Nash Equilibrium
Now well-known-through-Hollywood*, John Nash (1928-) won the 1994 Nobel Prize in the Economic Sciences with John Harsanyi and Reinhard Selten, "for their pioneering analysis of equilibria in the theory of non-cooperative games."
Basic (Micro-Economics) Definition:
A Nash Equilibrium is a set of mixed strategies for finite, non-cooperative games between two or more players whereby no player can improve his or her payoff by changing their strategy. Each player's strategy is an 'optimal' response (cf. optimality) based on the anticipated rational strategy of the other player(s) in the game.
Background:
At Princeton, in a series of papers published from 1950-1953, "Equilibrium Points in N-Person Games," "Non-Cooperative Games," "The Bargaining Problem," and "Two Person Cooperative Games," Nash outlined a new paradigm for mathematical and economic thinkers with his pioneering use of Equilibrium Theory. He had been accepted to study in New Jersey from his native West Virginia on a Scholarship for (Pure) Mathematics, and worked briefly under the advising of Albert Einstein. Many of Nash's contemporaries refer to him as a (post)modern day 'genius' for his reformations to some of Adam Smith's views on Economics and when considering his more personal characteristics, including his unorthodox teaching and research procedures, and his past experiences with schizophrenia.
The current (2003) home page of John F. Nash, Jr. at Princeton (Department of Mathematics) notes, "My current research interests include logic, game theory, and cosmology and gravitation."
Equilibrium Theory:
The Nash Theorem maintains its focus on rivalries with mutual gain; a perceptual focus of Nash's mathematical vision found in the light of Leon Walrus' General Equilibrium Theory (published 1874) and John von Neumann's and Oskar Morgenstern's theory of games (1944), now simply called Game Theory. Nash later established his own idea of dominant strategy equilibria through maximization solutions for zero-sum games. He did this with original mathematical techniques to demonstrate the existence of methods for finding a measurable equilibrium in a general class of non-cooperative games.
On the value of Nash equilibrium:
"The concept of a Nash equilibrium n-tuple is perhaps the most important idea in noncooperative game theory. ... Whether we are analysing candidates\' election strategies, the causes of war, agenda manipulation in legislatures, or the actions of interest groups, predictions about events reduce to a search for and description of equilibria. Put simply, equilibrium strategies are the things that we predict about people." - P. Ordeshook
Other academic theorists used the concept of 'equilibrium' in the 19th century (Maxwell, Walrus, Gibbs), for chemical and economic equilibrium in the early stages of the 20th century (van der Waals, Onnes, Keynes) before Nash used it in the middle of the 20th century. Others improved upon Nash's original formulation in the 1950's and 60's (Selten, Harsanyi) and explored different possible aspects of a General Equilibrium Theory (GET) from the 70's to the 90's (Arrow, Hicks, Debreu). Many students of economics still study GET today. Recent academic applications of equilibrium theory from non-economists (Kolmogorov, S. Nagel), and in directions other than those laid down by the neo-Classicalists (cf. neo-Keynesians below), persist as well. The proposed universality of equilibrium theory (i.e. that all situations or economic conditions can/should be considered in the paradigm of general or specific equilibrium thinking) by some theorists makes it difficult to analyze subjects or objects with(-in) a single interpretive framework, and often demands multiple perspectives or even 'relativized' equilibria to explain and interpret diverse economies across the disciplines. Ordeshook above shows us the reach of Nash's equilibrium theory over disciplinary boundaries, and its relevance for practical mathematical-economic applications; now (post)modern theorists must again find ways to deal with its implications in the 21st century academy.
The possible theoretical limitations of equilibrium theory have led to disequilibrium neo-Keynesian theories during the last fifty years (Hahn, Fisher). And stubborn questions remain, even with uncertainty: what if there is more than one Nash Equilibrium in a given game; or if the players in a game have incomplete information; or if the rationality thesis fails to clearly convince readers who live beyond the so-called Age of Reason...? How does a unified Nash Equilibrium maintain itself in a theoretically plural academic culture and with increasingly complex indicators and instruments used in the scientific pursuit? Such may be the cases, for example, when turn-of-the-century relativity theories or even practical evolutionism (i.e. applied morphology) in Economics disallow unification on any shared equilibrium goal(s) or value(s). But then again, this message is itself being written in a time of (post)war.
John Nash can be credited against astonishing odds with making a normative distinction between cooperative and non-cooperative games, and for using mathematical models to support and exemplify his research. But his contribution to theory has become (neo-Nash) a web of explanation(s) and justification(s) far beyond the original conceptions of the author, and has also progressed steadily into the social world; somewhere Nash himself may not have wanted it to go.
Nash and the Others:
As in a contemporary neo-Darwinian scientific notion of Nash Equilibrium, the gaming concepts of 'competition' and 'survival,' may be psychologically associated with the ideas of (non)'cooperation' and of 'aid' (Kroptokin), or with other conflict paradigms theorized in the human and/or social sciences. The four concepts highlighted above are used in mathematical, economic, biological and ecological, social and anthropological theories, in addition to philosophy, and suggest the possibility for further research to clarify conceptually-jumbled or 'tangled' discourses. The potential for reevaluating Equilibrium models in this view suggests comparative parallels with the Intelligent Design challenge to Evolutionary theory of the 1990's, and which still holds into the first years of the new millennium. It can be argued which theory runs deeper in the academy; Equilibrium theory or Evolutionary theory? But with relatively the same adoration that Einstein experienced during his life, and a similar late-life change of theoretical focus, John Nash today finds himself yet unable to realize his higher dreams of a Grand Unified Theory (GUT).
Equilibrium theory struggles to satisfy academic standards in contemporary social sciences (and economics), which require a double hermeneutical approach (Radder, 2003) in addition to the explanatory method given by the mathematical sciences, by neo-classical economics, and even in the new technological sciences. And when the will-full participation of individuals (scientists) disarmed with incomplete information, imperfect rationality and situated knowledge(s) is better recognized, human beings must then re-contextualize them-selves within the scientific process itself; that is, as socially relative and therefore relevant to the ultimate direction(s) of any scientific discourse under research, including equilibrium analyses (i.e., not only business and economics). By then, the post-modern positivism for Nash Equilibrium may have passed-its-own-shadow, or discovered the need to turn back reflexively upon itself; to the author of its theories.
Other Nobel Prizes for Equilibrium Theory in the Economic Sciences:
Kenneth Arrow and John Hicks (1972) for "their pioneering contributions to general economic equilibrium theory and welfare theory;" Gerard Debreu (1983) for "his rigorous reformulation of the theory of general equilibrium"
~~
*In love with "A Beautiful Mind:"
Incidentally (as if movies have no influence on science), the film "A Beautiful Mind" won the Oscar Award for Best Picture in 2001. The film was based (via Hollywood) on the life of John Nash; Russell Crowe was nominated for best Actor Oscar for playing the main character.
Web Resources On Nash Equilibrium
John Nash - Founder of Modern Game Theory
Nash Biography
Book Resources On Nash EquilibriumThe Essential John Nash by Harold Kuhn and Sylvia Nasar (eds.)
Equilibrium and Evolution: An Exploration of Connecting Principles in Economics by Brian Loasby (1991)
Editor(s): Greg Sandstrom
|
|
|
