An existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy

We establish an existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy. Instead of the traditional approach which depends on Kakutani’s fixed point theorem, we employ the theories of aggregative games and best reply potential games. We show that, if there exists a representative consumer, under some conditions on preferences and production technologies, the profit maximization game is a (pseudo) best reply potential game. Hence, the existence of the equilibria is proved independently of the well known convex-valued assumption on the best responses. Although our assumptions result in the additive separability on a utility function of a representative consumer, the existence of increasing returns and indivisible productions can be allowed. In our model, it is shown that the game played by firms exhibits strategic substitutes whether the products of firms are substitutes or complements, and this plays an important role for the existence of the equilibria.     

Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem

This study considers a situation in which agents choose the location of a public facility from a street according to a given mechanism. Agents have single-dipped preferences over a set of feasible locations. We analyze coalitional behavior for any given mechanism for this situation. We identify a necessary and sufficient condition for a mechanism to possess a strong Nash equilibrium by applying the minimax theorem of von Neumann and Morgenstern (1944). We introduce a class of core solutions and show that these solutions are characterized by strong Nash implementability. As a byproduct of these results, we propose a simple mechanism that implements any core solution in strong Nash equilibria.