Discrete time dynamic game model for price competition in an oligopoly

This article deals with the situation where some firms (agents) compete in an oligopoly market with a global demand constraint. Price competition in the oligopoly is modelled as discrete time dynamic n-agents game over a finite time horizon. Agents maximize the sum of their profits which depend on their own price and on their market demands. The evolution af agents' market demands is determined by all agents' price decisions. We introduce and analyze some simple classes of strategies. Our main interest is to assess some sort of strategies and to find the best response to them. In the final section we prove the existence of exactly one Nash equilibrium in the class of stationary strategies.