Convergence of output dynamics in duopoly co-opetition model with incomplete information

This paper explores the role of gradient learning on the convergence of output dynamics in duopoly competition model under incomplete information. For this purpose, we develop two scenarios dynamic co-opetition duopoly models under incomplete information. To this end, the gradient learning is adopted to update the strategy output. We propose dynamic co-opetition duopoly model with homogeneous gradient learning to analyze whether gradient learning enables two firm approach to the Cournot–Nash equilibrium state, when the output dynamics converges to interior stable point meaning the coexistence of two firms. It deduces that gradient learning decreases the profit difference between two firms. Furthermore, we highlight that the dynamics of output converges to the Cournot–Nash equilibrium. We mention dynamic co-opetition duopoly model with heterogeneous gradient learning to explore the survival of the firm that leaves the market, when output dynamics converges to the boundary stable point indicating one firm leaves the market while the other monopolies it. Our conclusion identifies that gradient learning can make the firm that leaves the market enter the market again. Finally, the numerical simulations are presented to verify our results.