Best-response potential for Hotelling pure location games. (English) Zbl 1398.91010
Summary: We revisit two-person one-dimensional pure location games à la S. P. Anderson et al. [Discrete choice theory of product differentiation. Cambridge, MA: MIT Press (1992; Zbl 0857.90018)] and show that they admit continuous best-response potential functions [M. Voorneveld, Econ. Lett. 66, No. 3, 289–295 (2000; Zbl 0951.91008)] if demand is sufficiently elastic (to the extent that the Principle of Minimum Differentiation fails); if demand is not that elastic (or is completely inelastic) they still admit continuous quasi-potential functions [B. C. Schipper, Pseudo-potential games. Working Paper. University of Bonn (2004)]. We also show that, even if a continuous best-response potential function exists, a generalized ordinal potential function [D. Monderer and L. S. Shapley, Games Econ. Behav. 14, No. 1, 124–143 (1996; Zbl 0862.90137)] need not exist.
Keywords:
symmetric games; location games; best-response potential games; pure Nash equilibrium existenceReferences:
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