Learning by doing with spillovers: Strategic complementarity versus strategic substitutability

“Learning by doing”, in which unit production costs decrease with cumulative production experience, is extensively observed in economies of scale. It has been shown that, in the case of mature technologies, learning curves exhibit a linear behavior in cumulative production. In this paper we consider two competing firms that produce fully substitutable products and whose experience levels have a linear effect on their unit production costs. We assume that production experience is affected by random causes, and that the learning process may involve spillovers of experience from the competing firm. As in the Cournot competition, in this differential game the firms compete by choosing the quantities of products that they will produce. In contrast to the Cournot assumption, according to which firms maximize their profits by taking as given the quantity produced by the competitor, we assume that a firm may not be able to determine its competitor’s reaction to a change in its output and instead may conjecture the competitor’s response. We find that, in contrast to the case of a steady state, an open-loop equilibrium over a finite planning horizon may result in greater output (more competitive behavior) compared with a subgame-perfect equilibrium. We show that this result is due to the fact that strategic behavior in feedback Nash equilibrium depends on the relationship between the level of proprietary learning by doing (which encourages strategic complementarity) and the level of spillovers (which involves strategic substitutability).