Finding equilibrium in von Neumann's model

Abstract

There is discussed the problem of finding an equilibrium position in von Neumann's model (A, B) under exact and interval settings. Effective numerical methods of finding equilibrium exact von Neumann's model are presented. This methods can be stably implemented with floating-point arithmetic. The proposed methods are based on reducing the problem to solving the corresponding matrix games. Considering interval von Neumann's model, in case of multiplicative uncertainty both primal and dual von Neumann's rays are obtained by point von Neumann's model with matrices of interval centers. Interval of the Frobenius number in case of interval von Neumann's model are obtained by finding equilibrium for two exact von Neumann's models with point matrices of interval upper and lower bounds. © 2009 IFAC.