Cournot and Stackelberg Equilibria in an Asymmetric Duopoly

Aims/Objectives: To study an asymmetric duopoly in gas market where two players produce a homogeneous commodity. One of the players maximizes its profit, while the other- its revenue. The asymmetry also includes a security constraint, saying that the revenue- maximizing player can sell no more than a certain proportion of the quantity of its rival.
Study Design: Interdisciplinary study.
Place and Duration of Study: Department of Information Technologies, College of Dobrich, Shumen University, Bulgaria, between October 2015 and February 2016.
Methodology: We assume that the industry is duopolistic, the product is homogeneous- natural gas and storage is impossible. We impose a security constraint that one of the players cannot produce more than a certain proportion of its rival's quantity and behaves as a revenue maximizer. Cournot and Stackelberg are compared, with and without security constraint.
Results: Results we have reached can be generalized as follows: There is an continuum of Nash- Cournot equilibria and theconstraint is active under some additional conditions; Stackelberg equilibrium is unique; In both Stackelberg and Cournot model the security constraint punishes player f and rewards player l; Stackelberg game with active security constraint punishes even further player f and the revenue is even lower compared to unconstrained market conditions; As typical to oligopolistic markets price is higher and quantity sold is lower even under imposed security constraint; A special Nash- Cournot equilibrium exists where player f maximizes its revenue. An additional condition should be introduced.
Conclusion: We estimate the constraint's impact on profits, consumer surplus, quantities and price. In addition we offer a special case where one of the player maximizes its revenue and the other earns the highest possible profit.