Asymmetric Cournot Duopoly: A Game Complete Analysis

Abstract

In this paper, we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in Topics in Game Theory (2012), Carfì ICT 2009, Carfì AAPP 2009, Carfì GO 2009; already employed by himself and others in Carfì TPREF 2011, Carfì AAPP 2010, Carfì ISGC 2009) and some new algorithms, using the software wxMaxima 11.04.0, in order to reach a total scenario knowledge (that is the total knowledge of the payoff space of the interaction) of the classic Cournot Duopoly (1838), viewed as a complex interaction between two competitive subjects, in a particularly interesting asymmetric case. Moreover, in this work we propose a theoretical justification, for a general kind of asymmetric duopolistic interactions (which often appear in the real economic world), by considering and proposing a Cobb-Douglas perturbation of the classic linear model of production costs.