Wants, Greed, and Capitalism

A special TV program on capitalism (link) will be broadcasted tomorrow by NHK from 11pm (50 minutes) in Japan. The Japanese title of the program is "欲望と資本主義", which roughly corresponds to the title of this blog post. The program aims to (re)consider essential aspects of our economic society and the future of capitalism (as well as its origin), focusing especially on people's wants and greed. I contribute to the program as a navigator, interviewing major players from academia, financial sector and IT industry. The persons whom I made interviews are listed below (alphabetical order):

- Alvin E. Roth, Professor at Stanford University (Nobel laureate)
- Tomas Sedlacek, Chief Macroeconomic Strategist at CSOB
- Scott Stanford, Co-Founder & Managing Partner at Sherpa Capital
- Joseph E. Stiglitz, Professor at Columbia University (Nobel laureate)
- William Tanuwijaya, founder & CEO at Tokopedia

I would be grateful for everyone involved in this wonderful program. Really look forward to watching it :)

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

New Papers

My new paper, "Exit Option Can Make Cooperation Easier" (joint with Takako Fujiwara-Greve) is uploaded at SSRN. The manuscript is very short (only 7 pages!). Please take a look if you are interested in how introducing exit option would affect cooperative incentives.

A completely different paper on matching, "Expanding "Choice" in School Choice" (joint with Atila Abdulkadiroğlu, Yeon-Koo Che) was finally published in the American Economic Journal: Microeconomics. (as a lead article!) Our earlier paper, "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered", appeared in the American Economic Review, was originally a part of this AEJ paper. Both are theoretical works but contains important policy implications on public school choice. It would be very nice if you could read (and hopefully cite) the articles :)

Sotomayor (1996)

Sotomayor, M. (1996), A non constructive elementary proof of the existence of stable marriages, Games and Economic Behavior, 13: 135–7.  Link 

Abstract  Gale and Shapley showed in their well known paper of 1962 (Amer. Math. Monthly 69, 9–14) that stable matchings always exist for the marriage market. Their proof was constructed by means of an algorithm. Except for the existence of stable matchings, all the results for the marriage market which were proved by making use of the Gale and Shapley algorithm could also be proved without the algorithm. The purpose of this note is to fill out this case. We present here a nonconstructive proof of the existence of a stable matching for the marriage market, which is quite short and simple and applies directly to both cases of preferences: strict and nonstrict. 

In this short note, the author establishes the existence of stable matchings for the marriage market, i.e., one-to-one matching market, without employing any algorithms. Her key idea is a new concept that she calls a simple matching, which is defined as follows:

A matching is simple if, in the case a blocking pair (m, w) exists, w is single.

Since the set of simple matchings is nonempty and finite, there must exist a specific matching that I call here (for notational convenience) an M-simple matching:

A simple matching is M-simple if it cannot be (weakly) Pareto dominated for men by any other simple matching.

Then, she shows that such M-simple matching is stable. The basic logic is that the existence of blocking pair necessarily induces Pareto improvement for men (since w is single), which contradicts to the Pareto efficiency of M-simple matching for men.

As the author claims, the proof is very shout and simple, yet quite novel I think. To explain her proof strategy in a different way, she

1. focuses on the subset of stable matchings, 
2. characterize it by "M-simple matching," and
3. shows that the set is non-empty. 

It is immediate that M-simple matching is unique and coincides with M-optimal stable matching when all the preferences are strict. In this way, we can see that her idea is somewhat related to the existence of one-sided optimal stable matchings, a widely known result in the literature.

A minor remark: The definition of matching in the paper incorporates individual rationality, and consequently that of of stable matchings pays attention only on blocking pairs. This looks a bit non-standard while nothing is lost in her analysis.

A final remark: I like this paper very much :)

How did GS algorithm come out?

Roth, A. (2008), Deferred acceptance algorithms: history, theory, practice, and open questions, International Journal of Game Theory, 36: 537-569.

In this survey article on the Gale-Shapley's deferred acceptance algorithm, Al Roth mentions (in footnote 3) an amazing story about how GS discovered the algorithm (which of course established the theory of two-sided matchings):

At his birthday celebration in Stony Brook on 12 July 2007, David Gale related the story of his collaboration with Shapley to produce GS by saying that he (Gale) had proposed the model and definition of stability, and had sent to a number of colleagues the conjecture that a stable matching always existed. By return mail, Shapley proposed the deferred acceptance algorithm and the corresponding proof. 

Frontiers of Science

I have been to Potsdam in Germany on Nov. 11 - 14 to attend 7th Japanese-German Frontiers of Science Symposium 2010 (link). It's a really interdisciplinary conference jointly organized by Alexander von Humboldt Foundation and Japan Society for the Promotion of  Science.

I was a invited speaker of the social science session titled "New Methods in Decision Making" (session list), and talked about "Recent Developments in Market Design and its Applications to School Choice" (slide). It was quite exciting to give a presentation to researchers from completely different fields, mainly from natural science. Although I didn't have enough time to cover the details of my own studies, many of them seem to get surprised to see how powerful and useful game theoretical tools are.

I also enjoyed the talks and discussions in other sessions very much. Most of topics were unfamiliar to me of course, but their frontier works looked truly exciting. This was a wonderful opportunity indeed! Many thanks to the organizers and participants :)