Existence of Equilibria and Complexity of Computation in Optimizing Complex Systems

Abstract

This paper characterizes the generic properties of interior equilibria in complex systems. The field of complexity has been growing and is concerned with the complexity of computation of complex systems. Complex systems are characterized as systems with a large number of adaptive interdependent parts. These systems demonstrate several properties including: emergence, where the whole does not act as the sum of the parts, and sensitivity to initial conditions. As the number of economic factors increases, the recursion of input–output and modeling error propagates. These two particular symptoms of complex systems make them difficult to model. Solutions to optimization problems of this sort may have different properties depending on the functional assumptions. The generic properties of solutions to these problems can help us have some expectations over the complexity of computation. One example of a complex system is the Game Theoretic Interaction between economic agents. The paper also attempts to shed light on the complexity of computation of such systems.