ABSTRACT
The chapter 9 contains the following main results: the concept of the generalized Cournot–Stackelberg–Nash equilibrium is introduced, special cases of which are the Cournot–Nash and Stackelberg–Nash equilibria; it is proved that the asymmetric uncertainty of strategies in a Cournot duopoly leads to a generalized Cournot–Stackelberg–Nash equilibrium, where the leader has a deterministic strategy and the follower has a random strategy; it is shown that the mutual uncertainty of strategies in a Cournot duopoly, under fairly general conditions, leads to a generalized Cournot–Stackelberg–Nash equilibrium, in which the leader has a better defined (determined) strategy than the follower. For important cases, it is possible to link the Cournot–Nash and Stackelbeg–Nash equilibria parametrically. Such a parameter is not only a controlling variable, but also a choice of the actual target function and mode of behavior: a larger value corresponds to a greater degree of leadership, and a smaller value corresponds to a greater degree of competitiveness (antagonism of interests). Uncertainty asymmetry places the decision maker (DM) with deterministic output in the leader position, and the DM with random output − in the follower position. Indeed, an DM with a deterministic output does not know the random value of another DM’s output, but it knows the expected value of the competitor’s random output. The results obtained show that the asymmetry of interaction between DMs, in particular the asymmetry of uncertainty, can be the reason of the leader’s advantages and lead to generalized Cournot–Stackelberg–Nash equilibria.
