# Game Theory for Integrative Knowledge

Game theory is a mathematical modeling and analysis of the strategic behavior of people where choices by a player affect the interests of a different player and vice versa. Its application is vast and continuously growing.

**Prof Takaaki Abe is an award-winning game theorist who has analyzed the strategies behind political alliances and the buck-passing drama of garbage disposal.**

## What is your specialty?

I research game theory.

## Why did you decide to pursue this career?

I first learned about game theory in high school, before attending university. In Japanese schools, beginning in elementary, junior high, to high school, students are expected to clean the communal areas after lunch and after school. We would clean the classrooms and sweep the hallways, and when I was in high school, I was on the committee that supervised the cleaning. Since everyone was still young, some students skipped cleaning. At the time, I thought skipping cleaning was an issue with the individual. I thought it was a matter of personal attitude of inattentiveness and a lack of motivation.

So, in the back of my mind, I wondered what I could do to help them chip-in and clean up properly. One day after school, I went to a bookstore near my house. The book “Game Theory” caught my eye, not because I thought it was something helpful, but because I thought it was about a video game like Pokemon. I picked it up and started reading the book. To my surprise it said that skipping cleaning was rational from a game-theory point of view.

It caught me off guard. In the book it said for example, if there are 30 people in a class and 29 people clean up, the class will be clean. Then, even if one person doesn’t take on the trouble of sweeping, wiping and moping, the room would be clean, and that person could enjoy the clean room to the fullest. So, that person could receive the full benefit of having a clean space without paying the cost.

In that sense, not cleaning is rational. I was surprised when I read that. Until then, I thought that not cleaning was a matter of lacking character and a bad personal attitude. However, I learned that not cleaning was a rational option from a game theory point of view. This is called the social dilemma, when the non-cooperative payoff for a player exceeds the cooperative payoff.

The book said that not cleaning was a rational option, and I began to think, "Well, that's one way to think about it.” I became intrigued and decided to study game theory when I entered university. So, the reason was I came across a book on the subject at a local bookstore.

## What is game theory?

Game theory is the mathematical modeling and analysis of situations in which your choices affect the interests of the other party and the other party's choices also affect your interests. A familiar example is rock-paper-scissors. If you play scissors when your opponent plays rock, you lose. If you play paper when your opponent plays rock, you win. Therefore, when both players have the option of playing “rock, paper, scissors,” their winners and losers depend on each other's choices, and so rock-paper-scissors is a game-theoretic situation. Rock-paper-scissors is only one example, but situations in which choices affect each other's interests can be found throughout society, which is why game theory is being applied to various situations and continues to spread to a wide-range of fields.

## In what situations is game theory applied?

Originally, game theory was developed by a mathematician named John von Neumann, and later, a book was published by von Neumann and an economist named Oskar Morgenstern. It has since been applied to a wide range of fields, including political science, biology, information technology, psychology, and business administration. An auction is a good example where game theory is applied, like an auction where people bid on paintings, drawings, and vases.

There are auctions like that, and there are other types of auctions that governments at a national level use to sell some spectrum resources for cellular phones and broadcasting. Auctions happen at many levels, from individual to national levels. Auctions can be better understood with game theory. Game theory can be used to design a market, ensuring that the desired items are delivered to the people who want them. Other examples of using game theory are when insurance companies set premiums for car and fire insurance. Traffic congestion can be alleviated with game theory modeling. Insight can be obtained about stock markets too.

## Do you specialize in economic game theory?

I am mainly concerned with economics; however, it is difficult to classify. Game theory researchers are in many departments. For example, there are game theorists in engineering, law, politics, psychology, and so on. Of course, I am at the economics department now, but I was in the engineering department before. So there is a wide range of applications for game theory.

## What did your paper, “Buck-passing Dumping in a Garbage-dumping Game” elucidate? (Why does garbage disposal gather in certain countries or regions?)

This paper analyzed why we push the disposal of garbage to certain regions. For example, when you are thirsty and buy a bottle of tea at a convenience store, you don't hand the empty plastic bottle to someone else after drinking it, do you? But at the national level, this buck-passing happens often. For example, the plastic issue in 2017 where 60% of the plastic waste worldwide was sent to China. Another example is in the 2010s, garbage was being sent unilaterally from Canada to the Philippines. When President Duterte found out, he protested to the Canadian government, and it became a big issue between the two nations.

This garbage-dumping happened in Japan too, in the 1960s and 1970s. Almost all of the garbage generated in the 23 wards of Tokyo was sent to Koto Ward. The mayor of Koto Ward demanded that it be stopped. It was called the Tokyo Garbage War. It is not uncommon for people to impose garbage to others, and there are many such instances of these problems that transcend regions and times. To elucidate the general root of the problem, we used the mathematical modeling of game theory, in which the person making the decision is called the player. We analyzed the situation by setting up a condition in which the player imposes his garbage on the other players. We found that the behavior of forcing one's own garbage on others leads to equilibrium or gaining some stability from a game theory viewpoint.

When we model, we need to identify who the players are, what strategies they have, and what choices they make. Each player has a set of strategies to choose from: A has this strategy, B has this strategy, C has this strategy, and so on. So, when everyone’s strategy is determined, we see where the equilibrium is. The movements are quite dynamic. So, there is an awareness to capture and articulate that. The equilibrium in game theory can be seen as a kind of prediction for events.

The fact that garbage collects in one location is not necessarily a bad thing. If A is bad at garbage disposal, and B has developed technology for garbage disposal and B can dispose of garbage cheaply, it is not bad to have it collect all in one place because it is more efficient.

## What did you elucidate in Stable Coalition Structures and Power Indices for Majority Voting? (Why do political parties repeatedly merge and split?)

I used game theory to explain why political parties join or break up. If you look at the past 30 years in Japan, parties have been merging and splitting up quite frequently. Even recently, the Democratic Party of Japan has split off, and even when it seems to be getting back together, it splits off again.

To answer why parties join or break up, I model it with game theory. Game theory has many tools, among which is the power index. The power index is a measure of how powerful each voter is to make the final decision in a voting environment. Simply put, it measures power. When voters in a party behave to increase their influence, parties may frequently merge. We can see the characteristic of structures of political parties, such as a two-party system or a one-party system, by applying game theory.

With such research, I would like to clarify things that have not been clarified before, or to explain things that are not easily put into words, even if they are vaguely suspected in our daily lives, or explain things that have become vague, such as customs, practices, and culture, by clearly defining what is related to what, in a precise formula. It is one of the powers of game theory to clarify what is related to what and what is not related.

## I don't understand how people's power relationships translate into mathematical formulas.

This is simple; for example, you have a group of three high school seniors and juniors. Let's say they want to go to karaoke: A, B, and C. A and B are seniors, so each has three votes; C is a junior, so he has one vote. Let’s say four affirmative votes are needed to go to karaoke. Since A and B have three votes, they seem to be powerful, don't they? However, as I said, four votes are enough to decide to go to karaoke, so in fact, if A and B want to go to karaoke, or if B and C want to go to karaoke, or if A and C want to go to karaoke, it is the same outcome. So, C looks weaker than AB, but they are equal in power. The tool to calculate these things is the power index. There is a gap between what we intuitively think and the mathematically formulated outcome. Game theory reveals the gap between what we intuitively think and what is.

## Is game theory a new discipline?

Some say it began in the 1920s - 1940s, so it is newer than, say, physics and mathematics. Physics and mathematics have been around for a long time. If you look at it in the context of economics, it may indeed be new. It's still a hundred years old, or some would say it's seventy, or eighty years old. So, things are developing, and game theory itself is changing, because what we know now is very different from what we knew 70 years ago. Game theory itself is also evolving. Our social systems are also changing. As society changes, more things that can be analyzed using game theory. We are mutually evolving.

## How do you conduct your research?

My research is basically theoretical. I write down ideas on paper, and my notes are comprised of a lot of formulas. These notes are about patent pools. Many companies have patents, and it is now an inconvenient system where the patents are scattered. A patent pool provides a one-stop system to make it possible to obtain all the patents in one place. We are searching for ways to return the profits received from the patents to the patent holders and reduce the possibility of dissatisfaction. I refer to actual cases and data, but my focus are general structures underlying those cases.

I also work with experimental economics. The good thing about game theory is that you can test ideas in real-world applications. We can apply the theory in laboratory experiments too. We then collect data to see if the system we have designed really works and verify that the data is consistent with the theoretical predictions. We also have a way of verifying whether the mechanism is working well.

We explain auctions, for example, in theory, and then conduct experiments to see if they really work. If it doesn't work, we revise the theory, conduct another experiment, and so on. Social systems are difficult to experiment with in an actual country, so instead, one could experiment with the help of students or other people at a university for example. Once you test out some ideas with experiments, we can apply them in the real world.

## What are some things you hope to work on in the future?

I would like to work to advance game theory so that it can analyze more situations. There are many detailed classifications, but broadly speaking, game theory comes in two traditions. One is called cooperative games and the other is called non-cooperative games. Non-cooperative game theory is mainly used to analyze what strategy each individual player chooses. The main point is to behave strategically.

In cooperative games, when several players work together, there are costs and benefits. We analyze how to divide the profits and costs among the members, and what kind of cooperative groups can be formed. If you look around you in the real world, not all cases are 100% non-cooperative or 100% cooperative. Some situations are mixed. There can be cooperative sub-groups inside a larger non-cooperative group. Perhaps in some situations, in a cooperative group, there are strategic interactions. There are complex and rich aspects all around us.

If we work to extend game theory in a way that can include these unique aspects, we can apply game theory in such a way that it can be utilized more in our society. Game theory can be used in various types of situations where our actions can benefit or hinder those around us, and in return where the actions of others have an impact on us.

## How will your research contribute to Vision 2030?

Vision 2030 is a comprehensive vision of integrative knowledge, and I believe that game theory can contribute to drive this social change. Game theory is a common language that can be used to mathematically model situations of various disciplines. For example, what is happening in a certain field A and what is happening in a certain field B may seem to be unrelated, but in fact, from a game-theoretic point of view, they may have similar structures at work. In this way, the solution in A can be proposed by game theory, and the same solution can be used in B. Conversely, the solution in B can be applied to A. I believe that awareness of a problem can be applied to a solution across different fields. In this sense, game theory is a bridge between different fields.

Recently, the extreme specialization and fragmentation of various fields has become an issue, but I believe that game theory can connect a wide range of fields that have become disjointed, without being confined to the social and natural sciences. If we can do this, I believe that we will be able to connect multiple fields, which is necessary for the kind of integrative knowledge that we are aiming for in our Vision 2030.

For more information on Prof Abe’s work, please look at his site: https://sites.google.com/view/takaakiabecv/takaaki-abe.

Buck-passing Dumping in a Garbage-dumping Game, Theory and Decision 93:509-533, 2022 [doi:10.1007/s11238-021-09858-5]

Stable Coalition Structures and Power Indices for Majority Voting, Journal of Public Economic Theory 24:1413-1432, 2022 [doi:10.1111/jpet.12574]