![]() ![]() ![]() The mixed strategy equilibrium is unique and converges to the equilibrium of the standard model from above, indicating that the use of a continuum is a reasonable approximation of the mixed-strategy equilibrium for a market with a large number of buyers. This paper characterises both the ex-ante stable mixed strategy Nash equilibrium and the ex-post stable undercut-proof equilibrium for the model, and compares them with the equilibrium of the standard Hotelling model with a continuum of consumers. Combining the Hotelling line with the realistic assumption that markets contain finitely many consumers, produces a model of spatial competition that does not possess a Nash equilibrium in pure strategies. ![]()
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