Stochastically stable states in an oligopoly with differentiated goods: equivalence of price and quantity strategies

This paper presents results on a stochastically stable state (or long-run equilibrium) in evolutionary dynamics based on imitation of strategies by firms in a symmetric oligopoly with differentiated goods. We consider both quantity setting and price-setting oligopoly games, and define a globally surviving strategy (GSS). It is a strategy that can invade any configuration where the population monomorphically adopts some other strategy, and closely related to a finite population evolutionarily stable strategy (ESS), defined by Schaffer (Schaffer, M.E., Evolutionarily stable strategies for a finite population and a variable contest size, Journal of Theoretical Biology 132, 1988, 469-478). In a quantity-setting oligopoly, the unique GSS output is equal to the unique finite population ESS output, and is a stochastically stable strategy. In a price-setting oligopoly, the unique GSS price is equal to the unique finite population ESS price, and is a stochastically stable strategy. The GSS in a quantity-setting oligopoly and that in a price-setting oligopoly an equivalent. Therefore, stochastically stable states in both cases coincide. (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification: C72; L13.