Game Theory and Society

Weiying Zhang

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351330978
• Edition: 1
• Topic: Betriebswirtschaft
• Subtopic: Business allgemein

The progress of society can only happen through interpersonal cooperation, because only cooperation can bring about mutual benefit, thus bringing happiness to each person. This should be our collective rationality, but we often see it conflicts with individual interests, which leads to the so-called "Prisoners' Dilemma" and does not bring happiness to all.

From a game theoretical perspective, this book addresses the issue of how people can cooperate better. It has two objectives. The first is to use common language to systematically introduce the basic methodologies and core conclusions of Game Theory, including the Nash equilibrium, multiple equilibriums, dynamic games, etc. Mathematics and theoretical models are used to the minimum necessary scope too, to make this book get access to ordinary readers with elementary mathematical training. The second objective is to utilize these methods and conclusions to analyze various Chinese social issues and institutional arrangements, with a focus on the reasons people exhibit non-cooperative behaviors as well as the institutions and cultures that promote interpersonal cooperation.

In addition to economics, specialists in sociology, law, history, politics and management will also be attracted by this book for its insightful analysis on the issue of cooperation in these fields. Also, readers curious about Chinese society will benefit from this book.

1
Individual rationality and social cooperation

Coordination and cooperation are the two primary issues faced by human societies that affect the interests of each member of society. Aligned expectations must be formed to resolve the coordination issue. The incentive mechanism must overcome the misalignment between individual rationality and collective rationality to resolve the cooperation issue. The basic function of social institutions is to coordinate expectations and promote cooperation, thus resolving the conflicts caused by the “Prisoner’s Dilemma” and unaligned expectations.

Game Theory is a tool for analyzing interactive decision-making. It studies how people in societies act, how people coordinate with each other, how social institutions evolve, and how to better design institutions to realize cooperation. Game Theory assumes that people are rational. Although this assumption is a bit extreme, Game Theory built on the rationality assumption still provides a good analytical tool to predict people’s behavior and evaluate institutions. It is precisely economist’s rationality assumption that promotes the human cooperative spirit and increased moral standards, not the contrary.

All men created equal means each person is the best judge of his own happiness. This point applied to economics is the utilization of the Pareto efficiency criterion to judge whether a person’s behavior is proper or not and should be incentivized (or sanctioned). The Pareto criterion means a person implementing an action that does not harm the interests of others is proper, otherwise it is improper. Under the equality of opportunity premise, a Pareto optimal satisfies Rawls’s social justice requirements and thus is a collective rationality standard.

This book’s title is Game Theory and Society. The hope is to emphasize the ways in which to utilize Game Theory methodology to analyze social issues and analyze the types of institutions that assist interpersonal coordination and cooperation. The goal is to make human life happier.

Section one: basic issues of society

In the book Robinson Crusoe, English novelist Daniel Defoe told the story of a seafarer named Robinson Crusoe who, because of an accident at sea, lived alone on an island for twenty years. Every day on the island, Crusoe had to consider the amount of time he would allocate between farming, hunting, and fishing. This is a classic resource allocation problem. The issues faced by Crusoe are the same issues we as individuals face: With limited resources and time, how do we decide to produce (or purchase) different items so that we can obtain the most satisfaction from economic activity?

As for the resource allocation problem, economists have already undertaken profound systematic research. The basic conclusion reached is that if in each additional application of resources the marginal return of production declines,¹ then the optimal allocation of resources must satisfy the condition that the last unit of resources will create the same gain no matter what application it is used for. Thus, the marginal contribution of each application must be equal. In economics, this is called the equi-marginal principle.²

However, the vast majority of us do not live on an isolated island like Crusoe. Instead, we live in groups, so not only are each person’s choices limited by resource restraints, but are also limited by restraints from the choices of others. If we say that the main issue faced by each individual³ is the resource allocation problem, then what is the main issue faced by society? In other words: What is the basic issue faced by a society?

To answer this question, we must first clarify the meaning of “society”. We use the word “society” almost every day, such as “contemporary society”, “social issues”, and “underground societies”, but what is society?

This is a question that each of us can grasp, but not explain clearly. In different contexts, the meaning of the word “society” is different. The basic concept refers to a group in contrast to an individual. American biologist Edward O. Wilson defined “society” as a group of similar individuals that is formed through mutual cooperation.⁴ More simply, we can define society as interaction and interdependence between a group of individuals. When each person makes a decision, consideration must be given to personal choices and the choices of others. Because no person’s choices are given, the results of each person’s decisions will be influenced by the decisions of others. This type of interaction within a group will determine the social attributes of each individual. The social attributes of a person mean that one person’s choices are not entirely something that person can decide. A person’s choices are influenced by social values and cultural factors. Concepts like virtue and vice, right and wrong, and fairness only have meaning when humans are members of society. Our language, manners, cuisine, and clothing all indicate that humans are social animals.

One example using language would be a student of mine that did not turn his homework in on time. My teaching assistant asked him the reason, and he replied that he got sick because of a lack of moral character. When my teaching assistant reported this to me, I did not understand the connection between lacking moral character and getting sick. My assistant explained to me that among young people, “moral character” (“rénpǐn”) meant “luck” (“yùnqi”), not “moral conduct” (“pǐnxíng”). I asked him how “moral character” would come to have this meaning among young people. He said he did not know, but because everyone else spoke like that, he did, too.

In Game Theory, a person doing something because everyone else is doing it is called herd behavior. Herd behavior does not only exist for language, but also manners, clothing, cuisine, investment, etc. Herd behavior can be considered an obvious reflection of people’s social attributes.

From the above descriptions, we could consider society as an interdependent group. From there, we can ask again: What is the basic issue faced by society?

Perhaps each reader will have a different understanding of this issue. Academic circles also have different viewpoints. Traditionally, economists focused on the issue of efficient allocation of social resources. Sociologists focused on the issue of interests between different members of society. Jurists focused on the issue of how individuals undertake responsibilities and duties. These understandings make sense from certain perspectives, but from the perspective of interpersonal interaction, there are two most basic issues of society: The coordination problem and the cooperation problem.⁵ Because in most practical issues these problems are often combined together, people often believe that they are the same problem. Actually, the coordination problem and cooperation problem are vastly different, so separating them is extremely important.

1.1 The coordination problem

What is the coordination problem? Below, we use traffic as an example. This example is a pure coordination problem because conflicts of interest do not exist.

For two people considering which side to travel one, each person has two choices: The left or the right. If their choices are not compatible, meaning one person chooses to travel on the left side and the other on the right side, at some point they will run into each other. If their choices are compatible, meaning they both choose to travel on either the left or the right, they can proceed unhampered. We can explain this using Figure 1.1.

Figure 1.1 Traffic Game

In the figure, the numbers represent the benefit each of the two people gain from making each choice. The first number represents the benefit for Pedestrian A, and the second number represents the benefit for Pedestrian B. If both people chose to travel on the left (the top left corner) or travel on the right (the bottom right corner), then each will proceed unhampered, so we can say that their payoff is 1. If their choices are incompatible, meaning Pedestrian A chooses to travel on the left but Pedestrian B chooses to travel on the right (the top right corner) or the other way around (the bottom left corner), then they will bump into each other, so we can say that their payoff is −1.

The reader should note that this figure assumes that under each situation, both parties obtain the same benefit from each, either 1 or −1. In some cases, this assumption is untrue because one person may fare worse than the other in the collision or because one person may benefit more from proceeding unhampered. However, by assuming that their benefit is the same and that the benefit of complementary action is higher than the benefit of contradictory action we can depict the essence of the coordination problem. The essence is that both benefit from coordinated interaction and both lose from uncoordinated interaction.

The core of the coordination problem is the way in which people anticipate other’s actions. The most direct method of understanding expectations is mutual communication and exchange. For example, if Pedestrian A and Pedestrian B travel on foot, when they approach each other, they can communicate via language or hand signals to coordinate each other’s actions.

Communication is the exchange of information and knowledge between people. To make the correct predictions, the people involved must grasp relevant knowledge. This includes knowledge about the scope of behavior, the other party’s special characteristics, and the other party’s expectations about one’s own knowledge. This is known as higher-order knowledge.⁶ In China, there is a saying “to enter the village and adapt to the customs”. When people go to other parts of the country to take care of matters, they often must understand the way local people get along with each other to adjust their own behavior. This knowledge of customs and social norms is extremely important for resolving the coordination problem. In some parts of northeastern China, when toasting someone else, it is considered polite to finish the alcohol in your own glass before the person being toasted. In Henan, however, the other person should be allowed to drink first. When a northeasterner and a Henanese drink together, how should they display respect? Depending on their location, they should become accustomed to the local custom to resolve the coordination problem.

Knowledge about the other party’s special characteristics is also extremely important for resolving the coordination problem. In the traffic example given above, if one of the people involved is blind and the other finds this out, they will coordinate with the blind person by changing their own choices. For new drivers, putting a sticker that indicates as so on the back of their car warns others that they are not accustomed to driving, which helps coordination. In many situations, coordination means that different people should respect different rules. At that point, understanding the special characteristics of others is even more important. In ancient China, traveling officials banged on gongs to clear the streets. It was a way to communicate their special status so that others could adjust their behavior.

Grasping higher-order knowledge of other’s expectations about one self is also very important. In the traffic example we observed, Pedestrian A’s decision to keep to the left or right must consider Pedestrian B’s expectation of Pedestrian A’s decision. If Pedestrian A believes Pedestrian B will expect Pedestrian A to keep to the left, Pedestrian A’s best choice is to keep to the left. If Pedestrian B predicts that Pedestrian A will keep to the left, but Pedestrian A mistakenly believes that Pedestrian B predicts he will keep to the right so that Pedestrian A chooses to keep to the right, then there will be a collision. This shows that the coordination problem not only requires expectations to be consistent, but also that expectations about expectations are consistent. In reality, this requires the ability to correctly predict other’s behavior to be quite high. Because of differences in the structure of knowledge, beliefs, and biases, it is very difficult to correctly judge other people’s intentions, while at the same time it is difficult to know other people’s expectations of our judgments. At this point, there will be a failure of coordination. Many conflicts in human society are not conflicts of interest, but instead of misunderstandings or incorrect expectations.

Generally speaking, because of the various types of knowledge required to make correct predictions, we often have too little knowledge, or no usable knowledge at all. As for knowledge about norms, when traveling to the unfamiliar, we often find that we have difficulty completely grasping the local customs. In daily interaction with friends, we often also find out that close friends sometimes surprise us. This means that we have not completely grasped all of our friends’ special characteristics. Of course, sometimes we will have too much knowledge that our minds cannot comprehend, so we are at a complete loss at what to do. Another situation that causes us to be unable to form correct expectations is our failure to use knowledge. In real life, we often discover that we know something, but when making decisions, because of various reasons, including forgetfulness, we do not correctly utilize this information.⁷

In any case, communication is costly. If the cost of communication is high, or even impossible, how can coordination happen? Imagine two people are driving fast and their point of contact is around a curve. Before contact, they cannot see each other, but once they come into contact, it is already too late to communicate. This type of situation in which coordination via communication is difficult is common in reality. After all, communication requires certain prerequisites, such as language, ideas, and knowledge; otherwise, it is ineffective.⁸

For the traffic issues we observed, one of the means to resolve this issue is to establish traffic rules. For example, in China, the law states that we drive on the right, but in England and some other countries, they drive on the left. Why is it that laws can resolve the coordination problem? The reason that laws and formal institutions can resolve the coordination problem is that they aid people in correctly judging (or predicting) other people’s behavior. For example, when the traffic laws dictate that people drive on the right, each driver will anticipate that other drivers will drive on the right, so driving on the right is everyone’s best choice. Of course, in many situations, the formation of expectations relies on the authority behind laws. The existence of authority means that when someone violates the law, they will be punished. When it is expected that everyone else will respect authority or abide by the law, then abiding by the law becomes each person’s best choice. As soon as the law loses authority, it cannot play a coordinating role because at that point, people lose the ability to predict other’s behavior. The significance of this is that an important reason people are willing to accept authority is to better coordinate. Conducting an orchestra is a classic example. In reality, this is the reason that during an emergency situation, such as a serious traffic jam, people will follow the guidance of a volunteer that orders people about.

We can see that in order to resolve the coordination problem, people must all be able to correctly predict the actions of others. In order to make correct predictions, people must communicate, grasp, and correctly apply relevant information. Some clear rules are also necessary. Communication and rules both play a role in coordinating predictions. The relative advantage and importance of the latter depends on the specific issue. In reality, in a situation with clear rules and rules that are in play, we can rely on rules to predict other’s behavior. In a situation with unclear rules and rules that are not in play (including different people’s different perceptions of rules), communication is more important.

1.2 The cooperati...