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Theoretical and Applied Economics
No. 1 / 2021 (626), Spring

Equilibrium in a Stackelberg duopoly

Bucharest University of Economic Studies, Romania

Abstract. Theory of the games offers perfect tools for modelling imperfect competition specific processes, manifested in relation with product quantity (Cournot/Stackelberg type), product price (Bertrand type) or quality. The equilibrium solution in terms of output is highlighted in a Cournot situation, whilst the price equilibrium solution can be revealed in a Bertrand scenario. Despite the different strategy type based on, the common denominator of these two models is given by the fact that strategic choices are made simultaneously. The Stackelberg model instead, represents a perfect information sequential game – firms advocating for quantity competition – having both theoretical and practical applicability. In the simplest possible case, with two players moving in two stages, the leader will always choose a certain output level, and the follower observes this decision and then establish his action path accordingly. Present paper’s main goal is to analyze a duopoly market with players adopting a Stackelberg behavior. Regardless the analyzed scenario, both firms are expected to survive and a stable equilibrium will manifest (the Subgame Perfect Equilibrium). The price will be invariable at market demand curve slope, whilst player’s choosed quantities and also gained profits level will be in an inverse dependence relation with it. The leader’s chosen output and also registered profit levels will be double vs the follower’s profit.

Keywords: Stackelberg equilibrium, Stackelberg model, Cournot model, oligopoly, stability.

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