PIGA, C., 2000. Competition in a duopoly with sticky price and advertising. International Journal of Industrial Organization, 18, pp.595-614.
This paper develops a differential duopolistic game where price is sticky and firms can invest in market-enlarging promotional activities which have a public good nature. One finding indicates that advertising, and not output as in Fershtman and Kamien (Econometrica 55 (1987) 1151–1164) is responsible for the higher stationary price found in the open loop equilibrium relative to the linear feedback one. That is, free-riding is more intense when firms play linear Markov feedback strategies. However, the collusive outcome can be approximated, and opportunism eliminated, if firms can engage in preplay negotiations where they select a nonlinear Markov perfect strategy for output and advertising. Achieving the collusive outcome requires (as in the Folk Theorem for infinitely repeated games) the discount rate to be sufficiently small.