Bertrand-Cournot Comparison in a Mixed Duopoly with Advertisement

Abstract

We examine the Bertrand-Cournot comparison with advertisement in a differentiated mixed duopoly market, and compare with the social optimum. We show that not only both firms' quantities but also both firms' advertisements are higher (lower) in Cournot (Bertrand) than the social optimum. Thus, both firms engage in excessive (insufficient) advertisement in Cournot (Bertrand). We also show that despite lower both firms' prices in Cournot, both firms' profits and social welfare are strictly higher in Bertrand and thus, both firms prefer Bertrand to Counrnot.

A Game-Theoretic Model of Strategic Interaction Using Advertising: Simulating the Evolution of the Cournot Nash Equilibrium under Different Competitive Scenarios

“…Researchers have explored the dynamics of a Cournot duopoly where advertising alters the slope of the demand function [5]: Refs. [6][7][8] examine closed-form equilibrium solutions to Cournot and Bertrand differentiated duopolies where advertising alters the intercept of the demand function; Ref. [9] use numerical simulation and adaptive control theory to explore the chaotic dynamics inherent in duopoly competition where advertising directly influences quantity sold and the amount of advertising is proportional to firm profit; Ref.…”