The Golden Rule in the Model of Cournot Duopoly

Source of the Golden Rule: «Do with respect to someone in such way as you would like him to do with respect to you» one can find in New Testament.
Such approach in economics results to altruistic rules of behavior «help others, forgetting about yourself». The concept of Berge equilibrium strictly formalized in Russia in 1994 in thesis and first articles of Vaisman K.S. fully meets such approach. Then this method of conflict balancing began to be used in works of western colleagues.
However the matter of its practical application to problems of mathematical economics was left open.The offered article maybe is one of the first concerning this application. It is constructed the explicit form of Berge equilibrium solution in dynamic one-step variant of controllable Cournot duopoly – the mathematical model of interaction of two sellers on the market.
Nash equilibrium is a common optimality concept for non-cooperative games. The key difference is that in case of Nash equilibrium an individual player’s deviation from the equilibrium cannot increase the player’s own payoff, therefore it has «egoistic character». On the contrary Berge equilibrium is characterized by «altruistic character» dictated by the Golden rule.
The monograph written by French economist, philosopher and mathematician Antoine Augustin Cournot (1801-1877) is one of the first scientific studies of the use of game theory in economics. It was published in 1838. Cournot considers a duopoly model on the market in this book.

Key words: Cournot duopoly, Berge equilibrium, Nash equilibrium, one-step positional noncooperative linear-quadratic game, dynamic programming.