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.
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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

Reny's new exsistence theorem

In the plenary session on the third day of BWGT conference (link), Professor Philip Reny talked about his new research on monotone pure strategy equilibria:

Title: On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games (link to pdf)

Abstract: We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure strategy equilibria in Bayesian games. We allow action spaces to be compact locally-complete metrizable semilattices and type spaces to be partially ordered probability spaces. Our proof is based upon contractibility rather than convexity of best reply sets. Several examples illustrate the scope of the result, including new applications to multi-unit auctions with risk-averse bidders.

According to Prof. Reny, while the topic of the paper is related to many fields such as mathematical economics, mechanism design, and auctions, there are two seminal papers that strongly motivated his research. Athey (2001) first establishes the sufficient conditions to guarantee the existence of monotone pure strategy equilibria in Bayesian games with one-dimensional and totally ordered type and action spaces. The key condition is a Spence-Mirlees single-crossing property. McAdams (2003) extends Athey's analysis to multi-dimensional and partially ordered spaces.

Prof. Reny succeeded to derive weaker conditions than McAdams in Bayesian games with multi-dimensional strategy spaces, and also extend to the infinite type and action spaces. The key insight is to use a fixed point theorem derived by Eilenberg and Montgomery (1946) instead of Kakutani's (used by Athey) or Glicksberg's (used by McAdams) ones. The latter two theorems require best reply sets to be convex while the former requires only contractibility, which turns out to be (almost) automatically satisfied in Bayesian games.
His main result says the following:

Theorem: (Under some conditions) If, whenever the other players employ monotone pure strategies, each player's set  of monotone pure-strategy best replies is nonempty and join-closed, then a monotone pure strategy equilibrium exists.

Note that a subset of strategies is join-closed if the pointwise supremum of any pair of strategies in the set is also in the set.

The idea of join-closedness (in the different context, though) recently showed up when I discussed my jointwork on the structure of stable matchings with co-authors. It may have some connection...

References
Susan Athey (2001), "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information,"  Econometrica, Vol. 69: 861-889.
Samuel Eilenberg and Deane Montgomery (1946), "Fixed Point Theorems for Multi-Valued Transformations," American Journal of Mathematics, Vol. 68: 214-222.
David McAdams (2003), "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Vol. 71:1191-1214.

JEP for FREE

Here comes a great news!

Online issues of the Journal of Economic Perspectives published since 1999 are now publicly accessible at no charge, compliments of the American Economic Association.

You can access to the Journal of Economic Perspectives from here. The symposium in the latest volume (Spring 2010), Con out of Economics, contains interesting debate among leading econometricians that may attract much attention.

Reserach Advice by Don Davis

Original article (link) posted: 04/09/2005

Professor Davis at Columbia University put the note "Ph.D. Thesis Research: Where do I Start?" on his web site.
There are many interesting advices. Especially the following two are helpful for me.

Don’t Take Courses!
By the third year of a PhD program, your job is research, not more courses! You can take more courses (of course), but you should have a very good reason for doing so. Acceptable reasons include (a) It is a course that takes you to the frontier of research in an area in which you plan to do research or (b) It develops mathematical or econometric techniques that you plan to use in short order. The reason that I advise not taking courses is that it is a convenient, comforting, and seemingly rationalizable way of avoiding the harder, more frustrating, but necessary conversion from being a consumer of research to being a producer of research. Focus on your primary task – developing your own research program.

Don’t teach!
. . . more than you have to. For many, teaching is attached to a stipend or is otherwise economically unavoidable. In this case, do what you must! Moreover, there are some real intellectual and practical advantages from doing a couple of terms of TA work. Explaining the concepts to others is very useful in consolidating them in yourself. But beyond this, the returns become strongly negative. Your job is research – and anything that distracts you from this is a heavy cost. The first cost, which may seem remote at the time that you are deciding on the teaching, is that it could delay completion of the thesis by a year or more. An even larger cost is if it crowds out time to write a really great thesis. As a PhD student, your time is very valuable; treat it that way.

Hum, as Professor Obara recommended to me, I shouldn't teach this year even like a small group seminar... Also, instead of attending classes, it must be better for me to use time for focusing on my own research or going to seminars.