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.