ON THE STABILITY OF STRATEGIES IN COMPETITIVE-SYSTEMS

This work discusses in some details the mathematical properties of com petitive systems. It is demonstrated how an optimal strategy of any dy namic matrix game can be derived analytically. The number of various p ure strategies contributing to the optimal strategy is found by analys ing the properties of the gain matrix. A relationship between the stab ility and fitness of equilibrium states is established. It is shown th at the fitness of the system can be expressed in terms of the eigenval ue spectrum of the system's stability matrix. The methods developed ar e applied to a few examples.