On the Stability of a Cournot Dynamic Game Under the Influence of Information
Abstract
In this paper we study the impact of information on the stability of a dynamic Cournot – type duopoly game. We suppose that one player searches for information about his rival before he makes his decision. We study how the amount of information acquired by player, influences the stability of Nash equilibrium. The game is modeled with a system of two difference equations. Existence and stability of equilibrium of this system are studied. We show numerically that the model gives chaotic and unpredictable trajectories as a consequence of change in the information parameter, but in our case there are also stable trajectories for each value of the information parameter. To provide some numerical evidence for the chaotic behavior of the system we present various numerical results including bifurcation diagrams, strange attractors, Lyapunov numbers and sensitive dependence on initial conditions.
Keywords: Cournot dynamic game, Nash equilibrium, Stability, Chaos.
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