game theory in the following textbook on auction theory:

The below is the (partial) quotation from the chapter 2.3.1, titled "What is an Auction?":

[A]uctions Have become an effective tool to implement public policy. Their use now ranges from the allocation of radio spectrum necessary for mobile communication, to spot markets trading electricity and pollution permits, as well as being widely used in government procurement. 

We can now define an auction by one of its central properties: as a market clearing mechanism, to equate demand and supply. Other market mechanisms include fixed price sales (as in a supermarket) or bargaining (as in the negotiated sale of a house or a used car). Within the class of market mechanisms which allocate scarce resources, one particular characteristic of the auction is that the price formation process is explicit. That is, the rules that determine the final price are usually well-understood by all parties involved. 

Auctions are often used in the sale of goods for which there is no established market. Auctions were instrumental in the mass privatization in Eastern Europe given the absence of a price system that could guide the valuation process for firms being privatized. Rare or unique objects are typically sold in auctions as the markets for these objects are likely to be very thin. However, auctions are also used to sell Treasury bills and the markets for these assets are very thick. The reason is that only governments can legally produce such bonds and therefore the sale in an auction is an exercise in revenue maximization. 

Auctions are more flexible than a fixed price sale and perhaps less time-consuming than negotiating a price. Auctions are used to sell hundreds of goods, such as bales of wool or used cars, in a few hours. One can imagine how many hours it would take to sell 100 used cars through negotiated sales.

3G Auctions in UK: Q&A

The last chapter of Paul Klemperer's famous auction book provides non-technical answers to the FAQs on spectrum auctions, especially on the 3G auction that he (and Ken Binmore) designed and implemented in the UK.



The chapter titled "Were Auctions a Good Idea?" is based on his newspaper article, "The Wrong Culprit for Telecom Trouble" appeared in Financial Times (Nov. 26, 2002) where he listed three typical critics against 3G auctions:

The critics assume three things, that 

1: the telecoms companies paid more for the licenses than they thought the licenses were worth

2: this expenditure has reduced investment in 3G

3: it destroyed the telecoms companies' market value

Paul answers to each question as follows:

1. It is now hard to imagine any company voluntarily paid billions for a 3G license. But volunteer they all did - and they celebrated their victories. (...) Like any other market, an auction simply matches willing buyers and willing sellers - it cannot protect them against their own mistakes.

2. The auction fees are history; they have (almost) all been paid in full, cannot be recouped by cutting investment, and make no difference to its profitability. (...) Investment in 3G, as in anything else, is primarily motivated by attractive returns in the future - not by money spent in the past.

3. All in all, it seems a stretch to blame $100bn of shareholder misery on $100bn of 3G license fees.

Then, he concludes the article by saying:

There is nothing special about an auction: it is just another market. Buying houses or shares at the peak of a housing or stock-market boom does not entitle anyone to compensation. Why should we make an exception for the phone companies?

(...)

The main effect of the license fees was simply to transfer $100bn from shareholders around the world to certain European governments. This was both equitable, since the companies were buying a public asset that they valued this highly at the time, and efficient, since such a lump sum transfer is much more efficient than most forms of taxation. Efficient, equitable and voluntary government funding is not easy to find: perhaps we should be more enthusiastic about it.

Theory Seminar (Sigurdsson)

Original article (link) posted: 05/10/2005

Sigurdsson (2005) "Auctions as Mechanism: An Application to Bankruptcy Reorganization" Job Market Paper

In the paper, he proposes the new mechanism of reorganization of firms in cases of bankruptcy. As a matter of fact, a firm that files for bankruptcy must either liquidate under Chapter 7 of the Bankruptcy Code or reorganize under Chapter 11. The distribution follows the absolute value priority rule (APR) which states that no creditor shall receive any value until all claims senior to his have been paid in full. Legal scholars have proposed several mechanisms as alternatives to the current system of judicially supervised bargaining, widely believed to be costly, lengthy, and to result in inefficient capital structures and violations of the APR. A major drawback of those proposals is their reliance on cash payments.
In the mechanism he proposes, the entire reorganized firm is sold in a cash auction and the proceeds are distributed to creditors according to the APR. He mentions 4 advantages of his mechanism. That is, the mechanism
1) implements the APR for far more general capital structures than the simple debt and equity structures assumed in previous mechanisms.
2) all but eliminates the need for cash payments and therefore works under tight financial constraints.
3) offers the advantage of familiarity over its more novel competitors in an auction.
4) allocates ownership efficiently when creditors do not agree on the firm's value.

It seemed that the participants of the seminar liked his paper. Hope he will get a good job!!
By the way, his main advisor is Eric Maskin. I heard a rumor that he did not take a student, but it should be wrong. I would like to talk to him about my research too.

Auction theory: Myerson and mechanism design approach

Continued from the previous two articles, we still focus on Introduction of the auction book:

After referring early literature on auction theory, the authors introduce mechanism design theory and explain Myerson's path-breaking contribution.

The early work of Vickrey, Wilson, and Milgrom was largely focused on an equilibrium analysis and comparison of standard auction formats. Myerson led the development of mechanism design theory, which enables the researcher to characterize equilibrium outcomes of all auction mechanisms, and identify optimal mechanisms - those mechanisms that maximize some objective, such as revenues. His first application was to auctions.

Myerson (1981) determined the revenue-maximizing auction with risk-neutral bidders and independent private information. He also proved a general revenue equivalence theorem that says that revenues depend fundamentally on how the items are assigned - any two auction formats that lead to the same assignment of the items yield the same revenues to the seller.

The trick in Myerson's analysis was recognizing that any auction can be represented as a direct mechanism in which bidders simultaneously report their private information and then the mechanism determines assignments and payments based on the vector of reports. For any equilibrium of any auction game, there is an equivalent direct mechanism in which bidders truthfully report types and agree to participate. Hence, without loss of generality we can look at incentive compatible and individually rational mechanisms to understand properties of all auction games. Incentive compatibility respects the fact that the bidders have private information about their values; individual rationality respects the bidders voluntary participation decision. This key idea is known as the revelation principle (Myerson, 1979).

The following is a brief summary of other related papers.

Myerson and Satterthwaite (1983)

• applied revelation principle
• proved the general impossibility of efficient bargaining

Related Papers

• Cramton, GIbbons, and Klemperer (1987) showed that efficiency becomes possible when the traders jointly own the items
• Wilson (1993) also showed efficient mechanisms when the roles of buyers and sellers are not fixed ex ante

References
Cramton, Gibbons, and Klemperer, "Dissolving a Partnership Efficiently," Econometrica, 1987.
Myerson, "Incentive Compatibility and the Bargaining Problem," Econometrica, 1979.
Myerson, "Optimal Auction Design," Mathmatics of Operations Research, 1981.
Myerson and Satterthwaite,  "Efficient Mechanism for Bilateral Trading," Journal of Economic Theory, 1983.
Wilson, "Design of Efficient Trading Procedures," in Friedman and Rust ed., The Double Auction Market: Institutions, Theories, and Evidence, Addison-Wesley Publishing Company, 1993.

Auction theory: Vickrey and early literature

Continued from the previous post, let me quote interesting parts from the editors' introductory summary.The following nicely illustrates the contribution of the pioneer of auction theory, William Vickrey.

Vickrey's seminal paper (Vickrey, 1961), mentioned in his 1996 Nobel Prize in economics, introduced the independent private value model, demonstrated equilibrium bidding behavior in a first-price auction, and then showed that truthful bidding could be induced as a dominant strategy by modifying the pricing rule: let each bidder pay the social opportunity cost of his winnings, rather than his bid. Finally, he showed in an example what would later be proven generally as the revenue equivalence theorem: different auction mechanisms that result in the same allocation of goods yield the same revenue to the seller.

Then, the authors explain a few important papers in the early literature of auction theory since Vickrey. The followings are my summary.

Wilson (1969)

• (pure) common value
• first analysis of equilibrium bidding with common values
• demonstrated the importance to avoid (what would be later called) the winner's curse

Milgrom (1981)

• common + private values
• discovered the importance of monotone likelihood ratio property (MLRP)
• showed that MLRP + conditional independence implies that

1. bidders use monotonic bidding strategies
2. a monotonic strategy satisfying the first-order condition constitutes an equilibrium

Milgrom and Weber (1982)

• affiliated values: if one bidder has a high signal of value, it is more likely that the signals of the other bidders are high
• showed that under affiliated values

1. Vickrey's revenue equivalence result no longer holds when we introduce a common value element
2. ascending auctions yield higher revenues than sealed-bid auctions

References
Milgrom, "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, 1981.
Milgrom and Weber, "A Theory of Auctions and Competitive Bidding," Econometrica, 1982.
Vickrey, "Counterspeculation, Auctions, and Competitive Sealed Tenders," Journal of Finance, 1961.
Wilson, "Competitive Bidding with Disparate Information," Management Science, 1969.

Combinatorial Auctions: Introduction

This book is a great collection of papers on a rapidly growing filed, "combinatorial auctions."


Let me quote a couple of useful sentences below taken from Introduction written by the editors, Peter Cramton, Yoav Shoham, and Richard Steinberg.

• The study of combinatorial auctions thus lies at the intersection of economics, operations research, and computer science.
• There are numerous examples of combinatorial auctions in practice. As is typical of many fields, practice precedes theory. Simple combinatorial auctions have been used for many decades in, for example, estate auctions.
• Recently, a variety of industries have employed combinatorial auctions. For example, they have been used for truckload transportation, bus routes, and industrial procurement, and have been proposed for airport arrival and departure slots, as well as for allocating radio spectrum for wireless communications services.
• Auction theory is among the most influential and widely studied topics in economics over the last forty years. Auctions ask and answer the most fundamental questions in economics: who should get the goods and at what prices? In answering these questions, auctions provide the micro-foundation of markets. Indeed, many modern markets are organized as auctions.

Kamien (Handbook of GT 1992)

Original article (link) posted: 12/09/2005

Kamien (1992) "Patent Licensing" Handbook of Game Theory, vol.1, chapter 11

This survey focuses on game-theoretic analysis of patent licensing. In the paper, the interaction between a patentee and licensees is described in terms of a three-stage game. In the first stage, a patentee sells the patent by using some mechanism. Firms in the industry simultaneously decide their buying strategies in the next stage. And finally, patents are distributed according to the rule of a mechanism and market competition (Cournot competition) is realized.
The main focus on the paper is comparison between different mechanisms which are (1) auction (2) fixed fee licensing (3) royalty (4) hybrid of (2)&(3). The interesting result is that licensing auction yields higher revenue than fixed fee or royalty does. In some situations, however, the hybrid mechanism colled "chutzpah" mechanism yields even higher revenue than auction does.
The analyses introduced in this survey has several restrictions such as; no private information, identical firms, only considering profit maximization.
In the end, the paper concludes as follows.

It is often the case that a survey of a line of research is a signal of it having peaked. This is certainly not true for game-theoretic analysis of paten licensing.

I hope this comment is still true although it has been written in 15 year ago...

Interesting Papers on References

Jensen (1989) "Reputational spillovers, innovation, licensing and entry" IJIO, 10-2
Katz and Shapiro (1985) "On the licensing of innovation" Rand, 16
Katz and Shapiro (1986) "How to license intangible property" QJE, 101
Muto (1987) "Possibility of relicensing and patent protection" EER, 31
Reinganum (1989) "The timing of innovation: Research, development and diffusion" in Handbook of IO

Open-bid auctions facilitate collusion

Original article (link) posted: 02/08/2005

Milgrom (1987) makes the point that collusion may be easier to sustain for infinitely repeated "descending" auctions (notice we think about procurement auctions here) than for infinitely repeated sealed-bid auctions.
...
In a repeated descending auction, a deviation is discovered immediately (instead of one period later) and thus can be made unprofitable, even from a static point of view (the deviator's rival can refuse to give up before the price equals "c" in the current auction). Collusion is feasible for any discount factor. The market organization thus affects detection lags and the amount of feasible collusion.
(Tirole p.262)

Second price auctions also sustain collusions even in a static setting, because they can make deviations unprofitable by the same way as the open-bid auctions. Graham and Marshall (1987) is the pioneering paper about collusions in English (second-price) auctions.

References

Graham and Marshall (1987) "Collusive Behavior at Single-Object Second-Price and English Auctions" JPE, 95
Milgrom (1987) "Auction Theory" in Advances in Economic Theory

Two Auction Examples in FT

Original article (link) posted: 23/07/2005

FT illustrates two examples of First-price Auction, Ex 6.5 (continuous) and Ex 6.6 (discrete).
In Ex 6.5, they establish the uniqueness of the equilibrium when the reservation price is higher then the lowest valuation, and the equilibrium is symmetric. Their basic argument is that when the above condition holds, Lipschitz continuity is also satisfied, which implies the unique solution to the differential equation derived by FOC.
In the footnote, they mentioned the multiplicity of the solution of the war of attrition.

Standard results on the uniqueness of solution to differential equations require Lipschitz continuity. The war of attrition of example 6.3 is not Lipschitz continuous at s=0, which is why it is possible for the system represented in equation 6.3 to have multiple solutions.

Auction Literature (papers)

Original article (link) posted: 23/07/2005

Some imprtant papers in Literature on single-unit auctions.

The following three papers are survey and lecture notes.
1. Milgrom (1989) "Auctions and Bidding: A Primer" J. of Econ. Perspectives, 3
2. Bulow and Roberts (1989) "The Simple Economics of Optimal Auctions" JPE, 97
3. Matthews (1995) "A Technical Primer on Auction Theory 1" Mimeo, Northwestern Univ.

1 is bit old but excellent survey of single-unit auction theory. It is still worth reading.
2 is the first paper which pointed out that auction models can be analyzed by the same way as IO. They initiated graphical analysis in auction theory.
3 is an unpublished lecture note, which is suite for those who have no background.

The next is the most important paper in the literature. The author got the Nobel prize at 1996 because of this work.
4. Vickrey (1961) "Counterspeculation, Auctions and Competitive Sealed Tenders" Journal of Finance, 16

The following paper initiated revolution of auction theory. Everyone interested in auction theory MUST read this!
5. Myerson (1981) "Optimal Auction Design" Mathematics of Operations Research, 6

One of the most important contributions in auction theory after Myerson. It became a classic that you should know.
6. Milfrom and Weber (1982) "A Theory of Auctions and Competitive Bidding" Econometrica, 50

Collusions in auctions are exciting topic. You should first read the following.
7. McAfee and McMillan (1992) "Bidding Rings" AER, 82

Recent research on auction has been focusing more and more on experiments and multi-unit auctions. Multi-unit auctions are strongly related to matching problems. To study matching theory, the following textbook is must read.
8. Roth and Sotomayor (1990) "Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis"

Auction Literature (textbook)

Original article (link) posted: 23/07/2005

The followings are references for auction theory.
There are at least 4 textbooks now.

1. Krishna (2002) "Auction Theory"
2. Klemperer (2003) "Auctions: Theory and Practice"
3. Milgrom (2004) "Putting Auction Theory to Work"
4. Menezes&Monteiro (2005) "An Introduction to Auction Theory"

1 is the most standard and concise, yet very rigorous textbook. Those who want to focus on auction theory should read this book first. He also spends many spaces for multi-unit auctions, using 6 chapters out of 17.
2 is the collection of the articles by Klemperer. Easy to read and recommended for beginners. It does not cover theory of auction comprehensively.
3 contains both auction theory and detailed survey of actual auction design. You would get motivated by this book written by one of the legend in this field.
4 is a recent book. The style is similar to Krishna but mainly focus on single-unit auction.

The chapter of Auction in the following book is well written and highly recommended for the readers who don't have enough background on game theory.

5. Wolfstetter (1999) "Topics in Microeconomics : Industrial Organization, Auctions, and Incentives"

The following two books might be useful for those who have interest on auction designs in real world.

6. Illing and Kluh (2003) "Spectrum Auctions and Competition in Telecommunications"
7. Janssen (2004) "Auctioning Public Assets"