the Theory of games — is the mathematical theory of strategy which assumes that there is at least two player and the result of game is defined by their choice. If among players there is a conflict of preferences, this conflict not necessarily has to be total. Unlike sports if one player wins, another not necessarily is lost. The conflict of interests can be partial, and both players can win and lose at the same time. The theory of games is focused on equilibrium strategy of players.
History of researches
the Theory of games thought up the Hungarian mathematician Neyman John a background Neyman John and the German economist Morgenshtern Oscar who in the late thirties moved to United States of America. They met at Institute of perspective researches of Princeton university in the 1940th years and wrote the book "Theory of Games and Economic Behaviour" (1944). The book was republished in 1947 and in 1953.
before, in 1928, Neyman John a background Neyman John wrote article in which output the theorem of the minimax, considered fundamental in the theory of games. In Princeton it worked with Morgenshtern Oscar applying the theory of games to economy, and also to salonny games like poker.
In the book a background Neyman John and Morgenshtern Oscar simulated the simplified version of poker and analysed optimum strategy which are chosen by players. But years later many people found their ideas useful to economy, biology and in particular for political science. Moreover, the theory of games began to be applied in sports and even in such disciplines, as philosophy. The theory of games offers structure of decision-making both in the conditions of the conflict, and in the conditions of cooperation for games, in which two players or more.
Other scientists also made a considerable contribution to development of the theory of games. Among them — Nesh John who is well-known thanks to balance Nesh John, and some mathematicians and economists who at different times got the Nobel Prize on economy for the works.
Game in the theory of games
Game — is a situation in which there is an interdependence between participants or players. If there are two players, that you do, that other player does depends on that other player does, and, depends on that you do. And the result depends on a choice of both players. But in game there can be more than two players. In that case players most often unite in the coalition.
a strategy Choice
People choose by p strategy, based on result. One player chooses strategy which, in his opinion, is favorable to it, and another does the same. And none of players will not win if recedes from the strategy. It is called "an equilibrium outcome".
It is one of types of decision-making in games. But the theory of games — is history not only about a choice of optimum strategy, but also about a benefit assessment. Money, but, besides, can be benefit it has to include other things which players can wish. Question in how to distribute benefit. The question of justice is often brought up in the theory of games. What distribution of the benefits fairly on the attitude towards all players? As a rule, it is a compromise in which both players are satisfied with an outcome. This part of the theory of games is called "cooperative game". In not cooperative game players simply choose good and bad strategy.
Nesh John designated this distinction between two different approaches in the early articles in the 1950th years. It made a fundamental contribution to theory development. In the second half of the XX century not cooperative theory of games in which players look for the optimum stable strategy conducting by an equilibrium outcome also strongly developed. But the cooperative theory of games also is very interesting, especially for philosophers who study questions of justice of result.
Ravnovesiye Nesh John and the dilemma of the prisoner
Balance Nesh John is defined by p as an outcome in which there are two players, and any of players does not refuse the strategy because differently it will suffer. But it does not mean obligatory existence of a favorable outcome for both players. There is the well-known game which is called "A dilemma of the prisoner". In this game two players choose optimum strategy, but the result turns out not absolutely favorable to both. There is more favorable outcome for both players, but this outcome is unstable, and it is not in balance Nesh John. There is a conflict between a choice of optimum strategy and receiving the best result.
History about a dilemma of the prisoner the following. Two criminals are in separate chambers. Everyone ask, whether it is guilty of a certain crime. If both recognize that are guilty, everyone receives rather severe punishment — we will tell, five years of imprisonment. But if both refuse to admit guilt, will receive rather good result — for example, one year of imprisonment. But if one prisoner admits guilt, and another does not recognize, the result will be very sad for this purpose who admitted guilt — ten years in prison. Him find guilty, and the second criminal will be released for that helped to define the present guilty.
Oba prisoners receive relative benefit (a cooperative outcome — 1 year in prison) if nobody confesses. But everyone has a temptation to betray other prisoner. If one admits, and another is not present, that admitted, will avoid punishment while the second will receive 10 years of imprisonment. But if both admit, to them too it will be bad (not cooperative game — 5 years of imprisonment). It also is called as a dilemma. It is unclear that prisoners have to do: whether they have to choose not cooperative game and confess or they have to try good luck and not admit, strongly risking?
It seems to p that the most reasonable decision for players — cooperation. But it is an unstable outcome because each player has an incentive not to cooperate, and, on the contrary, to betray other player. Good example of such dilemma — race of arms between Soviet Union and United States of America in the 1950-1990th years. Within 45 years two countries conducted not cooperative game, spent a lot of money for arms to bypass other party. Both countries would win to spending so many funds for arms, and to spend them for socially useful benefits. But each country did not trust another therefore both parties continued to make the weapon, and anybody from it did not win.
the Fair sharing
We know that negotiations often happen difficult. We always look for ways which will allow both parties to reach a cooperative outcome in spite of the fact that game can remind a dilemma of the prisoner sometimes. One of ways — to try to define, what questions divide players, and to use procedure of distribution of justice to define who in what questions will win. It is necessary to make so that everyone won in that question which is most important for it. You do not receive everything that want, but you can receive that for you is the most important, especially if you and your opponent want different things. In other words, both parties can win. It also is safe decisions.
Teoriya games in everyday life
Safe decisions can be applied by h3 in everyday life. For example, Taylor Alan and I in our book "We Divide on Justice, or a Prize Guarantee to Everyone" ("The Win-Win Solution: Guaranteeing Fair Shares to Everybody") considered divorce Donald Trump and his first wife, Ivana. We showed that each spouse could receive the benefit if they came to the agreement under which everyone would receive what wished most of all.
For example, Ivana most of all wanted to receive the house in State of Connecticut where her children grew up, and Donald Trump wanted to leave a mansion in State of Florida. We showed how they could divide property, especially real estate that everyone remained is happy. Actually they and arrived. But in many cases participants cannot come to the agreement because players cannot come to such procedure.
It is procedure which helps to resolve the conflicts. We often see that the conflicts and remain the conflicts because each party opposes to cooperation. Therefore people cannot come to the agreement. Stains happen very heavy — not only in respect of financial high cost and money which it is necessary to pay to lawyers, also in sense of emotional exhaustion. These are situations with which the theory of games can help.
it is logical to p to use similar procedure, but many people simply do not know about it. They fight with each other though can find a compromise which will suit all. They worry that if do not fight, they will lose because other player will conduct dishonest game. Therefore it seems to them that they too should not make a compromise to create balance. But we know that there are situations in which both players can compromise and as a result to a relative prize. Emotions also play an important role because the parties start being angry at each other, and it prevents to reflect logically.
We intuitively use the theory of games every day. For example, when the person has a problem in the relations with the friend, the girlfriend or the spouse, he or it thinks of good and bad strategy for a prize in dispute. Though nobody does calculations to which theorists of games resort, people come to them intuitively. But they often make mistakes. The theory of games can help to think more clearly and to take into account of preference of the opponent as well as the.
the Theory of games and the politician
the Conflicts between United States of America and Russian Federation, United States of America and China, China and Russian Federation are quite typical. These countries have a number of questions on which they clash: territories, trade, alliances. The theory of games can help them to reach a compromise to which it is difficult to come if to use informal negotiations.
the vote Theory which also is called as the theory of a collective choice, can help with a choice of the best way of election of the leader. In the democratic countries candidates often win, receiving a majority of votes. But, for example, at presidential election of 2016 to United States of America any of candidates from two leading parties — Donald Trump and Hillary Clinton — did not receive a majority of votes because there were also candidates from the third and fourth party who too received votes. But there are voting procedures at which people can express more stoutly the choice and not be limited to one voice. For example, at approving vote the voter can vote for more than one candidate if more than two candidates participate in race.
Pobeditel which is chosen by means of approving vote, reflects preferences of voters better. For example, on elections of 2016 to United States of America against Hillary Clinton won a straw vote, having received more than two million votes, but lost in electoral college vote which defines a result of elections. But even if not to take an electoral college into account, we often observe how the most popular candidates who are in the vote center, divide among themselves voices, and that received the majority as a result wins. Approving vote is contrary to it because voters can approve not only one candidate. Thus, it is possible to choose the candidate who suits all, instead of the one who simply gathered the greatest poll.
do not need to be the theorist of games to apply some of the principles of this theory. For example, Henry Alfred Kissindzher who was the state secretary at Nixon's administration, never studied the theory of games, but was able to find optimum solutions. The understanding of the theory of games can be useful in the analysis of situations in which the result depends on a choice and interaction of two people or more.
Open questions
Questions concerning the theory of games arise all the time in such areas, as economy, policy, biology. But very often extension of the standard theory is necessary. For example, in the 1970th years in biology the new understanding of balance which call evolutionarily stable strategy was offered. This strategy seems more applicable for the analysis of the conflicts between individuals, than balance Nesh John. The theory of games — is history how really to comprehend problems and to try to find new solutions for them. Bases of the theory of games lie in mathematics, but new ideas which appear from its application, promote her growth and development.
Source: <= "http://serious-science.org/game-theory-7846"> Serious Science
-
About us
-
- That such Post-science?
- 3 years to Post-science
- Who my?
- Statistika
Uchastiye
All rights zashchishcheny.