Nomination: For the development of the theory of contracts in neoclassical economics. The neoclassical direction implies the rationality of economic agents, widely uses the theory of economic equilibrium and game theory.
Oliver Hart and Bengt Holmström.
Contract. What it is? I am an employer, I have several employees, I tell them how their salary will be arranged. In what cases and what will they receive. These cases may include the behavior of their colleagues.
I will give five examples. Three of them illustrate how an attempt to intervene led to a worsening of the situation.
1. Students crossed the street in different places. Cars slowed down, students ran across, traffic was somehow “organized”. Chaotic, but everything is fine, life goes on.
A couple of years ago, a decree was received that it was necessary to organize a single pedestrian crossing. On a section of the road 200-300 meters. There are fences around and all students go to this one passage. As a result, students completely block traffic from 25-8 to 45-9 for 10 minutes. No car can pass. A typical example of a "negative contract".
2. I haven't found a definitive confirmation. Factoid, something that everyone knows as a fact, but in reality, may not have confirmation.
In the eastern country began to fight with rats. They began to pay for a killed rat (“10 coins”). Then everything is clear, everyone abandoned their business and began to breed rats. (They shouted out from the audience that the incident took place in India with cobras ().)
3. There were two auctions for the sale of mobile frequency bands, in England and in Switzerland. In England, the process was led by Roger Myerson, a Nobel laureate. He directed that the cost of the contract was about 600 pounds for each Englishman. And in Switzerland failed the auction completely. They conspired and got 20 francs per person.
4. I can't speak without crying, but the tears have already run out. The USE has destroyed school education. It was conceived to fight corruption, so that everything was fair and just. How it all ended, I can say that in most schools, except for the best ones, there is coaching for the Unified State Examination, studies are stopped, and coaching continues. Teachers are told directly: “Your salary and your presence at school depends on how your students pass the exam.”
It's the same with articles and scientometrics.
5. Tax policy. There are many successful examples and many unsuccessful ones. Most of the report will be devoted to this issue.
Mechanism design
I saw many different hiking groups, including huge ones - 30-40-50 people. With a properly organized process, this is such a combat unit, it lives like one organism. Everyone has their own role, their own work. And in other places - a relaxed mess.
How to solve the problem of control, if there are very few controllers?
This problem often occurs in different ways. It has not always been solved successfully.
Example.
There is a subway with a transition to trains. 20 turnstiles and one checking guard. And from this side, 10 people with one stone are crowding in the corner. The train arrives and everyone, as if on cue, tumbled down. The guard grabs one of them, but the rest will run through. If we look at this situation from the point of view of game theory, then this is a situation in which there are two completely different equilibrium scenarios.
In one, no one goes and everyone knows that no one goes, no one tries, this is a self-sustaining scenario. It's a balance, everyone is doing the "right" thing. And one man holds back the whole crowd.
But there is another balance. Everyone is running. If you believe that everyone is running, then the probability that you will be captured is 1/15, you can take a chance. Having two options is a big challenge for game theorists. Maybe half of game theory is devoted to handling such situations. How to put a thought in the brains of hares so that they are afraid to “slip through”?
This is John Nash. He proved a very general theorem on the existence of an equilibrium in games with interconnected solutions. When the result depends not only on your decisions, but also on the decisions of all other participants.
Some examples of balance.
What's happened money? You have some strange piece of paper in your pocket. You have worked and there are more of these pieces of paper (numbers on the account). By themselves they mean nothing. You can light a fire and get warm. But you believe they mean something. You know that you will go to the store and they will be accepted. The one who accepts also believes that they will also accept it from him. The general belief that these pieces of paper have value is a social balance that, from time to time, is destroyed when hyperinflation occurs. Then from a situation where everyone believes in money, it turns into a situation where everyone does not believe in money.
Right- and left-hand traffic. Some countries are different, but you follow these rules.
Why do people go to physics and technology? Because there is confidence that they teach well there. There is confidence that other strong students will go there. Imagine for a second that some company of very strong schoolchildren suddenly agreed and went to some weak university. He will immediately become strong.
How can a guard remove bad balance?
It is necessary to number all the hares aloud and inform that no matter who jumps, they will catch the minimum by number.
Suppose some company decided to jump. Then the one with the lowest number knows for sure that he will be caught and will not jump. Equilibrium is when we correctly guess other people's actions and our actions, which others guess about us. In the situation of “listing aloud”, the equilibrium has an additional property of stability. It is resistant against "coordination/cooperation". That is, in this balance it is impossible even to agree that at the same time a certain number of people will change their behavior so that as a result everyone will feel better.
If you make up complex rules and the company is unable to understand them, then you cannot expect them to behave according to the Nash equilibrium. They will make random selections.
Let us assume that we are forbidden (institutional restriction) to "list aloud". Our strategies must be symmetrical (anonymous). But we can refer to "coin". If something falls out - I do one thing, if another falls out - I do the second.
Serious task. Formulated and studied 20 years ago. Nobody paid taxes. We tried to organize the process this way and that way. Zero profits, bribes… The tax authorities turned to the institute where I work a little, to my supervisor. Together we formulated the problem as follows. There are n industries, each has its own inspector, but in some % of cases he colludes. % everyone chooses for himself. x1, x2…xn.
x=0 means that the inspector has decided to be honest. x=1 takes bribes in all cases.
Xs could be recognized by indirect signs, but we cannot use them in court. Based on this information, you need to build a verification strategy.
It can be simplified to the fact that there is only one check, but with a very large penalty. And we assign a probability to this test. The probability that I will come to you is this, and to you is this. And these are functions from x. And the sum does not exceed one. It is strategically correct, in some cases not to check at all and promise them this.
p is a mapping of an n-dimensional cube into the set of all probability distributions. It is necessary to register their winnings, to understand how much one of them will receive when they decide in what% of cases to take bribes.
bi is the “bribery intensity” of the industry (if you take a bribe instead of a tax everywhere).
The penalty is subtracted from the probability with which it will come. From what? First, you need to check it out. But that's not all, the check can run into the case when everything was clean. A simple formula, but the complexity is buried in "p".
We have slang that is not found in other branches of mathematics: xi. This is a set of all variables except mine. These are the choices made by everyone else. This is collective responsibility.
Now the question is: In what concept of equilibrium do we suppose that they will be?
In the 90s, there was the most puncture. The organizers of the check announced to everyone that the most impudent would be punished. He will be tested.
What will be the forecast for this situation?
The people who made the rules thought there would be independent interaction. The only equilibrium is all zeros. And in real life it was 100% Why?
The answer is that the balance is unstable to collusion.
We started scratching our turnips.
A leading example is individual responsibility. Let's imagine a terrible situation that the legal fine is less than the bribe fee. If the inspector sits in such an “oily” industry that his bribe fee is higher than the fine, can something be done? The penalty cannot be taken more than once.
I know that the inspector will pay off and will be in the black. But I can promise not to check you at all if your level of corruption is not higher than 30%. What is more profitable?
The classics already had it.
Threefold the level of corruption is reduced.
abstract situation. 4 people. Bribery is below the fine.
If you rely on individual contracts, you will not “put to zero” everyone. But I can bring everyone to zero with a strategy of collective responsibility.
I equally send a check with equal probabilities not to the maximum, but to non-zero. All thieves who are with a non-zero percentage - each will receive a check with a probability of 1/4. I don't even change the probability depending on the x's.
Then there are no equilibria other than zero. And there can be no collusion either.
And if there is not only tacit collusion, but also the transfer of money, then game theory completely fails. There is a strong proof.
A whole class of strategies has been developed, which is implemented through a strong collusion-resistant Nash equilibrium.
We assign several levels of tolerance to corruption. z1 - completely tolerant level, the rest - the level of intolerance increases. And for each level allocates the probability of verification. The formula looks like this:
λ1 - the probability of being tested at the first tolerance level - is divided equally between all those who exceeded it, in addition, λ2 is divided between all those who exceeded the second threshold, and so on.
I proved the following theorem 15 years ago.
This strategy was used before me, as a strategy for dividing costs.
Contracts cost money. Well-designed interaction patterns are a huge money saver, sometimes. Saving time.
Collective responsibility is effective. Attaching a person to a group is effective.
As I made a report to the Ministry of Internal Affairs.
I arrived, there were about 40 policemen of different ranks, they listened, looked at each other, whispered, and then the chief came up to me and said: “Aleksey, thank you, it’s interesting to listen to a person who is passionate about his science ... but this has nothing to do with reality.”
Experimentally observed Russian corrupt officials behave differently than experimentally observed American ones. Know what's the difference? A Russian, when he starts taking bribes, is no longer an economic agent who rationally maximizes his profit. [Applause]
A person begins to take bribes to the limit, never discussing anything. He must be seized and put in jail, that's the whole science.
Thank you.
Source: habr.com