Noncooperative oligopoly equilibrium in markets with hierarchical competition

In this paper we study a non-cooperative sequential equilibrium concept, namely the Stackelberg-Nash equilibrium, in a game in which heterogeneous atomic traders interact in interrelated markets. To this end, we consider a two-stage quantity setting strategic market game with a finite number of traders. Within this framework, we define a Stackelberg-Nash equilibrium. Then, we show existence and local uniqueness of a Stackelberg-Nash equilibrium with trade. To this end, we use a differentiable approach: the vector mapping which determines the strategies of followers is a smooth local diffeomorphism, and the set of Stackelberg-Nash equilibria with trade is discrete, i.e., the interior equilibria of the game are locally unique. We also compare through examples the sequential and the simultaneous moves games. A striking difference is that exchange can take place in one subgame while autarky can hold in another subgame, in which case only leaders (followers) make trade.