Każda skończona ma przynajmniej jedną równowagę Nasha, niekoniecznie w .
Równowaga Nasha nie musi być . Klasycznym przykładem tej nieefektywności jest paradoks znany jako .
Rozważmy grę dwuosobową. Równowagą Nasha jest następujący wybór. Wybór gracza A jest optymalny dla wyboru gracza B i wybór gracza B jest optymalny przy danym wyborze A. Inaczej: Wybieram to, co jest dla mnie najlepsze, gdy ty robisz to, co robisz. Ty robisz to, co jest dla ciebie najlepsze, gdy ja robię to, co robię.
Mixed strategy- consisting of possible moves and a probability distribution (collection of weights) which corresponds to how frequently each move is to be played. A player would only use a mixed strategy when she is indifferent between several pure strategies, and when keeping the opponent guessing is desirable - that is, when the opponent can benefit from knowing the next move.
Optimum w sensie Pareto (czy efektywność w sensie Pareto, efektywność Pareta) - termin oznaczający taki podział dostępnych dóbr, że nie można poprawić sytuacji jednego podmiotu (dostarczyć mu większej ilości dóbr) nie pogarszając sytuacji któregokolwiek z pozostałych podmiotów
Cardinal payoffs- Cardinal are numbers representing the outcomes of a game where the numbers represent some continuum of values, such as money, quantity, or market share. Cardinal payoffs allow the theorist to vary the degree or intensity of payoffs, unlike , in which only the order of values is important. For calculations, payoffs must be cardinal.
Ordinal Payoffs- Ordinal are numbers representing the outcomes of a game where the value of the numbers is not important, but only the ordering of numbers. For example, when solving for a in pure , one is only concerned with whether one payoff is larger than another - the degree of the difference is not important. Thus, we can assign values like "1" for the worst outcome, "2" for the next best, and so on. Thus, ordinal payoffs simply rank all of the outcomes. For calculations, must be employed.
What economists call game theory psychologists call the theory of social situations, which is an accurate description of what game theory is about. Although game theory is relevant to parlor games such as poker or bridge, most research in game theory focuses on how groups of people interact. There are two main branches of game theory: cooperative and noncooperative game theory. Noncooperative game theory deals largely with how intelligent individuals interact with one another in an effort to achieve their own goals. That is the branch of game theory I will discuss here.
In addition to game theory, economic theory has three other main branches: , and . All are closely connected to game theory.
Decision theory can be viewed as a theory of one person games, or a game of a single player against nature. The focus is on preferences and the formation of beliefs. The most widely used form of decision theory argues that preferences among risky alternatives can be described by the maximization of the expected value of a numerical utility function, where utility may depend on a number of things, but in situations of interest to economists often depends on money income. Probability theory is heavily used in order to represent the uncertainty of outcomes, and Bayes Law is frequently used to model the way in which new information is used to revise beliefs. Decision theory is often used in the form of decision analysis, which shows how best to acquire information before making a decision.
General equilibrium theory can be viewed as a specialized branch of game theory that deals with trade and production, and typically with a relatively large number of individual consumers and producers. It is widely used in the macroeconomic analysis of broad based economic policies such as monetary or tax policy, in finance to analyze stock markets, to study interest and exchange rates and other prices. In recent years, political economy has emerged as a combination of general equilibrium theory and game theory in which the private sector of the economy is modeled by general equilibrium theory, while voting behavior and the incentive of governments is analyzed using game theory. Issues studied include tax policy, trade policy, and the role of international trade agreements such as the European Union.
Mechanism design theory differs from game theory in that game theory takes the rules of the game as given, while mechanism design theory asks about the consequences of different types of rules. Naturally this relies heavily on game theory. Questions addressed by mechanism design theory include the design of compensation and wage agreements that effectively spread risk while maintaining incentives, and the design of auctions to maximize revenue, or achieve other goals.
sTOCKHOLM, Sweden - A pair of game theorists who defined chess-like strategies in politics and business that can be applied to arms races, price wars and actual warfare won the Nobel Prize in Economic Sciences on Monday.Israeli-American Robert J. Aumann and U.S. citizen Thomas C. Schelling won the award for research on game theory, a branch of applied mathematics that uses models to study interactions between countries, businesses or people.The theory, devised in 1944 by John von Neumann and Oskar Morgenstern, is often used in a political or military context to explain conflicts between countries. More recently it has been used to map trends in the business world, ranging from how cartels set prices to how companies can better sell their goods and services in new markets.“The understanding of game theory helps explain economic conflicts like price competition and trade wars,” said Jorgen Weibull, chairman of the prize committee. “I think the main impact is on economics, but it also applies to other social sciences.”Aumann, 75, and Schelling, 84, who know each other but have never worked together, were cited by the Royal Swedish Academy of Sciences for helping explain “economic conflicts such as price wars and trade wars, as well as why some communities are more successful than others in managing common-pool resources.”It said the pair’s work, which built on research by the 1994 winners of the same prize, could be applied to understand how merchant guilds, international trade treaties and even organized crime groups are formed and operate.Schelling, who teaches at the University of Maryland, used game theory in his 1960 book “The Strategy of Conflict” to focus on how the U.S. and the former Soviet Union maintained credible threats that were not likely to be used, given the threat of nuclear annihilation.“If you have second-strike capacity, then it makes your opponent think twice,” said Carl-Gustaf Lofgren, a member of the prize committee.Monday’s award also highlighted developments in game theory that were lauded with the 1994 economics prize to Americans John Harsanyi and John Nash and German ReinhardSelten. Nash was portrayed in the 2001 Academy Award-winning film “A Beautiful Mind,” starring Russell Crowe.Lofgren said Aumann’s theories differed from Nash’s by introducing an infinite repetition of the same game so as to find the best solution in long-term relationships instead of in a single encounter.The difference is illustrated in the so-called “prisoner’s dilemma,” one of game theory’s best-known situations in which two partners in crime are put in separate cells and given an ultimatum: If one implicates the other, he may go free while his partner faces a firing squad.
