Nash equilibrium stability of a Cournot game with differentiated goods and concave demand function

Abstract

In a non-cooperative game, the benefit of the agents involved in the game depends on their payment function and the strategy employed by each agent. In the particular case of a non-cooperative Cournot game, the strategic choice of each agent is the quantity of good to be produced and its payment function coincides with the benefit function. This paper set out to investigate the Nash equilibrium and its stability in a noncooperative Cournot game with differentiated goods and concave demand function. The method used was that of mathematical economics and, in addition, a methodology based on literature review, study of various mathematical procedures and numerical simulation in the statistical software R. As a result, we have a new bipersonal non-cooperative Cournot game where the demand function is concave and it is shown that this game has a unique Nash equilibrium which, in addition, is symmetric. It is concluded that, under the naive expectation strategic updating rule, the symmetric Nash equilibrium is asymptotically stable and the permanence in the market of the firms is only possible if both follow the imitation strategy, each firm produces the same amount of good as its opponent in each time period.