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Monday, February 18, 2008

Some food for thought "Game Theory"

Game Theory an Introduction

Game theory is a branch of applied mathematics which is used in the social sciences (most notably economics), biology, computer science and philosophy. Game theory attempts to mathematically capture behavior in strategic situations, where an individual's success in making choices depends on the choices of others. While initially developed to analyze competitions where one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria.
Traditional applications of game theory attempt to find
equilibria in these games—sets of strategies where individuals are unlikely to change their behavior. Many equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. These equilibrium concepts are motivated differently depending on the field of application, although they often overlap or coincide. This methodology is not without criticism, and debates continue over the appropriateness of particular equilibrium concepts, the appropriateness of equilibria altogether, and the usefulness of mathematical models more generally.
Although some developments occurred before it, the field of game theory came into being with the 1944 classic
Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930's. Game theory has been widely recognized as an important tool in many fields. In total eight game theorists have won Nobel prizes in economics and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.

Economics and business
Economists have long used game theory to analyze a wide array of economic phenomena, including
auctions, bargaining, duopolies, fair division, oligopolies, social network formation, and voting systems. This research usually focuses on particular sets of strategies known as equilibria in games. These "solution concepts" are usually based on what is required by norms of rationality. The most famous of these is the Nash equilibrium. A set of strategies is a Nash equilibrium if each represents a best response to the other strategies. So, if all the players are playing the strategies in a Nash equilibrium, they have no unilateral incentive to deviate, since their strategy is the best they can do given what others are doing.
The payoffs of the game are generally taken to represent the
utility of individual players. Often in modeling situations the payoffs represent money, which presumably corresponds to an individual's utility. This assumption, however, can be faulty.
A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of some particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type. Naturally one might wonder to what use should this information be put. Economists and business professors suggest two primary uses.

For further reading have a look at Game Theory: A Nontechnical Introduction-by Morton D. Davis (Author)



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