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Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers.
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts to the theory of partial equilibrium, which analyzes a specific part of an economy while its other factors are held constant. In general equilibrium, constant influences are considered to be noneconomic, therefore, resulting beyond the natural scope of economic analysis. The noneconomic influences is possible to be non-constant when the economic variables change, and the prediction accuracy may depend on the independence of the economic factors.
Kenneth Joseph Arrow was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972.
Gérard Debreu was a French-born economist and mathematician. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize in Economic Sciences.
In mathematical economics, the Arrow–Debreu model suggests that under certain economic assumptions there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.
Michio Morishima was a Japanese heterodox economist and public intellectual who was the Sir John Hicks Professor of Economics at the London School of Economics from 1970–88. He was also professor at Osaka University and member of the British Academy. In 1976 he won the Order of Culture.
Serbonian Bog was an area of wetland in a lagoon lying between the eastern Nile Delta, the Isthmus of Suez, Mount Casius, and the Mediterranean Sea in Egypt, with Lake Sirbonis at its center. The lagoon still exists, and is the second-largest in Egypt. The bog is used as a metaphor in English for an inextricable situation.
David Cass was a professor of economics at the University of Pennsylvania, mostly known for his contributions to general equilibrium theory. His most famous work was on the Ramsey–Cass–Koopmans model of economic growth.
Lionel Wilfred McKenzie was an American economist. He was the Wilson Professor Emeritus of Economics at the University of Rochester. He was born in Montezuma, Georgia. He completed undergraduate studies at Duke University in 1939 and subsequently moved to Oxford that year as a Rhodes Scholar. McKenzie worked with the Cowles Commission while it was in Chicago and served as an assistant professor at Duke from 1948–1957. Having received his Ph.D. at Princeton University in 1956, McKenzie moved to Rochester where he was responsible for the establishment of the graduate program in economics.
In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization of the concept of finite measure, which takes nonnegative real values only.
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Roy Radner was Leonard N. Stern School Professor of Business at New York University. He was a micro-economic theorist. Radner's research interests included strategic analysis of climate change, bounded rationality, game-theoretic models of corruption, pricing of information goods and statistical theory of data mining. Previously he was a faculty member at the University of California, Berkeley, and a Distinguished Member of Technical Staff at AT&T Bell Laboratories.
Nicholas C. Yannelis is the Henry B. Tippie Research Professor of Economics and Applied Mathematics and Computation at the University of Iowa. He is an emeritus Commerce Distinguished Alumni Professor of Economics at the University of Illinois at Urbana-Champaign. Also he was the Sir Johns Hicks Professor of Economics at the University of Manchester. His research includes the study of equilibrium concepts in games and economies with asymmetric information; equilibrium in infinite dimensional commodity spaces; equilibrium in games and economies with discontinuous preferences; and equilibrium theory and implementation under ambiguity. He has also done works in pure mathematics.
The Shapley–Folkman lemma is a result in convex geometry that describes the Minkowski addition of sets in a vector space. It is named after mathematicians Lloyd Shapley and Jon Folkman, but was first published by the economist Ross M. Starr.
Jon Hal Folkman was an American mathematician, a student of John Milnor, and a researcher at the RAND Corporation.
In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood. When convexity assumptions are violated, then many of the good properties of competitive markets need not hold: Thus, non-convexity is associated with market failures, where supply and demand differ or where market equilibria can be inefficient. Non-convex economies are studied with nonsmooth analysis, which is a generalization of convex analysis.
Convexity is an important topic in economics. In the Arrow–Debreu model of general economic equilibrium, agents have convex budget sets and convex preferences: At equilibrium prices, the budget hyperplane supports the best attainable indifference curve. The profit function is the convex conjugate of the cost function. Convex analysis is the standard tool for analyzing textbook economics. Non‑convex phenomena in economics have been studied with nonsmooth analysis, which generalizes convex analysis.
Robert Murdoch Anderson is Professor of Economics and of Mathematics at the University of California, Berkeley. He is director of the Center for Risk Management Research, University of California, Berkeley and he was chair of the University of California Academic Senate 2011-12. He is also the Co-Director for the Consortium for Data Analytics in Risk at UC Berkeley.
Disequilibrium macroeconomics is a tradition of research centered on the role of disequilibrium in economics. This approach is also known as non-Walrasian theory, equilibrium with rationing, the non-market clearing approach, and non-tâtonnement theory. Early work in the area was done by Don Patinkin, Robert W. Clower, and Axel Leijonhufvud. Their work was formalized into general disequilibrium models, which were very influential in the 1970s. American economists had mostly abandoned these models by the late 1970s, but French economists continued work in the tradition and developed fixprice models.
Jean-François Mertens was a Belgian game theorist and mathematical economist.
References
- ↑ Faculty profile, UCSD economics department, retrieved 2011-01-21.
