"A combination of actions by a set of agents such that, for each agent, granted that the other agents do not alter their own actions, its action is optimal" (S. KAUFFMAN, 1993,p.240).
However, John NASH, who first stated this rule around 1950, proved "that every game reaches a state of equilibrium where none of the players can improve his position.
Anyhow, according to KAUFFMAN, this theory of games rule has been used by J. MAYNARD SMITH as a model for an evolutive strategy.
"NASH (1950)… showed that in a "game" with any number of rational players who may have different aims but have full knowledge of the others' actions, there is at least one set of strategies which lead to an outcome where everyone's aims are fulfilled as nearly as possible" (Ch. ARTHUR, 1994, p.6))
"The Nash equilibrium was the mathematical basis for the nuclear standoff adopted by the major world powers from the 1950's onwards"( K. Devlin, New Scientist, sept.5, 1998, p. 48)
P. BAK observes however: "In the past, it has often been more or less tacitly assumed that large systems, such as those we find in biology and economics, are in a stable balance, like the sand on a flat beach. The leading economic theory up to now, the general equilibrium theory, assumes that perfect markets, perfect rationality, and so on bring economic systems into stable Nash equilibria in which no agent can improve his situation by any action. In the equilibrium state, small perturbations or shocks will cause only small disturbances, modifying the equilibrium state only slightly. The system's response is proportional to the size of the impact: equilibrium systems are said to be "linear". Contingency is irrelevant. Small freak events can never have dramatic consequences" (1996, p.28)
These assumptions must be considered sometimes as irrealistic and economic theories, for instance should be revised accordingly, in view of the deep technical and social evolution, worldwidely.
The rule remains true as long as the basic conditions of the game do not change. In ecosystems this could explain the-at least theoretica – possibility of a climax.
But of course, environment change or mutations frequently alter the basic conditions.
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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