In this article I keep the basic concepts of game theory, cut most of the theory, and add my own understanding, so that the article can be enlightening to as many people as possible. If I had to sum up what game theory is, I would very much like to use this metaphor: “Music can generally be divided into four elements: melody, harmony, rhythm and timbre, and for a piece of music to sound good, every element matters. I compare life’s journey of more than thirty thousand days to a piece of music; the age a person accumulates as the torrent of time flows on is the main melody, and game theory is the harmony of the piece.”

Many people have heard of game theory. When it comes up, most people think: “It must be useful; I’m not sure exactly what it can do, but I seem to roughly get what it’s about.” In fact, it is hard for anyone who has never truly grasped game theory to understand what use it could have. In this article I plan to give an introduction to game theory from an ordinary person’s perspective, and along the way offer readers some basic applications of it.

Friends who have never studied music may not understand the metaphor above, so here is a quick explanation: all four of the elements above are important in music, but if you had to pick the most important one, it would be melody. For fairly simple pieces, most people who know nothing about music can still hear what the melody is, for example: “A laugh at the vast sea, surging tides on both shores” (does it feel like my words are making music?). The role of harmony, simply put, is to make the music richer. Mapping this back onto the metaphor, game theory is what fills life with rich color.

Game theory is called “game theory” in English. Academically, it is mainly a branch of economics, and also a branch of applied mathematics; the theory is devoted to studying adversarial behavior between two or more independent individuals. Its founder was John von Neumann (for convenience, I will call him Old Von from here on), a super cross-disciplinary giant who made enormous contributions to mathematics, physics, computer science and economics. He was incredibly brilliant (those who know him need no explanation from me, and to those who don’t, I couldn’t explain it anyway). There was also a man named Oskar Morgenstern, something of a fanboy of Old Von, and it was at Oskar’s urging that in 1944 the two of them jointly published a work titled Theory of Games and Economic Behavior (in English, “Theory of Games and Economic Behavior”, a full 1,200 pages; in fact it was mostly written by Old Von, while Oskar, as a fan, wrote the introduction for him and did some promotion). In addition, some of the ideas in Theory of Games and Economic Behavior came from Old Von’s 1928 paper On the Theory of Parlor Games, which is why some scholars consider 1928 to be the true year of game theory’s birth.

Types of Games

The types of games are a basic concept of game theory. Games can be classified by type in the following ways.

Cooperative games & non-cooperative games

It should be stated up front that cooperation can occur during the course of a game, whether it is a cooperative or a non-cooperative game. The difference is that a cooperative game has some kind of external binding force, so a party who betrays in the game is punished by that external force, whereas a non-cooperative game has no such external force, and punishment for betrayal can only come from the participants in the game. Generally, in business cooperation, the well-known contract law is the external binding force, which makes it a cooperative game. However, when we talk about games, we usually mean non-cooperative games by default, academic research is also about the latter, and in this article I mainly talk about the latter too.

Simultaneous games & sequential games

Simultaneous games, also called static games, are games in which the participants do not know the other participants’ actions when making their own moves, such as rock-paper-scissors.

Sequential games, also called dynamic games, are games in which the participants’ actions follow an order in time. Before each player acts, they can see what the previous player did, and can think about their own next move based on others’ actions. Most board games are sequential games.

Zero-sum games & non-zero-sum games

A zero-sum game is not one in which the final payoffs of the game add up to zero; the total may be zero, positive or negative. Generally speaking, it tends toward equilibrium or toward one side of the game. Board games and rock-paper-scissors both belong to this category.

A non-zero-sum game is one in which the final payoff of the game is a variable, and this variable can go various ways: it can make all participants’ payoffs bigger, or all of them smaller, or favor one side; all of these are possible. In non-zero-sum games, participants have the possibility of cooperating. The most famous example of a non-zero-sum game is the prisoner’s dilemma; friends who are not very familiar with it can look it up, and I will mention it again later.

Repeated games & non-repeated games

This classification is easy to understand. Take the prisoner’s dilemma as an example: if two criminals are only locked up once, it is a non-repeated game; if they are locked up many times, it is a repeated game. Repeated games are further divided into finitely repeated games and infinitely repeated games. A finitely repeated game can be understood as a repeated game with a fixed number of rounds, and an infinitely repeated game as a repeated game with an uncertain number of rounds.

How Games Are Played

How games are played is the core of game theory and the focus of academic research in the field, so this section will be fairly long and contain some rather abstract concepts.

Move

A decision, called a “move” in English, is the smallest unit of action in a game. For example, in a game of rock-paper-scissors, what you throw in a given round is one move. Likewise, in a game of chess, which piece you move in a given turn, and from where to where, is also one move.

Strategy

A strategy is the sum of all moves from the first step to the last. You can think of a strategy, in plain terms, as a kind of guiding philosophy: it is an abstraction above moves, and it guides you from the first step to the last. So it is in chess, and so it is in life.

Strategy set

The strategy set, “strategy set” in English, is the totality of all strategies. In rock-paper-scissors, the strategy set is {rock, scissors, paper}, just these three strategies, while the strategy sets of chess or other board games have many elements. Strategy sets can also be divided into finite strategy sets and infinite strategy sets. Rock-paper-scissors and chess both have finite strategy sets. Although Go could in theory be infinitely large, once a board size is fixed, it also counts as a finite strategy set. Infinite strategy sets are different. Take the two-person cake-cutting game as an example: the first person cuts and the second person picks first, and there are infinitely many ways to cut. Many people intuitively assume that infinite strategy sets are more complex than finite ones. In fact, it is exactly the opposite: Go is complex, yet its strategy set is still finite; the cake-cutting game is much simpler, yet its strategy set is infinite.

Pure strategy

Make the same fixed choice every time you play: always rock!

Mixed strategy

Rock half the time, paper half the time!

Completely mixed strategy

Rock with probability 1/2, paper with probability 1/4, scissors with probability 1/4!

Dominant strategy

A dominant strategy, also called a superior strategy, means that among all strategies A and B, if strategy A is better than B in every situation, then A is said to dominate B, or B is dominated by A, and in this case A is the dominant strategy. In plain terms, no matter how many strategies you have, your dominant strategy always produces better results than your other strategies. Dominant strategies can be further divided into strictly dominant strategies and weakly dominant strategies. The former is better than other strategies in every situation; the latter is sometimes better than other strategies and sometimes just as good. Note that a dominant strategy is not necessarily a winning strategy, but a winning strategy is always a dominant strategy, at least a weakly dominant one.

How to find a dominant strategy

The importance of dominant strategies is obvious. There are at least four ways to find them: elimination, putting yourself in the other’s shoes, minimax, and backward induction.

Putting yourself in the other’s shoes

Elimination needs no explanation, so let’s start directly with putting yourself in the other’s shoes. Most readers basically understand this method already. If you want a deeper understanding, you can look at a classic case in game theory, the naval route battle off New Guinea. The popular-science book on game theory by Tom Siegfried, A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature, also cites this case.

Minimax

This method is called “Minimax” in English, which literally means minimizing the maximum loss; in plain language, it means minimizing your loss in the worst case. The theory was first proposed by Old Von in Theory of Games and Economic Behavior.

In static games (simultaneous games), explaining this method fairly rigorously requires a payoff matrix, so I will first explain it in a less rigorous way. Take Tian Ji’s horse race as an example. If there are only three races and Tian Ji wants to win (he can only win 2:1), there is only one possibility: Tian Ji’s top horse vs. the King of Qi’s middle horse, Tian Ji’s middle horse vs. the King of Qi’s bottom horse, and Tian Ji’s bottom horse vs. the King of Qi’s top horse. The third race is the worst case for Tian Ji, with the biggest gap between the two horses, but he only loses one point, minimizing his loss; that is the minimax method. Why do I say this is a less rigorous explanation? Because Tian Ji’s order of horses is based on his knowing the King of Qi’s order, while in a static game you don’t know what the other side will play (think of rock-paper-scissors). If both Tian Ji and the King of Qi understood game theory, and they played enough rounds (say more than 100), their horse racing would turn into a psychological game. If you’re interested, think about it: who would win?

In dynamic games (sequential games), take the two-person cake-cutting game as an example. When both sides are perfectly rational, the person choosing will certainly choose the bigger piece. Based on the minimax principle, the person cutting should minimize their own loss in the worst case, so they should cut the cake into two equal pieces. The beauty of the two-person cake-cutting game is that the person who cuts picks last and the person who doesn’t cut picks first, which perfectly solves the fairness problem of dividing a cake between two people. So, for the more complex case of dividing a cake among three people, is there some similar mechanism that can also perfectly solve the fairness problem? More generally, for dividing a cake among [N] people (N ≥ 3), is there some similar mechanism?

Backward induction

This method is called “backward induction” in English. Its essence is to look forward and reason backward. First, you need to consider each of your own moves, and which move the other side will use in response to yours. This thought process is like expanding a decision tree; I will explain decision trees later, and friends who are not familiar with them can simply picture a tree for now. This expansion has to be worked all the way through to the last step, that is, to the leaf nodes of the decision tree. At that point you can see clearly what each side’s best choice is at the last step, and then reason backward to the first step. Backward induction has its own limitations: when you use it to look ahead and reason, the precondition is that you must have sufficient information. Simply put, if a player does not know enough, they cannot use this method. The role of information in games will be explained later. This method leads to some reflections on the prisoner’s dilemma:

In an infinitely repeated game (with an uncertain number of rounds), will the two sides cooperate the first time?
In a situation with multiple rounds of the prisoner’s dilemma, is it possible for the two players to cooperate again?
In a finitely repeated game (with a fixed number of rounds), can cooperation be reached in the last round?

Let me analyze the third question for you. Suppose the number of rounds is fixed at 10. To think about these 10 rounds, we need backward induction. First analyze the last (10th) round: since there are no further rounds, the situation is equivalent to a single-round game. That is to say, both sides will choose to betray. If both are perfectly rational, then when they play the 9th round they should realize that the next round is the last and there will be no cooperation. That being the case, there is of course no need to cooperate in this round either (note: the point of cooperating is to be able to keep cooperating next time). This backward reasoning can continue all the way to the first round, so if both sides are perfectly rational, they will choose to betray each other in the very first round. If you find this example too simple and want to go further, you can think about the pirate gold-splitting puzzle.

The rarity of dominant strategies

Dominant strategies in games are extremely rare and very hard to find. Generally speaking, for all dynamic games (sequential games), in my understanding of game theory, a dominant strategy always exists even in complex games (it’s just that as the complexity deepens, the computing power required grows larger and larger, until it exceeds the limits of the universe, but the universe is not the boundary of theory). On this point I disagree with some scholars (the mathematical proof is still being worked out, and I cannot give it yet). For example, among board games, the most famous are chess, Chinese chess and Go. In Chinese chess, if two computers with enough computing power play each other, then as soon as Red opens with the central cannon, Black can calculate that it has lost; the opening guidance computers give also covers only the first few rounds, and the further into the game, the more computing power is required.

Outcomes of Games

Every game has winners and losers. To study games well, you need to do statistical analysis of their outcomes. Academically, the study of game outcomes is generally done with payoff matrices and decision trees. Those who are very familiar with these two terms can skip this section; for those who aren’t, let me first give a narrow explanation with a metaphor:

Payoff matrix: for now, you can simply think of it as keeping records in a table.
Decision tree: it’s a bit like your great-great-grandfather (your grandfather’s grandfather) dividing his property among all you descendants, assuming he were still alive and had saved up a billion tons of gold.

P.S. Friends who know these two terms, don’t laugh at me. Still laughing! You’re still laughing! OK, that’s enough.

Theories of Games

Academically, there is a very famous theory in game theory called the Nash equilibrium, “Nash Equilibrium” in English. In 1951, the American mathematician Nash published a short paper titled Non-Cooperative Games (Non-Cooperative Games), in which he proposed the concept of the Nash equilibrium and gave a corresponding mathematical proof (based on the [fixed-point theorem]). As for understanding the Nash equilibrium, in plain terms it means that in a non-cooperative game among multiple people, if no player can unilaterally improve their own situation, the state of play is called a Nash equilibrium. Old Von had already proved in Theory of Games and Economic Behavior that such an equilibrium point must exist in zero-sum games. Nash’s contribution was to generalize from zero-sum games to non-zero-sum games and prove that such an equilibrium point still exists. When a game is in a Nash equilibrium, the system is stable. That is to say, if every player is perfectly rational, none of them is willing to change their current strategy on their own. Take the prisoner’s dilemma as an example: the situation in which both sides confess is the Nash equilibrium. In this equilibrium, if either prisoner unilaterally changes strategy, it only makes things worse for themselves. By contrast, although both sides denying everything is a win-win situation, it is unstable, because in that situation either prisoner has an incentive to change strategy and gain more for themselves. In two-person rock-paper-scissors there is also a Nash equilibrium: both sides play rock, scissors and paper each with probability 1/3. Obviously this example is not as intuitive as the prisoner’s dilemma and needs a mathematical proof to confirm; I’ll be lazy here and skip the proof.

Misconceptions about the Nash equilibrium

Misconception one

Believing that the Nash equilibrium maximizes the sum of all parties’ interests. The Nash equilibrium has nothing to do with maximizing interests, and the opposite may even happen: when the game is in a Nash equilibrium, it can be bad for every party. The classic example is the prisoner’s dilemma, where the Nash equilibrium is precisely the lose-lose situation.

Misconception two

Believing that the Nash equilibrium is unique. In some games there can be multiple Nash equilibria; for the proof see Nash’s short paper Non-Cooperative Games (it proves there is at least one, implicitly acknowledging there can be several, not exactly one, nor always several).

Limitations of the Nash equilibrium

Limitation one

Nash’s proof is non-constructive. That is, he only proved that such an equilibrium must exist, but gave no method for finding it. So how do you find a Nash equilibrium? Since the beginning of the 21st century, mathematicians have proved one after another that even for some fairly simple games, the amount of computation needed to find the Nash equilibrium can exceed what the entire universe can handle.

In their 2006 paper The Complexity of Computing a Nash Equilibrium, the three mathematicians (computer scientists) Constantinos Daskalakis, Dionyssis A. Fotakis and Christos H. Papadimitriou proved that computing a Nash equilibrium (Nash Equilibrium) is PPAD-complete, which means that in general it requires enormous computing resources (exponential or quasi-polynomial time), and large-scale games cannot be solved in a reasonable amount of time.

From the work of these mathematicians, you can once again feel both the charm and the challenge of game theory. Even some seemingly simple games are far more complex than people imagine.

Limitation two

For any slightly complex game, reaching a Nash equilibrium depends on a great many constraints. In real life, it is unlikely to be reached.

Information in Games

This section looks short and easy to understand, but I have placed it fairly late and even given it a chapter of its own, which shows how important it is to the whole article.

perfect information VS imperfect information

These two concepts usually apply to dynamic games (sequential games). During a game, if every participant, when making each move, knows the information about every event that has already happened, it is called perfect information; otherwise, it is imperfect information. Go and chess both belong to the perfect information category, while most card games belong to the imperfect information category.

complete information VS incomplete information

The difference between these two concepts mainly concerns the players. If every player’s characteristics are public (everyone knows everyone else’s characteristics), it is called complete; otherwise, it is incomplete. What are a player’s characteristics? In plain terms, they include: the game objective, the utility function, the payoff function, the cost function and so on. The game objective is easy to understand; this series of functions are abstract academic concepts, which you can loosely understand for now as: how high a price one is willing to pay to reach goals of different levels. Go and chess also belong to the complete information category, while auctions belong to the incomplete information category.

In games of the incomplete information type, no player can know the other players’ characteristics precisely. For this kind of game, [Bayes’ theorem] (Bayes’ rule) has to be brought in for probabilistic analysis, so as to guess the other opponents’ characteristics. This is why such games are also called Bayesian games. For Bayesian games, the Nash equilibrium is called the Bayesian Nash equilibrium, abbreviated BNE (Bayesian Nash equilibrium) in English.

perfect information VS complete information

You may wonder why I use the English terms instead of translating them into Chinese. It’s because there is no consistent Chinese translation for these two concepts. One reason is that the concepts are similar and easily confused to begin with; another is that some book translators themselves do not have a comprehensive understanding of game theory. Although translation between languages inevitably loses some information, for two such simple terms, translation is easy: perfect information — 完美信息 (“perfect information”), complete information — 完全信息 (“complete information”). Because some translators call both of them 完全信息, from now on, whenever you read a book or article on game theory and see the Chinese term “完全信息”, you first have to figure out whether it actually means perfect information or complete information. To tell these two concepts apart, let me compare them with examples once more:

perfect information — I can see your every move (Go — the history is transparent)
complete information — I know how the game is played (rock-paper-scissors — the rules are transparent)

Games of perfect information can generally be found in real-world games, while games of complete information can be found not only in real-world games but also in every corner of the abstract world of life. For abstract games of complete information, you must think clearly about the game objective and the cost of that objective (the various academic functions).

The Game of Life

Life is a long journey of infinitely repeated games, and you only need to settle on life’s one and only game objective: happiness, the deep happiness of the heart. A very small number of people live their whole lives in pursuit of fame and fortune. To achieve this objective repeatedly over many rounds, they have to betray the faith of many people (making many people pay an enormous price), keeping themselves forever immersed in a paradise of sin. Perhaps they attain deep inner happiness, perhaps they cycle endlessly on the edge of suffering; what their hearts are really like, only they know best. In any case, no one can win forever, and no one can live forever, but you can be happy forever. With happiness, you will no longer fear death.

Conversations between people

For some people, or in some situations, a conversation between people is like a game. The purpose of conversation can generally be understood as the exchange of information, which can be subjective or objective.

For most people, ordinary conversation is an exchange of objective information. Other people want to know how you’ve been. Some ask out of sincere concern for you; they hope you’re doing well so that they can be happy for you. Others want to pry into your private life (to put it bluntly, they want to know how much money you have; in most people’s minds, having money means living well, and living well means having money). On the surface they hope you’re doing well, but if you really are doing better than them, they will be unhappy from the bottom of their hearts (out of a competitive or jealous mindset), and they will also want to get some benefit out of you; if you’re not doing as well as them, they get some psychological comfort, and some even go further and think they don’t need to show you much respect. My dear friend, when you are willing to carefully read this article that I have personally given you, it means I regard you as my friend, and you all have my heartfelt blessings. May you meet kind people and be happy every day. If you are wealthy, it is because you have created value and received the reward you deserve; if you are poor, you may not get much respect from all your friends, but those who don’t respect you are betting that you have no future. While heaven and earth are not yet settled, every traveler may be a dark horse. Yin and yang are formless, and good deeds are rewarded with fortune in the end. Fame and fortune were never life’s only goal; whether poor or rich, you can be happy.

For a small number of people, conversation is for amusement, which is actually a shallow exchange of subjective information. This kind of conversation not only puts people in a good mood but also deepens the bond between them. Speaking of amusement, it too comes in shallow and deep forms. Shallow amusement only makes you happy for a moment and cannot touch the soul, while deep enjoyment is often accompanied by a faint sadness that lingers with you and is hard to forget.

For a very small number of people, conversation is for exploring truth, which is a deep exchange of subjective information. What most people recognize as truth is actually not truth; it can only count as objective information, and what some people recognize as truth is even just subjective information. In fact, most people are mediocre; they just don’t want to admit it, and that may even include me. Among the multitudes of living beings, each of us is but a grain of millet in the vast sea. At least I can say with great certainty: “I am kind, I will stay kind, and I will do what I believe is right.” If you asked me to explain what truth is, that would be really hard; one article would be nowhere near enough. Broadly speaking, it contains the power of the entire universe and is an extremely complex system.

Someone always gets cheated

A transaction between people is actually also a game. Some transactions have an external binding force and count as cooperative games; others have no external binding force and are non-cooperative games. Some transactions seem to be cooperative games with an external binding force, but in some cases that external force is also limited and cannot fully guarantee fairness. Given this, almost all transactions in which people get cheated are non-cooperative games. In which situations in non-cooperative games are you more likely to be betrayed? Please carefully review what this article has covered, think about it seriously for 30 seconds, and then continue reading below.

As adults, almost everyone has been cheated, including me; after all, I was once naive too. Even now, at the very moment of writing this, I might be cheated, but that would be because I was willing to be cheated. When I am willingly cheated, I don’t fully trust the other person, so this kind of cheating isn’t really “cheating”. Without trust there can be no deception; all deception happens because people trusted someone they shouldn’t have. To make this section helpful enough for everyone, I will now go into the surface-level reasons people get cheated:

Ignorance

If it’s an extremely simple transaction, such as me giving you one yuan and you giving me a bottle of water, there is almost no chance of being cheated. However, in certain fields or industries, it is easy for someone who knows a lot to deceive someone who knows little. As the complexity of a transaction increases, the cognitive gap between people gradually shows, and someone with a strong desire for gain can exploit this gap to make money. Take this very article I’m writing: suppose I were a swindler; then all my kindness would be a disguise, and everything I wrote would have only one goal: to make you believe me. As long as you believed me and I betrayed you at the right moment, I could cheat you. To make this subsection more constructive, I will offer some suggestions for recognizing and reducing deception:

First, learn more. Of course, I’m just talking nonsense.
Second, always look the other person in the eye, because the eyes are the windows to the soul. When the other person is unwilling to meet your gaze, it means they don’t want to reveal what’s on their mind, and that’s when you need to pay attention. Of course, this isn’t absolute. Some people are afraid of others’ eyes even when they aren’t deceiving anyone, and obviously such people find it harder to win others’ trust.
Third, play the fool to catch the tiger: act dumb (the act should be below your actual level of understanding) and see whether they slip up. This is the most effective method, but using it well really tests your verbal skills (a game of minds). If your verbal skills are at that level, very few people can cheat you anymore, and you won’t need to act. So this is a chicken-and-egg piece of advice, practically useless.
Fourth, the person cheating you knows [you might know they’re cheating you], so they will try to prove they’re not a swindler. This isn’t absolute either and needs to be weighed together with other signs.
Fifth, always trust yourself and don’t trust anyone. Even if you are willing to spend money on certain people’s products, you don’t need to trust them completely. Without trust that reaches the depths of your heart, there can be no deception that cuts to the bone.

At this point, some friends may argue: I’ve already been cheated, so what good does telling me all this do? In fact, you will become smarter because of this experience (as long as you realize you were cheated and are willing to think about it), and the other person will also be punished in an invisible way. An adult’s punishment for betrayal is self-deception; it will inevitably backfire on their heart, and they will never be happy, because they surely know they deceived someone who trusted them. Therefore, even if you’ve been cheated, don’t deceive those who trust you, especially those who trust you and are weaker than you.

Greed

The original sin of greed lies in wanting to get an unequal return from others (while giving nothing or giving less), which is inherently contradictory between two people of the same level of understanding. Therefore, people who are cheated because of greed are essentially still at a lower level of understanding than those who deceive them. The deceiver may give a little at the beginning in order to win your trust. As your trust gradually deepens, you slowly become willing to give a lot in exchange for bigger returns, and they only need to choose to betray you at the right moment to take back all their earlier small investments, with interest. For the deceiver, this is a fairly sophisticated scheme. After all, they have to give something too, and you can betray at any time; as long as you betray before they do, you won’t lose anything. This sophisticated scheme makes it easier to win your trust, and if there are enough rounds, you will get deeply drawn in and find it hard to judge when to betray. There is also a crude scheme, in which they betray you from the very start, never giving anything, and it is a perfect world woven entirely of lies. This kind of scheme is usually hard to believe, but once you believe it, you will find that (within their lies) the cost of betrayal keeps getting higher, until you, having not betrayed, can no longer afford the cost of trust. The advice on being cheated through greed is actually very simple; you must already know it, so I needn’t say more. Note that some people are not greedy by nature, but comparing themselves with others breeds desires beyond reality, and these desires gradually turn into greed.

All in all, whether the cause is ignorance or greed, all deception actually happens because the number of rounds in the game is small enough. In the infinite prisoner’s dilemma, when there are enough rounds (more than a thousand), players passively develop wisdom. If you can actively develop wisdom when there are very few rounds (three or fewer), you can avoid 99% of scams (because a swindler’s tricks are nowhere near that complicated; if they really had the ability to devise complex scams, they wouldn’t settle for being a petty swindler). Losing to deception in one round is nothing to fear, because life is an infinitely repeated game; as long as you live long enough and are willing to think, you will win eventually. Or rather, once you learn to think, you have already won.

Creating value for yourself

Having read this far, we are nearing the end of the article. Perhaps you have already realized that game theory applies to every field, and that all thinking is an invisible game. Friends who know English fairly well may have noticed from the start that in the paper Old Von published in 1928, On the Theory of Parlor Games, there is a word, “parlor”. The word comes from the French “parler” (to talk) and originally referred to a room used for conversation. In Medieval Latin, its root is “parlatorium”, meaning the place where monks talked in a monastery. Over time, its meaning evolved from a dedicated conversation space into the modern “living room” or “reception room”, especially in Victorian-era English houses. So the modern Chinese translation of the paper’s title is Theory of Living-Room Games. Foreigners have many kinds of parlor games, and the well-known Werewolf is one of them, but in fact they all belong to “conversation games”. So how can you use game theory to create value for yourself through conversation?

The previous subsection actually already summed it up: most conversations between people are idle talk. If, in these seemingly useless conversations, you can use game theory to express your tangible or intangible strength, others will believe you more easily. Then you can ride the momentum, which The Art of War calls putting up a bold front. Going with the flow is the only shortcut to success, but not the only path. I don’t want to say too much here, but one saying must be left behind:

Do many good deeds and gain the power of faith. Go with the momentum, and success follows the Way of nature.

Just like what I’m doing now, it’s also creating value for myself. The value I give you far exceeds what you pay, but for you this isn’t greed, because you (or rather most people) don’t see it that way. If anyone can recognize how high its value is, that too is because I’m willing to share with everyone; in the process of spreading knowledge to you all, I gain deep inner happiness. So this is a win-win situation for both sides of the game.

Playing a game with yourself

Playing a game with yourself is really my interpretation of life, and it serves as the general outline of this article. Life is a game played with yourself. Most of the time you are alone with yourself; even the people closest to you can only accompany you for one stretch of the journey of your life. Some people, because of harm from outside (harm outside their true heart, which might be to their own body, or friends and family drifting away, or the loss of fame and fortune, and so on), become dispirited, fearful, and even depressed.

A brief loss of oneself is understandable, but what is your being lost for?

You may never have thought about this, so let me tell you the answer: your being lost is for the sake of finding your [true self]. But some people, once lost, spend their whole lives unable to find their true self, and that is when they fall ill with depression.

If life is a game, many people don’t understand how it should be played. In the earlier section on information in games, I talked about game objectives and various cost functions. The only objective in the game of life is happiness; just like playing a game, you should enjoy it rather than be played by it. Any happiness that might toy with you or make you lose yourself is false happiness. In that kind of happiness you lose yourself, and deep down you are in great pain and fear, afraid it is just a dream that will suddenly vanish. Constantly worrying about gaining and losing, you find no peace deep in your heart.

Generally speaking, people have six senses. To gain happiness, you get it from nothing other than these six senses. There are only five tangible senses: sight, hearing, smell, taste and touch. As long as one sense can reach deep into your soul, you can attain true, deep happiness through the heart sense (the sixth sense).

Sight

For most people, sight is the most direct sense and the source of most of their information. There are many visual joys, such as flowers, plants, trees, birds, beasts, insects and forests, or in other words, the uncanny workmanship of nature. That’s why almost everyone likes to travel, because it is the most direct and effective way to feel happiness. There are also calligraphy, painting, sculpture and so on; this kind of happiness is a higher visual joy, and relatively few people can feel it (except for body art, where most people feel sexual impulse, while artists feel the art of the human body itself). In addition, every scene that can make you feel happy visually can be called visual art, and nature is one of the greatest artists. Some people like machinery and feel the art of machines; some like architecture and feel the art of buildings.

Hearing

After sight comes hearing, which ranks second only to sight as a source of information. The most direct auditory joy is music, and music encompasses everything. I once even made a hypothesis: if music were the language of the gods, how should I prove this proposition? Besides music, speaking well is also an art, and wind, rain, thunder and lightning, the chirping of insects and the songs of birds are also nature’s art.

Taste

Putting taste here is my personal, subjective view; I think the information gained through taste is fairly limited. First, people have a pair of eyes and a pair of ears, but only one mouth. At the same time, the mouth has to take on two tasks: making sounds and taking in food. Second, I personally am not very interested in tasting fine food; on the contrary, what interests me is the process of making good food with care. Not only that, if the food I make lets others taste happiness, I am happy from the bottom of my heart too. Perhaps for some gourmets, taste is a very important source of information. And perhaps for some people, fine food can bring happiness that goes straight to the depths of the soul.

Touch

Every part of the human body has a sense of touch (except the nails, hair, and the enamel on the outermost layer of the teeth). You could say touch is the most important human sense, because it is through touch that you can feel your own existence. You could also say touch is the least important human sense, because some people who have lost limbs and part of their sense of touch feel their existence even more strongly. Physiologically, touch and pain cannot simply be equated, but pain can “disguise” itself as touch, a kind of pathway crosstalk. This touch-like pain can help people seek benefit and avoid harm, serving to protect life (in strictly scientific terms, pain is a branch of the heart sense, and humans seeking benefit and avoiding harm comes from biological instinct). In touch there is a simple, pure happiness: when facing a person or thing you like, you touch it. When you extend this happiness into your own heart, you can also feel deep happiness. For most people, with someone of the opposite sex they like, touch can bring them great happiness. This is a happiness rooted in biological instinct, and naturally also one that can reach straight to the depths of the soul.

Smell

Compared with the other senses, smell seems very low-key (due to evolution, the human body no longer needs much sense of smell to ensure a sense of safety; the vast majority of animals have far keener noses than humans, and a dog’s sense of smell is more than 100,000 times that of a human). Yet smell is the oldest human sense and the one that leads most directly to the brain’s emotional center. Moreover, the olfactory sensory nerves can keep regenerating, and they are the only sensory nerves that can. Smell not only travels the fastest of all the senses, but is also the most closely tied to human emotion. On this point, I have to bring up a serious topic: people whose sense of smell has weakened or been lost have a noticeably higher risk of depression than others. There are generally two ways to get happiness from smell: one is the scent of a partner’s body (which gives a sense of security), and the other is the natural, subtle fragrances of nature such as vanilla, lemon and coffee. Simply put, smell can bypass the logic of the body’s physiological structure and reach straight into the depths of the soul. Finally, here is a little secret about smell: the nose is not the only part of your body that can smell.

Some might ask: you’ve said so much, but are you happy yourself?

My answer: all five of these senses bring me deep happiness of the soul. Not only that, I also have a natural gift: teaching others. While teaching others, it gives me a feeling of happiness, a feeling even faster than smell, which can bypass everything and go straight to my heart.

Writing this, I can’t help wanting to express some nostalgic feelings, like picking up in the evening the flowers fallen in the morning. Everything I do is driven entirely by inner happiness. In college I taught others for the CET-4 and CET-6 English exams, advanced mathematics, languages, music and computers, but I have never formally taught children in a primary or secondary school classroom. This has always been a wish of mine, and I don’t know whether I’ll have the chance to fulfill it in this life. If the present me could teach the childhood me, it would surely have been a very happy thing for me back then. If the spring breeze has pity for the flowers, may it grant me my youth once more. The flowers bloom, worthy of the warm east wind; the young live up to their golden years.

After all this talk, some may feel it’s all nonsense. Indeed, games can also be called yin and yang, and the two poles of yin and yang are inherently void, yet they always exist in the universe. If people did not exist, if the universe did not exist, naturally there would be no such thing as games. But even without the universe, something would always exist.

Games exist because existence exists.