Information equilibriu, in dynamic model of collective behavior in a competitive market

The article presents a dynamic model of reflexive behavior which provides a unified approach to description of interactions of Cournot/Stackelberg agents in a competitive market in the absence of common knowledge. The approach based on game theory and the theory of collective behavior with incomplete information. The model is a conventional Cournout output competition with linear costs and the inverse demand function. Rational agents in the model have incorrect initial beliefs about marginal costs of their competitors. We investigate two cases: (1) all agents act simultaneously and (2) first agent is a Stackelberg leader. We study repeated interactions when the agents dynamically update their actions and beliefs based on observed actions of their competitors. A unified procedure of beliefs update is provided for both cases. Necessary and sufficient conditions for the convergence of dynamic processes to the equilibrium with true beliefs are obtained. The results are illustrated with numerical examples.