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The Hotelling game of pure location allows interpretations in spatial competition, political theory, and strategic forecasting. In this paper, the doubly symmetric mixed-strategy equilibrium forn  ≥  4   $n \ge 4$    firms is characterized as the solution of a well-behaved boundary value problem. The analysis suggests that, in contrast to the casesn  =  3   $n = 3$    andn  →  ∞   $n \to \infty $   , the equilibrium for a finite number ofn  ≥  4   $n \ge 4$    firms tends to overrepresent locations at the periphery of its support interval. Moreover, in the class of examples considered, an increase in the number of firms universally leads to a wider range of location choices and to a more dispersed distribution of individual locations.

Mixed Equilibrium in a Pure Location Game: The Case of n ≥ 4 $$n \ge 4$$ Firms