Mixed equilibrium in a pure location game: The case of n ≥ 4 firms - Christian Ewerhart (University of Zurich, Department of Economics, 2014)
The Hotelling game of pure location allows interpretations in spatial competition, political theory, and professional forecasting. In this paper, the doubly symmetric mixed-strategy equilibrium for n ≥ 4 firms is characterized as the solution of a well-behaved boundary value problem. The analysis suggests that, in contrast to the cases n = 3 and n → ∞ , the equilibrium for a finite number of n ≥ 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. The results are used to comment on the potential benefit of competition in forecasting markets.
Keywords: C72; D43; D72; L13; 330; Location; Hotelling game; mixed-strategy equilibrium; boundary value problem