Survival at the center—The stability of minimum differentiation

Abstract

a b s t r a c tWe model a Hotelling market with multidimensional product differentiation in an evolutionary framework. Both evolutionary stability (in the sense of Schaffer, 1989) and stochastic stability (following Kandori et al., 1993;Young, 1993) are analyzed. It is shown that firms move towards the center in product space, i.e. a "principle of minimum differentiation" on all dimensions of the product space applies.

Imitation by price and quantity setting firms in a differentiated market

“…This nuance is not captured in the differentiated market structure used in the earlier papers, but is conveniently encapsulated by the Salop circle -a firm is more affected by, and in turn affects to a greater extent, the immediately neighbouring firms. The result of our paper also complements Hehenkamp and Wambach (2010), who study the evolution of firm location by imitation in a two stage game where firm location is subject to evolutionary pressure in the first stage of the game and firms set prices according to the Nash equilibrium in the second stage; they find that evolution would lead to firms being located equidistantly on the Salop circle. Here, we fix the location of the firms and analyse the evolution of price and quantity, and show the emergence of Nash equilibrium in the price-quantity space.…”

Robust equilibria in location games

“…As already mentioned in Section 2, single-peaked preferences on a line are equivalent to our assumption of heterogeneous edge lengths on the line graph. 11 Some works show that it is not satisfied generically (see, e.g., d 'Aspremont et al, 1979;Eaton and Lipsey, 1975;Economides, 1986) but others support it for special cases (see, e.g., de Palma et al, 1985Palma et al, , 1990Hehenkamp and Wambach, 2010). Similar considerations also hold for minimal differentiation on graphs.…”

Imitation and price competition in a differentiated market

“…A consumer maximises utility and purchases only if the net utility from doing so is at least 0, in which case, the firm providing the highest (non-negative) net utility is chosen. 5 We follow Apesteguia and Selten (2005) and Khan and Peeters (2015) in describing the 4 Even though this assumption is guided by our motivation to study a differentiated market, it is noteworthy that Hehenkamp and Wambach (2010) show that the equidistant locations of firms on a Salop circle is the predicted long-run outcome in a two-stage evolutionary model where firms choose location by imitation in the first stage, and choose the Nash equilibrium price corresponding to the first stage location profile in the second stage. 5 When the maximum net utility that a consumer receives on purchase is exactly equal to 0, we assume the good is purchased.…”

“…8 The resulting experimentation-augmented imitation dynamic (or the perturbed process) has no absorbing 6 See Khan and Peeters (2015) for details. 7 For ease of exposition, we restrict attention to prices being at least equal to marginal cost (consideration of lower prices does not affect any of the results).…”