Nobel Prize in 2005: R. Aumann & T. Schelling
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Aumann, Robert John (b. 1930) - Israeli-American mathematician and Nobel Prize winner in economics in 2005 (together with Thomas Schelling) "for his work on conflict and cooperation through analysis in the framework of the theory of games."
Unlike Schelling Aumann worked almost exclusively mathematical analysis of game theory. Commenting on the award of the Nobel Prize in economics, he even said that in the economy as such understands not too deep.
If Schelling studied mainly strategic cooperation of the conflicting parties (non-cooperative games), the Aumann charge of strategic interaction between the parties aimed at long-term co-operation (repeated cooperative games).
In the works of Aumann proved that in repeated cooperative games each player is beneficial to comply with the interests of their partners, because if they come after quick profits, they will lose the trust of partners and their long-term losses exceed gains. Israeli mathematician studied the impact on the co-operative games number of participants, the regularity of their interaction, the quality of forecasting certainty the behavior of other players.
One of the most important objects of analysis Aumann was common knowledge (common knowledge) of competitors - when "I know you know I know ". Originally the game theory assumes complete knowledge of all the players in all aspects of their interactions, and secondly with Aumann in the study were more limited knowledge of the real situation of players against each other.
His results are used primarily to explain the mechanism of the "invisible hand" of the market, where each of the participants in market transactions is interested in a fair contract compliance. They argue, for example, that in the competition of several large firms is not profitable for them to lead a "price war", and agree on the division of markets.
Aumann's research was influenced by the theory of war and conflict. In 1964-1965 he worked for the U.S. Agency for Arms Control, developing an optimal strategy for the U.S. negotiating Geneva Agreement on arms control. In his Nobel lecture, entitled War and Peace Aumann proposed to consider the long-term military conflicts (for example, the Arab-Israeli war) as repetitive game: he argued that in such games conciliatory politics raises expectations for new concessions and objectively lead to new wars. Hence, it was made a pragmatic conclusion that prevention is more effective arms race, creating a credible threat of war. Thus, according to the concept of Aumann if you want peace - we must deliberately prepare for war.
Aumann actively protects the requirement to keep Israel's land previously inhabited by Arabs. Is a member of the right-wing movement "Professors for a Strong Israel," criticizing any agreement with the Palestinians based on the assignment of their requirements. His eldest son was killed in 1982 in the Israeli army during the fighting in Lebanon.
Aumann religiosity affected the subjects of his research. Among his works is the study of Torah and Talmud, proving in particular that set out in the religious precepts of Judaism rules of fair division of the inheritance line with the latest scientific data, obtained with the help of game theory.
Talking about the contribution of R. Aumann is very difficult without resorting to mathematics. As stated in the decision of the Nobel Prize Committee, R. Aumann has done a lot for the formation of the modern image of game theory. In my opinion, it was raised by R. Aumann game theory to its current mathematical level.
Payoff matrix of this game is the following.
Assume that both suspects are in different cells. Obviously, the most profitable strategy for each is not recognized. However, each thinking that the other will begin to confess, does the same, and this leads to the fact that both receive 10 years in prison. In other words, do not co-operative (with respect to a partner), the behavior is the only equilibrium in this game, and not beneficial for both partners. What would happen if the prisoner's dilemma game is played more than once? Will also beneficial to each offender to continue non-cooperative behavior? A brilliant answer to these questions was given by R. Aumann and his disciples and followers in the theory of repeated games. Applications of these games are very diverse. These models describe the price and trade wars, the arms race. These models described the functioning of the various institutions of the Union of Entrepreneurs to the Mafia.
Thomas Schelling
Schelling, Thomas (b. 1921) is an American economist and Nobel Prize winner in economics in 2005 (shared with Robert Aumann) for "deepening the understanding of conflict and cooperation through game theory analysis."
For Schelling, as for many other economists, institutionalists, characterized by thematic diversity studies (See ECONOMIC neoclassical theory). The unifying aspect of his work was a common methodological approach - the study of the strategic rational behavior when people tend to interact with each other to maximize their benefits, not immediately, but over a long period of time. This behavior is studying game theory, one of the founders believe that it is Schelling. The award in 2005 was the second prize, awarded by the Nobel committee for the study of game theory (the first was awarded in 1994 "for pioneering work on the analysis of equilibria in the theory of non-cooperative games").
Schelling's most famous work is the strategy of conflict (1960), in which he formulated many of the new principles of rational strategic interaction.
According to him, in the course of long-term interaction "players" formed the focal point (focal points) - win-win solutions, which are due to the knowledge of the mutual preferences of the parties.
At the same time, the party of the conflict can strengthen its position by providing credible commitments (credible commitments) - strong evidence that it will follow the chosen strategy despite no matter what. In particular, the nuclear arms race profitable to follow the concept of automatic retaliation, when the objects of protection are, first of all, not the city, and missile silos.
In the course of negotiations between the parties to the conflict profitable is "bluffing" when to strengthen its position one of the parties intentionally hides its awareness of its opponent. For example, in the negotiations on nuclear weapons can be beneficial to portray faith in the ability and willingness to apply the automatic enemy retaliation.
In addition to modern political economy - the economic analysis of political problems - Schelling studied strategic cooperation in many other areas of human behavior. Thus, investigating organized crime, he came to the conclusion that its purpose is largely coincide with those of society (in particular, it is also interested in minimizing the murders, which activate the police), so for the preservation of the society of organized crime can be profitable to the "war on mafia . " One of the first economists, he began to study the socio-cultural issues - for example, the reasons for the formation of spatial segregation (formation of ghettos, "Chinatown", etc.).
Schelling's ideas caused a mixed assessment.
On the one hand, after the promulgation of the decision to award the Nobel Peace Prize in 2005 at the Royal Swedish Academy of Sciences has come an open letter calling for the annulment of the decision, accusing the researchers of game theory of "aiding the war" for the fact that they were preparing a theoretical basis for the militant policy of the USA and Israel. In particular, Schelling was accused that his ideas were the foundation of American power strategy of the 1960s in Vietnam. Anti-globalists criticized for its support of Schelling in the 2000s, the Bush administration's refusal to sign the Kyoto Protocol (see also anti-globalization movement).
On the other hand, many noted that the Nobel Prize for Economics in 2005 was a sort of second Nobel Peace Prize. The fact is that in the works of Schelling 1950-1970's it was proved that a rational approach to foreign policy, nuclear proliferation leads to a decrease in the probability of any military conflict (even with the use of conventional weapons) between the participants of the arms race. Schelling's arguments were the basis of the U.S. nuclear strategy and contributed to the growth of nuclear arsenals leading to a global military conflict. In 1993, in connection with the 30th anniversary of the Cuban missile crisis, Schelling was awarded the Prize of the National Academy of Sciences of the United States for work related to the "prevention of nuclear war."
If both countries announce mobilization, it is very likely lead to war. For this case, we conditionally assume that the gain of each country is equal to zero. If both countries refuse to mobilize their prize is equal to b> 0. Finally, if one country is mobilizing the army, and the other not, the attacker can take the disputed territory.
It can be assumed that the gain of the aggressor in this case is a, a win is another country with, and a> b> c> 0.
Consider the so-called payoff matrix of the game. In the rows of the matrix in the strategy are the first country in the columns - the second strategy of the country, and in the intersection of rows and columns - two numbers. The first of them is winning the first country if it chooses a strategy, and the second number is the country's second win in selecting an appropriate strategy.
Based on this example, Schelling comes to the following important conclusion: how countries come to a peaceful existence? Through the threat of force.
Another conclusion arrived at by T. Schelling, considering this problem is that the aggression itself and confrontation to it are being made with small steps - as the country would check each other's intentions, to be able to retreat. The obligations of each party and intentions must be perceived by the other party as credible.
Hence, for example, in a nuclear conflict, to ensure an adequate response, it is necessary first of all to protect the mines, where missiles are based, but not the city.
Sources
- http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2005/aumann-lecture.pdf
- http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2005/schelling-lecture.pdf
