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Summary: Dynamics of non-homogeneous systems. Proceedings of ISA RAS, 2000, v. 3, pp. 3564.
Antipin A.S.
Computing Center of Russian Academy of Sciences
Moscow, Russia
e-mail: antipin@ccas.ru
FROM OPTIMA TO EQUILIBRIA1
1 Introduction
In recent years there has been a great deal of interest in the expansion of the main concepts
of optimization problems to the field of equilibrium problems. Interest has increased
because optimization problems are not an adequate mathematical tool for modelling in
situations of decision making with multiple agents. Optimization problems can be more
or less adequate in situations where there is one person making decisions working with
an alternative set, but in situations with many agents, each having their personal set
and system of preferences on it and each working within the localized constraints of their
specific situation, it becomes impossible to use the optimization model to produce an
aggregate solution that will satisfy the global constraints that exist for the agents as a
whole.
Such a solution can be found only with the use of diverse equilibrium models. These
situations include saddle point problems, n-person games with Nash equilibrium, inverse
optimization problems, models of economic equilibrium, etc.
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