Two competing firms first choose locations, and then — having observed each other — choose prices so as to attract consumers, who must also pay a linear ‘transport’ cost. Hotelling (1929) assumed a unit continuum of consumers in order to solve this model, but unfortunately this didn’t accomplish its purpose: a series of papers since then have shown that fully characterizing the (necessarily mixed) equilibrium is essentially intractable. Here we instead assume only two consumers and are able to completely describe actions in both stages of the unique symmetric subgame-perfect equilibrium. For some parameters it represents naturalistic behavior (e.g. differentiation and random sales), while for other parameters it is surprisingly complex (e.g. a countable infinity of accumulation mass-points in the location sub-game).
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