Human Existence A Competitive Game.

For life is nothing more than chaotic game filled with evolutionary winners and losers.


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Game theory

In mathematics, game theory models strategic situations, or games, in which an individual's success in making choices depends on the choices of others (Myerson, 1991). It is used in the social sciences (most notably in economics, management, operations research, political science, and social psychology) as well as in other formal sciences (logic, computer science, and statistics) and biology (particularly evolutionary biology and ecology). While initially developed to analyze competitions in which 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 broad types of games. Prominent examples include cooperative and non-cooperative games and games with perfect and imperfect information. Today, "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as non-human players (computers, animals, plants)." (Aumann 1987).

Traditional applications of game theory define and study equilibria in these games. In an equilibrium, each player of the game has adopted a strategy that cannot improve his outcome, given the others' strategy. Many equilibrium concepts have been developed (most famously the Nash equilibrium) to describe aspects of strategic equilibria. These equilibrium concepts are motivated differently depending on the area of application, although they often overlap or coincide. This methodology has received criticism, and debates continue over the appropriateness of particular equilibrium concepts, the appropriateness of equilibria altogether, and the usefulness of mathematical models in the social sciences.

Mathematical game theory had beginnings with some publications by Émile Borel, which led to his 1938 book Applications aux Jeux de Hasard. However, Borel's results were limited, and his conjecture about the non-existence of mixed-strategy equilibria in two-person zero-sum games was wrong. The modern epoch of game theory began with the statement of the theorem on the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by his 1944 book Theory of Games and Economic Behavior, with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

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 1930s. Game theory has been widely recognized as an important tool in many fields. Eight game-theorists have won the Nobel Memorial Prize in Economic Sciences, and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.

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There is a Yale introductory course available on line for free on Game theory. You might find this interesting. The initial classes are rather drawn out however but then again, that's how school is typically.

I can't post the link but you can google academic earth game theory if you'd like.

WW III ANGRY wrote:

There is a Yale introductory course available on line for free on Game theory. You might find this interesting. The initial classes are rather drawn out however but then again, that's how school is typically.

I can't post the link but you can google academic earth game theory if you'd like.

Neat. I'll look into that.