Pareto optimization: Make at least one person better without harming anyone.
Pareto optimal: It is a state, at this time, the resource efficiency has been maximized, and it is impossible to perform Pareto optimization.
collective optimization
Individual rational choices may not achieve collective optimal results, so how to establish a mechanism to avoid falling into the prisoner's dilemma and achieve collective optimality?
1. Institutionally, establish a centralized authority, whether public or private
2. Moral constraints, moral constraints are linked with decentralized rewards and punishments
social microcosm
If there are multiple people participating in the hunting game; and when the prey is distributed, there are vested interest groups and disadvantaged groups, then what will be the result?
example:
A medium-sized coal mine has achieved both production and safety harvests. To this end, the superiors allocated 150,000 yuan in incentives. The mine manager convened a meeting with middle-level leaders and determined the distribution plan: 550 yuan for the mine manager and 500 yuan for the deputy mine manager. 400 yuan for section chiefs, 200 yuan for general managers, and 5 yuan for workers. After the bonus was issued, the whole mine seemed calm on the surface, but a few days later, safety accidents in the mine continued one after another: first, the people and vehicles of the operation team in the transportation area jumped off the track, then the coal cutter motor in the mining area was burned, and then the development Two people were injured in the top of the area. The minemaster couldn't sit still. Personally organize and lead the working group to each work team to trace the cause of the accident. First track the jumping accident. The locomotive driver said that the road studs that nailed the road studs were loose, and the inspection and maintenance were not careful. The nailer said the driver was driving too fast, causing the track to jump. Behind the scenes, everyone said what they said in their hearts: "We get less safety bonuses, we don't have that safety responsibility, and cadres get more bonuses, let them do it." Officials get the safety award." The mine leaders made various adjustments. Finally, the safety accident was suppressed, but the scene where everyone talked about safety and obeyed the rules in the mine was no longer seen. Procedural fairness on the surface cannot guarantee efficiency. If there is no fairness in the distribution of safety awards like the above coal mine, how can the fork ensure efficiency? In fact, this small coal mine is the epitome of our social life today.
This is a discussion of collective optimization at the distributional level, and the solution to this problem is to create centralized institutions, whether private or public. However, even with the establishment of a centralized authority, new problems will still arise. For example, the United Kingdom solved the excessive use of public land by establishing a property rights system. Although it improved the overall economic efficiency, it also changed the distribution of income. The grazing fee made the landlord richer and the shepherd poorer.
Smart Pig Game
There is a big pig in the pigpen. A little pig. Assuming they are fully rational, the two ends of the pigsty
are far apart and a pedal is installed at each end. The other end is the export of feed.
Every time the pig steps on the pedal. The other end will have 10 feeds into the trough. But the "labor" required to step on the pedals and
run to the trough adds up to the equivalent of 2 servings of feed.
There are two strategies that the two pigs can choose: to step on the pedal by themselves or wait for the other pig to step on the pedal:
if a pig makes the choice to step on the pedal by itself. Not only to pay the labor, consume 2 feeds.
And since the pedal is farther away from the feed, it will go to the trough later than the other pig. This reduces the amount of feed consumed. Assumption: If the big pig arrives first (that is, the little pig steps on the pedal), the big pig will eat 9 portions of feed. The little pig can only eat 1 portion of the feed, and the final benefit for both parties is [9,-1]; if the little pig arrives first (that is, the big pig steps on the pedal,
the big pig and the little pig will eat 6 and 4 portions respectively) Feed. In the end, the benefits for both parties are [4,4]; if two pigs step on the pedal and run to the trough at the same time, the big pig will get 7 feeds, and the little pigs will get 3 feeds. That is, the benefits for both parties are [5, 1]; If both pigs choose to wait, they will not be able to eat feed, that is, the benefit of both parties is [0, 0]
According to the principle of repeatedly eliminating the disadvantaged strategy, the small pig chooses to wait is the dominant strategy, so the big pig can only choose to act, and the final income is [4,4]
There is a phenomenon of "more work, less gain, less work, less gain" . In reality, there is also the exploitation of the weak by the weak
For example: American Frey Cosmetics Co., Ltd. has almost monopolized the black cosmetics market, and the slogan of a newly established company is: "When you have used Frey's products to make up, and then rub Johnson's powder cream, you will receive attention. Unexpected effect"
In the game, it is not always a good thing to seize the opportunity and take the first shot. Sometimes following the strategy has miraculous effects.
The sooner the risk-taking strategy, the better
From the point of view of rule design, it is unreasonable to have a rule loophole for pigs to free-ride, and the game of smart pigs is a typical case of rule incentive failure.
So how to change the rules?
Change plan one: reduction plan. The food intake is only half of the original. As a result, the little pigs and the big pigs stopped stepping on the pedals. Little pig to step on. The big pig will finish the food; the big pig will step on it. The piglets will also finish their food. Whoever steps on the pedal means contributing food to the other party, so no one will have the motivation to step on the pedal. If the purpose is to get the pigs to step on the pedal more, the design of the rules of the game is also a failure. Change plan 2: Incremental plan. Feed twice as much. The result is that both the little pig and the big pig will go to the ankle pedal. Whoever wants to eat will step on the pedal. Anyway, the other party will not finish the food at one time. The little pigs and the big pigs are equivalent to living in a "communist" society with relatively abundant material, and they have enough food, so the sense of competition is not strong. For the designer of the rule, the cost of this rule is quite high, and because the competition is not strong. The purpose of wanting the pig to step on the pedal more is not achieved. Change plan three: reduction plus shift plan. The feeding amount is only half of the original, but at the same time, the feeding port is moved to the vicinity of the pedal. As a result, the little pig and the big pig were desperately rushing to step on the pedal. Those who wait do not get food, and those who work harder get more. For game designers, the decrement shift scheme is the best solution. The cost is not high, and the harvest is the greatest. It can be said to be the best solution. Use the game of smart pigs to analyze the company's incentive system design. If the incentives are too strong, both stock holdings and options, all employees will become millionaires. Not to mention the high cost, the enthusiasm of employees is not necessarily very high. This is equivalent to an incremental scheme. But if the reward is not strong, and the people who see it have a share (there are also "little pigs" who don't work), the "big pig" who once worked very hard will have no motivation - like a reduction plan. The best incentive mechanism is like Scheme 3. Rewards are not shared by everyone, but are directly aimed at individuals (such as business proportional commissions), which not only saves costs (for the company), but also eliminates the phenomenon of "free riders", which can achieve effective incentives. The general idea of this approach is to increase the speculative cost of the "little pig".
mixed game
There is only one policeman, one thief, one pub, and one bank in the town. Police can only patrol one place at a time; thieves can only go to one place. If the police choose to patrol the place where the thief steals, they can catch the thief; and if the thief chooses to steal from the place without the police, the theft can be successful. Suppose the property that the bank needs to protect is worth 20,000 yuan. The property price of the tavern is 10,000 yuan. How can the police patrol for the best results?
The police's best strategy is to draw lots to decide whether to go to the bank or the pub. Because the value of the bank is twice that of the tavern, it is represented by two lots. For example, the 1st and 2nd lottery is drawn to the bank, and the 3rd lottery is drawn to the tavern. In this way, the police have 2, 3 chances to go to the bank to patrol, and 1, 3 chances to go to the pub. In this case, the thief's optimal strategy is to decide whether to go to the bank or go to the pub to steal by the same way of drawing lots. The difference from the police is that the 1st and 2nd lottery is drawn to go to the pub, and the 3rd lottery is drawn to the bank. In this way, the thief has a v3 chance to go to the bank, and a 2,3 chance to go to the tavern. The game between the police and the thief provides the idea of mixed strategies, and there is no pure strategy equilibrium. The strategy should be random. You can't let the other party know your strategy, or even the inclination of your strategy. Once the opponent knows that the possibility of a certain strategy increases, the possibility of losing in the game also increases.
The actual random inspection system is to use the randomness of the strategy
cockfighting game
When two fighting cocks of equal strength meet on a narrow road, each fighting cock has two choices of action: one is to retreat, the other is to attack: if Fighting Cock A retreats, but Fighting Cock B does not retreat. Then B wins, A loses face, and the income is [1,-1]; if B also retreats. Then the two sides are tied; if A does not retreat and B retreats, then A wins and B loses; if both fighting cocks advance, both sides will suffer, and the profit will be [-2,-2]. Both sides retreat, and the payoff is [-1,-1]. Therefore, for each fighting cock, the best result is . The opponent retreats. And don't go back. But this pursuit can lead to a lose-lose outcome.
When encountering this kind of irreconcilable game in practice, it is necessary to make decisions based on strength, but it cannot carry out actual fighting behaviors.