We study the R&D investment strategies of two compteting firms in a dynamic setting where the probability of a discovery increases with accumulated investments.

The Bertrand and Cournot equilibria, for a differentiated duopoly engaging in process R&D competition, are derived and compared. The findings suggest that: (i) Bertrand competition is always more efficient, (ii) Bertrand competition yields low prices and higher quantities, (iii) Cournot outcomes are more favorable, from the point view of the firms.

We study in this paper dynamic equilibrium advertising strategies in a duopoly. with asymmetric information structure. The advertising model of Lanchester is used in a game where the relevant solution concept is Feedback Stackelberg equilibrium which has the desirable property of being subgame perfect. An algorithm is devised for the computation of this equilibrium and numerical results are reported and discussed. Using the data involving Coca-Cola and Pepsi-Cola for the period 1968-1981 and the data available for the beer industry over the period 1971-1988, we analyze the advertising strategies and we provide a comparison with closed-loop and open-loop Nash equilibriums. A significant contribution of this paper is the empirical study of the Feedback-Stackelberg equilibrium and the comparison with the published literature.

We experimentally examine the applicability of criticisms on mixed strategy equilibria in the context of Narasimhan’s (1988) model of competitive price promotions. We also study the impact of factors that may influence whether firms behave competitively or cooperatively, including (a) the relative size of loyal customer segments, (b) brand preference of switchers, and (c) whether players can communicate with each other (using a “chat” box).