Nash Equilibrium Points in an Asymmetric Duopoly: Comparative Analysis
AbstractBased on , we considerВ an asymmetric duopoly modelВ in the gas marketВ В where two players produce a homogeneous commodity. One of the players maximizes its profit, while the otherВ В maximizes 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. Cournot and Stackelberg models are compared, with and without security constraint  and the comparative analysis is executed.
Conclusions can be generalized as follows. There is an continuum of Nash-Cournot equilibria and the constraint is active under some additional conditions; the Stackelberg equilibrium is unique. In both Stackelberg and Cournot model the security constraint punishes player f and rewards player l; the Stackelberg game with active security constraint punishes even further player f and the revenue is even lower compared to unconstrained market conditions. A special Nash-Cournot equilibrium exists where player f maximizes its revenue. As typical to oligopolistic markets price is higher and quantity sold is lower even under imposed security constraint.
 I. Ivanov, T. Mateva, Cournot and Stackelberg Equilibria in an Asymmetric Duopoly, British Journal of Mathematics & Computer Science, 15(6), 1-13, 2016.
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