On October 15, 2012, it was announced that this year's Nobel Prize in Economics was to be awarded to Harvard University's professor Alvin Roth and UCLA's professor Lloyd Shapley "for the theory of stable allocations and the practice of market design." This year also saw Kyoto University's professor Yamanaka awarded the Nobel Prize in Physiology or Medicine, so you would think that the Nobel Prize was a topic of interest on TV, but it seems that the economics prize was hardly noticed by the public. One reason for that could be that, until now, no Japanese has ever been awarded the economics prize, but also possibly because economic science is not something thought of as practical in real life. However, the research of this year's Nobel Prize in Economics winners involves medical intern matching, school choice mechanism and kidney exchange etc. and is being put to practical use.

In this essay I would like to comment on this year's Nobel Prize in Economics winning research and explain its practical possibilities. And I would also like to touch upon some of the research I have begun as it is deeply related to this research.

1. Game theorist wins again

This year's Nobel Prize winning research belongs to a field which is generally called matching theory or market design. Moreover, this field is considered as an application field of game theory.

Looking at the list of Nobel Economic Prize winning researches in recent years, what first attracts attention is that the percentage of winning research being related to game theory is extremely high. Game theory is a theory related to the way people make decisions in strategic situations, and with the publication of von Neumann and Morgenstern's Theory of Games and Economic Behavior in 1944 leading the way, is a relatively new field of study. Put simply, the strategic situations here are situations where choices made by opponents would change the optimal choice for your side (think of a game of paper-scissors-rock.) In this kind of situation, it is necessary for both sides to "read" your opponent's approach, so, at a quick glance, you may think it is impossible to predict what kind of action will be chosen, but game theory has developed that kind of theory. After that, things have become clearer through various research, and actually, strategic situations are omnipresent around us, and game theory which can predict what will occur there possesses an extremely wide application range. Today, everywhere in economics, be it micro or macro, and even going beyond economics, game theory has been recognized as an analysis tool used in sociology, political science, and biology.

Through the accumulation of this kind of research, starting with 1994, the 50^th anniversary of the publication of Theory of Games and Economic Behavior, John Nash, John Harsanyi and Reinhard Selten were awarded the Nobel Prize in Economics for their achievements in the basic research of game theory. And then two years later in 1996, James Mirrlees and William Vickrey were awarded the prize for their contribution to the incentive theory when economic information is asymmetrical. Even after entering this century, George Akerlof, Michael Spence and Joseph Stiglitz (2001) were awarded for their analyses of markets with asymmetric information, Robert Aumann and Thomas Schelling (2005) for having enhanced our understanding of conflict and cooperation through game theory analysis, and Leonid Hurwicz, Eric Maskin and Roger Myerson (2007) for having laid the foundations of mechanism design theory. It is no exaggeration in saying that there is no field of economic theory that isn't related to game theory to some degree, and other award winners have greatly relied on the game theory model.

2. Matching theory

First of all, as the simplest and most familiar (?) example, I will explain matching theory by using the situation of a match-making party.

Let's think that at a certain party there were three males (Ichiro, Jiro and Saburo), and three females (Matsuko, Takeko, and Umeko). Each male has a preference ranking of which female they like (table 1), and the females also have a preference ranking of which male is their type (table 2). Matching completely designates who (male) becomes a pair with who (female), like in tables 3 and 4. When comparing these two matchings, we can see that while Ichiro and Jiro's level of satisfaction will be higher in Matching B (table 4) than in Matching A (table 3), Saburo's will remain unchanged. Thus, moving from a matching to another can improve somebody's condition while not worsening the condition of others. In this kind of situation, Matching B is said to Pareto-dominate Matching A, and when there can be no more matchings that Pareto-dominate the current one (from the male's point of view, in the present context), it is called Pareto-efficient matching. Matching B is a Pareto-efficient matching. Also, when we look at Matching B, if Saburo and Matsuko are paired together, both of their levels of satisfaction will rise. In this way, in a given matching, if a couple not paired together can improve their current situation when paired together, that matching is called unstable, and if that kind of pair doesn't exist, it is said to be a stable matching. While Matching A has stability, Matching B is unstable.

Table 1 Male preference rankings
Male1	1st choice	2nd choice	3rd choice
Ichiro	Takeko	Matsuko	Umeko
Jiro	Matsuko	Takeko	Umeko
Saburo	Matsuko	Takeko	Umeko

Table 2 Female preference rankings
Female	1st choice	2nd choice	3rd choice
Matsuko	Ichiro	Saburo	Jiro
Takeko	Jiro	Ichiro	Saburo
Umeko	Jiro	Ichiro	Saburo

Table 3 Matching A
Ichiro	Jiro	Saburo
↓	↓	↓
Matsuko	Takeko	Umeko

Table 4 Matching B
Ichiro	Jiro	Saburo
↓	↓	↓
Takeko	Matsuko	Umeko

This example shows that matchings can be characterized as having several properties, and the problem lies in how to achieve a matching which possesses desirable properties. This year's Nobel Prize winner Shapley, along with David Gale, proposed the following type of algorithm (the example is a version where males propose to females, but there are also female to male versions.) Today, this is called the Gale-Shapley algorithm.

First, all the men and women hand in their preference rankings. On top of that, based on these preferences, the algorithm proceeds as follows. Each man proposes to the woman he prefers the most. If the woman has one suitor, she is provisionally "engaged" to that suitor, if there are two or more suitors, she will be engaged to the man highest on her list. At this stage, the males who have not been accepted propose to the second female on their list. If the woman proposed to is free at that time, they will become engaged. If she is already engaged from the first stage, she will then choose the highest ranking male from the first stage and the new suitor. At this stage, there is a chance that the already engaged male will be turned down. In doing so, the turned down male will propose to the next female on his list in the next stage. This procedure concludes after a limited number of rounds, and at that stage, the final match pairs will have been decided.

The Gale-Shapley algorithm has excellent properties in the following sense. First of all, at the stage of presenting their own preferences in the beginning, the presentation of one's true preference always becomes optimal. Accordingly, the necessity to strategically think about what preferences other people will hand in is eliminated. Secondly, the matching realized in the Gale-Shapley algorithm is certain to be stable (in this example, Matching A is realized.) As mentioned above, Matching A is unfortunately not Pareto-efficient, but stable.

I hope I have given you the general idea. The match-making party example is the simplest example dealt with in matching theory. Matching is also applied in the matching market of interns and medical institutions, and kidney exchange (transplants cannot take place if the patient and family member are non-transplantable types, but other patients and family members in the same situation may be able to have the kidney transplant.) Professor Roth, who won this year's prize, has fervently pushed ahead with this research over many years, and has worked hard to see the use of his devised mechanisms become a reality. "The practice of market design" was given as one of the reasons behind receiving this year's award.

3. Are affirmative action policies valid? : Experimental research of school choice mechanisms

One of my current research topics is testing school choice mechanisms. In the past, the primary school and junior high school which you attended was decided by the area you lived in and there was no room for choice, but in recent years it has become possible for students to select a school from a wide range of choices. However, in the case where a certain school gains a lot of popularity, a decision on allotting every student to each school through some kind of procedure must be made. This kind of system is called the school choice mechanism. Depending on what kind of concrete procedures are used to decide the allotment, there is the possibility that student's levels of satisfaction will be greatly affected. The school choice mechanism theory can also be analyzed by using the above mentioned matching theory.

In Boston, the following school choice mechanisms have been used. First, the students state their preferred schools in order, and if the number of students designating a school as their most preferred school falls within that school's quota, those students' admission into the school will be confirmed. The students whose admission isn't decided will then apply for their second choice, and if there is room left in the quota, their admission will be decided. If there are still students who haven't been placed in a school, they will then apply for their third-choice school and so on.

In this type of mechanism, it may not be optimal for students to state their true preferences as it breeds the necessity for the students to "read" into each other's applications. Professor Roth pointed this out and proposed that the Gale-Shapley algorithm be used in the school choice mechanisms in Boston. His proposal was actually adopted.

Furthermore, recently Japanese researchers Fuhito Kojima and Taisuke Matsubae have conducted research related to the effects of affirmative action policies on school choice mechanisms. For example, in the case where students are divided into a majority and minority, school choice mechanism where the maximum quota for the majority is decided, or the maximum number of preferential entrants from the minority applicants is decided, can be envisioned. Theoretically, it has been pointed out that this kind of affirmative action policy does not necessarily improve the welfare of the minority. However, whether or not that would actually occur on a regular basis cannot be made clear by theoretical research alone.

Therefore along with Future University Hakodate professor Toshiji Kawagoe and the National Graduate Institute for Policy Studies' professor Yosuke Yasuda, I have been conducting experimental research into those mechanisms. Just the other day, as part of our research, laboratory experiments were carried out on students at the Chuo University Tama Campus. We plan to release the results of those experiments to the institute in an essay in the coming weeks.

Hirokazu Takizawa
Professor of Game Theory, Experimental Economics, and Philosophy of Economics, Faculty of Economics, Chuo University

Born in Tokyo in 1960. Completed credits at the Graduate School of Economics, University of Tokyo in 1997. Entered current position in 2010 after working as a visiting research fellow at the Stanford Institute for Economic Policy Research, assistant professor at the Faculty of Economics, Toyo University, and fellow at the Research Institute of Economy, Trade and Industry. Major publications include, Kawagoe, T. and H. Takizawa (2009), "Equilibrium Refinement vs. Level-k Analysis: An Experimental Study of Cheap-talk Games with Private Information," Games and Economic Behavior, Vol. 66, pp.238-255, Kawagoe, T. and H. Takizawa (2012), "Level-k Analysis of Experimental Centipede Games," Journal of Economic Behavior and Organization, Vol. 82, pp.548-566.