1. "the income of pigs" in economics

This example is about: there are two pigs, a big pig and a little pig in the pigsty. There is a pedal on one side of the pigsty. Every time you step on the pedal, a small amount of food will fall on the feeding port on the other side of the pigsty far from the pedal. If one pig steps on the pedal, the other pig has a chance to eat the food that has fallen on the other side first. As soon as the pig steps on the pedal, the big pig will eat all the food just before the pig runs to the trough; If the big pig steps on the pedal, there is still a chance for the little pig to run to the trough and compete for the other half before eating the fallen food.

So, what strategy will the two pigs adopt? The answer is: Piglets will choose the "hitchhiking" strategy, that is, they will wait comfortably in the trough; The big pig ran tirelessly between the pedal and the trough, just for a little leftovers.

What is the reason? Because, little pigs can get nothing by pedaling, but they can eat food without pedaling. For piglets, it is always a good choice not to step on the pedal whether the big pig does or not. On the other hand, the big pig knows that the little pig can't step on the gas pedal. It's better to step on the accelerator by himself than not to step at all, so he has to do it himself.

The phenomenon of "the little pig is lying down and the big pig is running" is caused by the rules of the game in the story. The core indicators of the rules are: the number of things falling each time and the distance from the pedal to the feeding port.

If we change the core indicators, will there be the same scene of "pigs lying down and big pigs running" in the pigsty? Give it a try.

Change scheme 1: reduction scheme. Feeding is only half of the original weight. As a result, neither the little pig nor the big pig kicked. The little pig will step on it, and the big pig will finish the food; If the big pig steps on it, the little pig will finish the food, too. Whoever pushes means contributing food to each other, so no one will have the motivation to push.

If the goal is to make pigs pedal more, the design of this game rule is obviously a failure.

Variation scheme 2: incremental scheme. Feed twice as much as before. As a result, both the little pig and the big pig can pedal. Anyone who wants to eat will kick. Anyway, the other party won't eat all the food at once. Piglets and big pigs are equivalent to living in a materialistic society with relatively rich materials, and their sense of competition is not very strong.

For the designer of the rules of the game, the cost of this rule is quite high (providing two meals at a time); Moreover, because the competition is not strong, it has no effect to let the pigs push more.

Variant 3: Decreasing plus shifting scheme. Feed only half the original weight, but at the same time move the feeding port near the pedal. As a result, both the little pig and the big pig pushed hard. Those who wait will not eat, and those who work hard will get more. Every harvest is just a flower.

This is the best solution for game designers. The cost is not high, but the harvest is the biggest.

The original story of "Smart Pig Game" inspired the weak (pigs) in the competition to wait for the best strategy. But for the society, the allocation of social resources when piggy hitchhiked is not optimal, because piggy failed to participate in the competition. In order to make the most efficient allocation of resources, the designers of rules don't want to see anyone hitchhiking, so does the government, and so does the boss of the company. Whether the phenomenon of "hitchhiking" can be completely eliminated depends on whether the core indicators of the rules of the game are set properly.

For example, the company's incentive system design is too strong, and it is still holding shares and options. All the employees in the company have become millionaires. Not to mention the high cost, the enthusiasm of employees is not necessarily high. This is equivalent to the situation described in the incremental scheme of Smart Pig Game. However, if the reward is not strong and the audience is divided (even the "little pigs" who don't work), the big pigs who have worked hard will have no motivation-just like the situation described in the first phase of the "Smart Pig Game". The best incentive mechanism design is like changing the third scheme-reducing staff and changing shifts. Rewards are not shared by everyone, but for individuals (such as business proportion commission), which not only saves costs (for the company), but also eliminates the phenomenon of "hitchhiking" and can achieve effective incentives.

Many people haven't seen the story of "smart pig game", but they are consciously using pig strategy. Retail investors are waiting for the dealer to get on the sedan chair in the stock market; Waiting for profitable new products to appear in the industrial market, and then copying hot money on a large scale to make huge profits; People in the company who do not create benefits but share the results, and so on. Therefore, for those who make various rules of economic management, they must understand the reasons for the index change of "smart pig game".

Second, the prisoner's dilemma game

In game theory, a famous example of dominant strategic equilibrium is Tucker's "prisoner's dilemma".

Dilemma) game model. This model tells us the story of a policeman and a thief in a special way. Suppose two thieves, A and B, commit a crime together, enter the house privately and are caught by the police. The police put the two men in two different rooms for interrogation. For each suspect, the policy given by the police is that if a suspect confessed his crime and handed over the stolen goods, the evidence was conclusive and both of them were convicted. If another suspect also confessed, they were each sentenced to eight years in prison; If another suspect denies it without confession, he will be sentenced to two years in prison for obstructing official duties (because there is evidence to prove that he is guilty), and the confessor will be released immediately after eight years of commutation. If both of them deny it, the police can't convict them of theft because of insufficient evidence, but they can each be sentenced to 1 year in prison for trespassing. The table below gives the payoff matrix of this game.

The game of prisoner's dilemma [prisoner's dilemma]

B confesses, B denies

Confessions–8,–80,–10

Rejected-1 0,0-1,1

Let's see what the predictable equilibrium of this game is. For A, although he doesn't know what B chooses, he knows that no matter what B chooses, choosing "confession" is always the best for him. Obviously, according to symmetry, B will also choose "confession". As a result, both of them were sentenced to 8 years in prison. But if everyone chooses "denial", each person will only be sentenced to 1 year. Among the four action choice combinations in Table 2.2, (Rejection, Denial) is Pareto optimal, because any other action choice combination that deviates from this action choice combination will at least make a person's situation worse. It is not difficult to see that "confession" is the dominant strategy of any criminal suspect, and (confession, confession) is a strategic balance of superiority.

To understand Nash's contribution, we must first know what is a non-cooperative game problem. At present, almost all game theory textbooks will talk about the example of "prisoner's dilemma", and the examples in each book are similar.

Game theory is, after all, mathematics, or rather, a branch of operational research. When talking about classics and theories, mathematical language is indispensable, which is just a lot of mathematical formulas in the eyes of laymen. Fortunately, game theory is concerned with daily economic life, so we have to eat fireworks. This theory is actually a term borrowed from chess, poker, war and other issues with the nature of competition, confrontation and decision-making. It sounds a bit mysterious, but it actually has important practical significance. Game theory masters look at economic and social issues just like playing chess, and often have profound truth in the game. Therefore, it is not boring to start with trivial matters in daily life and explain them with stories around us as examples.

One day, a rich man was killed at home and his property was stolen. During the investigation of this case, the police arrested two suspects, Scafi and Nakul, and found the lost property in the victim's house from their residence. But they denied that they killed anyone, arguing that they killed the rich first, and then they just stole something. So the police isolated the two and put them in different rooms for trial. The D.A. will talk to everyone individually.

The prosecutor said, "Because you have conclusive evidence of theft, you can be sentenced to one year in prison." But I can make a deal with you. If you plead guilty to murder alone, I will only sentence you to three months' imprisonment, but your partner will get ten years' imprisonment. If you refuse to confess and are reported by your partner, you will be sentenced to ten years in prison, and he will only be sentenced to three months in prison. However, if you all confess, then you will all be sentenced to five years in prison. "What should Scalfi and Nacoors do? They are faced with a dilemma-confession or denial. Obviously, the best strategy is that both sides deny it, and as a result, everyone only gets one year. However, because the two are in isolation, they cannot confess. Therefore, according to Adam Smith's theory, everyone starts from the purpose of self-interest, and they choose repentance as the best strategy. Because if you confess, you can expect three months of short-term imprisonment, but only if your partner denies it, which is obviously better than your own denial of 10 years imprisonment. This strategy is at the expense of others. Not only that, but confession has more benefits. If the other party denies it frankly, they will go to jail 10 years. It's so uneconomical! Therefore, in this case, you should still choose to confess. Even if two people confess at the same time, they will only be sentenced to five years at most, which is better than being sentenced.

/kloc-0 0 year. All right. Therefore, the reasonable choice of the two is confession, and the strategy (denial) and the ending (sentence 1 year imprisonment) that were originally beneficial to both sides will not appear.

In this way, both of them chose Frank's strategy and were sentenced to five years' imprisonment. The result is called "Nash equilibrium", which is also called non-cooperative equilibrium. Because, when each party chooses a strategy, there is no "collusion" (collusion), they just choose the strategy that is most beneficial to them, regardless of social welfare or the interests of any other opponent. In other words, this strategy combination is composed of the best strategy combination of all participants (also called parties and participants). No one will take the initiative to change their strategy in order to gain greater benefits for themselves. The "prisoner's dilemma" has a wide and profound significance. The conflict between individual rationality and collective rationality and everyone's pursuit of their own interests lead to a "Nash equilibrium", which is also an unfavorable outcome for everyone. Both of them think of themselves first in the strategy of frank denial, so they are bound to serve long sentences. Only when everyone thinks of each other first, or colludes with each other, can we get the result of the shortest imprisonment. Nash equilibrium first challenges Adam Smith's "invisible hand" principle. According to Smith's theory, in the market economy, everyone starts from the purpose of self-interest, and finally the whole society achieves the effect of altruism.

Let's review the famous saying of this economic sage in The Wealth of Nations: "By pursuing (personal) self-interest, he often promotes social interests more effectively than he actually wants to do." A paradox of the principle of "invisible hand" is drawn from Nash equilibrium: starting from self-interest, the result is not self-interest, neither self-interest nor self-interest. This is the fate of two prisoners. In this sense, the paradox put forward by Nash equilibrium actually shakes the cornerstone of western economics. Therefore, from Nash equilibrium, we can also realize a truth: cooperation is a favorable "self-interest strategy". But it must conform to the following Huang Jinlv: Treat others as you want them to treat you, but only if others do the same. That's what China people say, "Don't do to others what you don't want others to do to you". But only if you don't do to me what you don't want me to do. Secondly, Nash equilibrium is a non-cooperative game equilibrium. In reality, non-cooperation is more common than cooperation. Therefore, "Nash equilibrium" is a significant development of the cooperative game theory of von Neumann and Morgan Stern, and even a revolution.

From the general sense of Nash equilibrium, we can deeply understand the common game phenomena in economy, society, politics, national defense, management and daily life. We will give many examples similar to the "prisoner's dilemma"

Such an example. For example, price war game, military competition game, pollution game and so on. The general game problem consists of three elements: players, also known as the set of parties, participants and strategies. Strategy.

(strategy) set and each player's choice and income set. Among them, the so-called win refers to the utility that people in each game get if they choose a specific strategic relationship. All game problems will encounter these three elements.

Robert axelrod of the University of Michigan. Axelrod is a political scientist. He organized a computer competition. The idea of this competition is simple: anyone who wants to take part in this computer competition will play the prisoner in the prisoner's dilemma case. They input their strategies into computer programs, and then their programs will be paired into different combinations. After grouping, the participants began to play the game of "Prisoner's Dilemma". Each of them must choose between cooperation and betrayal. The key is that they don't just play the game once, but play it 200 times over and over again. This is what game theory experts call "repeated prisoner's dilemma".

Repeated Prisoner's Dilemma more truly reflects frequent and long-term interpersonal relationships. Moreover, this repeated game makes the program can refer to the previous choice of the opponent program when making the choice of cooperation or betrayal. If the two programs only play one round, betrayal is obviously the only rational choice. However, if the two programs play against each other many times, both sides have established their own historical files to record their contacts with their opponents. At the same time, each of them has established a good or bad reputation through many fights. Even so, it is extremely difficult to determine what the other party's program will do next. In fact, this is one of the things that axelrod, the organizer of this contest, hopes to learn from this contest. Does a program always take a cooperative attitude no matter what the opponent does? Or, can it always take betrayal actions? Should we respond to the opponent's actions with more complicated measures? If so, what kind of measures will it be?

In fact, the 14 scheme handed in in the first round of competition contains various complicated strategies. But to the great surprise of axelrod and others, the title of competition belongs to the simplest strategy: answer blows with blows. I call it "deal with a man as he deals with you".

The strategy of "answer blows with blows" is this: it always starts with cooperation, but since then it has adopted the strategy of dealing with a man as he deals with you. In other words, the tit-for-tat strategy is based on the principle of carrot and stick. It never betrays each other first. In this sense, it is "kindness". It will reward the cooperation before the next round (even if the opponent has betrayed before). In this sense, it is "tolerant". But it will take treacherous actions to punish its opponents for their previous betrayal. In this sense, it is "tough". Moreover, its strategy is extremely simple, and opponents can know its intention at a glance. In this sense, it is "simple and clear".

Third, the price war game.

Now we often encounter all kinds of home appliance price wars, such as color TV wars, refrigerator wars, air conditioning wars, microwave oven wars ... The beneficiaries of these wars are consumers first. Every time I see the price war of home appliances, ordinary people will "have nothing to steal." It can be explained here that the outcome of the price war of manufacturers is also a "Nash equilibrium", and the result of the price war is that no one has money to earn. Because the profits of both sides of the game are exactly zero. The result of competition is stable, that is, a "Nash equilibrium". This result may be beneficial to consumers, but it is disastrous to manufacturers. Therefore, the price war means suicide for manufacturers. From this case, we can draw two questions. First of all, competitive price reduction or "Nash equilibrium" may lead to efficient zero-profit results. Second, if the price war is not used as a hostile game theory.

(Long live!

What will happen? Every enterprise will consider adopting normal price strategy or high price strategy to form a monopoly price and try its best to obtain monopoly profits. If a monopoly can be formed, the profits of both sides of the game will be the greatest. This kind of situation is what monopoly does, which usually raises the price. At the other extreme, if the manufacturer uses the normal price, both parties can make a profit. From this point, we draw another basic rule: "Build your own strategy on the assumption that your opponent will act in his best interests." In fact, the equilibrium of perfect competition is Nash equilibrium or non-cooperative game equilibrium. In this state, each manufacturer or consumer makes decisions based on all the prices set by others. In this equilibrium, every enterprise should maximize its profit, and consumers should also maximize its utility, resulting in zero profit, that is, price equals marginal cost. In the case of perfect competition, non-cooperative behavior leads to the state of economic efficiency expected by society. If manufacturers take cooperative actions and decide to turn to monopoly prices, the economic efficiency of society will be destroyed. This is why it is of great significance for WTO and governments to strengthen anti-monopoly.

Fourth, the game theory of trade war.

This issue is particularly important for China, which has just joined the WTO. Any country is faced with the dilemma of maintaining trade freedom and implementing trade protectionism in international trade. The issue of trade freedom and barriers is also a "Nash equilibrium", which is a strategy of non-cooperative game between the two sides of trade. As a result, both sides are damaged by the trade war. If country X tries to impose import trade restrictions on country Y, such as raising tariffs, then country Y will definitely fight back and raise tariffs, and no one will benefit. On the other hand, if X and Y can reach a balance of cooperation, that is, starting from the principle of mutual benefit, both sides will reduce tariff restrictions, and as a result, everyone will gain the greatest benefit from trade freedom, and the total income of global trade will also increase.

Game theory case analysis

Case 1: the application of game theory in enterprise human capital investment [1]

I. Introduction

Whether an enterprise can gain an economic advantage in the market depends on its scientific and technological advantages, the market adaptability of its products, etc., all of which come from the talent advantage. Therefore, an enterprise is faced with how to maintain its advantages in human resources as much as possible, how to attract outstanding talents to join the enterprise to add new impetus, how to effectively train existing employees to improve their skills, how to make employees adapt to changes in the external environment, how to effectively retain the company's core talents and so on. However, the statistical survey shows that the present situation of training in China is not satisfactory. Generally speaking, the degree of institutionalization and standardization of enterprise training management in China needs to be strengthened, the training plan is poorly implemented, the tracking and evaluation of training effect is weak, the effectiveness of training in improving employee performance has not been brought into play, and the training results have little impact on employee promotion. There are many reasons for this situation, one of which is the lag and uncertainty of human capital investment income, and it is not worth the loss to worry that employees will "fly away with hard wings". Whether enterprises increase investment in human capital and whether employees stay in enterprises is an interest game, and the result is to choose a strategy that is beneficial to them. This paper analyzes the human capital investment of enterprises with the method of game theory, which shows that enterprises should invest in human capital and take measures to ensure the acquisition of the investment income of human capital after investment.

Two. Concepts and assumptions

1. Concept definition

① Human capital. Human capital is formed by investing in existing human resources, and it can realize value-added variable capital with complex labor as the carrier.

② Enterprise human capital investment. Enterprise human capital investment refers to an investment behavior that an enterprise obtains human resources through a certain investment (currency, capital or material object), increases the knowledge, skills and health level of employees, improves the management, cultural level and corporate image of the enterprise, thereby enhancing the stock of enterprise human capital and improving the economic benefits of the enterprise.

2. Basic assumptions

(1) economic man. The hypothesis of economic man means that both organizations and individuals pursue the maximization of their own interests.

② The information is complete. Complete information means that the information is completely smooth, there is no stagnation, and the acquisition of objective information does not require cost.

③ Sufficient material capital. The production of goods is always carried out through the combination of material capital and human capital.

In order to make production efficient, material capital and human capital must maintain an appropriate ratio.

Thirdly, the game analysis between human capital investment and individual employees.

This paper makes a complete information static game analysis of human capital investment from the perspective of enterprises and employees, focusing on whether enterprises increase human capital investment and how to act after investment.

It is assumed that both enterprises and employees are rational under the condition of complete information. Enterprises can choose whether to train employees. According to the choice of enterprises, employees will choose to stay or quit to other enterprises. Suppose that the enterprise does not train employees, and the employee's income is D. When the enterprise chooses training, it is assumed that the training fee allocated to employees is C, the salary paid to employees after training is e(e can be zero, that is, the salary will not increase after training), and the added value of benefits brought by employees after training is B. Suppose that employees leave their jobs and go to another unit to get rewards. Here, in order to make the analysis simpler, it is assumed that the turnover income of trained and untrained employees is the same, both of which are A. Sometimes, after training, employees will get more income by changing jobs because of the improvement of their skills, but it will not affect the following analysis. The game analysis of enterprise training is shown in table 1: when B-C-E

When b-c b-c-e & gt；; 0, the game is established and there may be two equilibria: if the income d+e obtained by employees choosing to stay at this time is greater than the income A obtained by choosing to quit, rational employees will definitely stay in the original enterprise, and enterprises will inevitably choose training investment, which is also the optimal decision of both parties in this game; If the income d+e of the employee who chooses to stay at this time is less than the income A when choosing to quit, the rational employee will inevitably choose to quit, and the loss of the enterprise is C, which is the most serious. For enterprises, if they know that this will make employees jump ship, then enterprises might as well not train at the beginning, so the loss will be smaller. What needs to be pointed out here is that whether employees change jobs does not simply depend on the salary provided by the other company. There are many influencing factors, such as whether the employee's personality matches the enterprise, the employee's personal development prospects, the matching of the employee's interests and positions, and so on. In the above table, if the enterprise does not train employees, then whether the employees will stay or not depends on the existing income D and the salary A of the job-hopping enterprise.

If d>a and employees stay: On the contrary, employees leave.

In short, whether employees stay in the enterprise is a game of interests, and there is information asymmetry between enterprises and employees. Enterprises must take the initiative to send a signal to weaken the motivation of employees to leave. As long as enterprises can retain employees, human capital investment will bring huge economic benefits to enterprises.

[Editor] Case 2: Application strategy of game theory in business activities [2]

Professor Porter's five competitive forces in Harvard Business School give us a comprehensive and detailed analysis method when we think about the competitive situation and trend of the industry market, one of which is the threat of potential entrants.

Then, according to the market types (perfect competition market, monopolistic competition market, complete monopoly market and oligopoly market), because most industry markets belong to monopolistic competition market, there is an entry and exit game between existing enterprises and new entrants, which depends on structural entry barriers, control over key resources, economies of scale and market advantages of existing enterprises.

If you are the monopolist and influencer of the existing industry to a certain extent, the game strategies to prevent potential entrants from entering the market or to curb the vicious competition of existing enterprises are as follows:

1. Strategies for expanding production capacity

Monopolists may threaten potential entrants to prevent them from entering the market. However, whether the monopolist's threat can achieve the purpose of preventing entry depends on its commitment. The so-called commitment refers to some action taken by the player, which makes his threat credible. So, under what conditions will the threat become credible? Generally speaking, the main reason why short threats can't effectively prevent market entry compared with promised actions is that they don't need any cost only when participants will suffer greater losses if they don't implement such threats. It is easy to make a statement, but people who declare what they want to do or flaunt their intransigence lack substantive significance. Therefore, only when the player takes some action, and this action requires high cost or price, the threat will become credible.

2. The strategy of guaranteeing the lowest price clause

The so-called "guaranteed lowest price" clause strategy can adopt a restrictive pricing strategy to prevent entry by charging a price lower than that when entry occurs. A certain store stipulates that if any other store sells the same product at a lower price within a certain period of time (such as one month), the store will refund the difference and compensate a certain percentage of the difference (such as 10%).

)。 For example, you spend 5 in the store.

000 yuan to buy a Nikon camera, and a week later you find that it costs only 4,500 yuan in another store. You can negotiate with the store and get a refund from 550 yuan.

For example, suppose there are two markets. There is only one manufacturer in 1 period, and there are two options:

(1) To create a monopoly high-priced 60 yuan, you can get 1.

000 yuan profit, but it will make potential enterprises think that the industry is profitable, so they choose to enter the second stage; Once there are two enterprises in this market, the market price will drop to 30 yuan and the profits of enterprises will drop to 200 yuan. In this way, the total profit of the two periods is 1000+200= 1200 yuan.

(2) The formulation of low-price 40 yuan, if potential enterprises come in and the price drops to 20 yuan, the profits of both enterprises will be zero.

Therefore, enterprises with potential will not enter at this time. In this way, the price of the second phase can determine a monopoly high-priced 60 yuan, and the total profit will be 600+ 1000= 1600 yuan.

For consumers, the guaranteed minimum price clause will make you not regret buying for at least one month because of price reduction, but this clause is a promise to consumers and a warning to competitors, which is undoubtedly a means of competition between enterprises.

Guaranteeing the lowest price clause is a promise. Due to legal restrictions, stores have to implement this clause after publishing it to consumers, so it is absolutely credible. This kind of commitment implies the threat from enterprise A to enterprise B not to reduce the price, and makes this threat have the expected effect.

3. Restricted entry pricing strategy

Restricted entry pricing refers to the strategy of existing enterprises to prevent entry by charging a price lower than the entry price. After seeing this low price, potential entrants speculate that the price will be so low or even lower after entering, so it is unprofitable to enter the market and give up entering.

4. Predatory pricing strategy

Predatory pricing refers to setting a price below the cost to expel other enterprises, and expecting that the predatory enterprises can exercise their market dominance after the new enterprises or competitors are expelled from the market, and the resulting losses may be compensated, that is, after expelling other enterprises, setting a monopoly high price to make up for the previous losses. This is also a price retaliation strategy. The difference between predatory pricing and restrictive pricing is that restrictive pricing is aimed at those enterprises that have not yet entered the market, and it is to maintain low prices for a long time to limit the entry of new enterprises, while predatory pricing is aimed at enterprises that have entered or are about to enter. If you have excess capacity, you can expand the capacity when new enterprises enter, greatly reduce the price of goods and prevent them from entering.

5. Advertising game

Some goods don't know their true quality until they are used. We call this kind of goods experience products. Only those enterprises that produce high-quality experience products will choose to make huge advertisements, and low-quality enterprises will not advertise. The reason is that high-quality experience products will have a large number of repeat customers, while low-quality experience products are rarely patronized.

In addition, the game of output and price competition among existing manufacturers can be described by Cournot model and Bertrand model. Game theory is of guiding significance for enterprises to participate in competition and formulate competitive strategies at macro and micro levels. Heaton, a famous marketing expert, once said that the art of entrepreneurs is the strategic operation and management of enterprises. As a strategy, enterprises need games in today's fierce market competition!