Uncertainty, Competition, and the Adoption of New Technology

Faced with the decision of whether or not to adopt a new technology whose economic value cannot be gauged with certainty, the manager of the firm may elect to decrease the uncertainty by sequentially gathering information (at a unit cost of c > 0), updating his prior beliefs in a Bayesian manner. Uncertainty regarding the actions of a competitor, however, cannot be reduced. Our model allows a manager to account for potential competition, either substitute or complementary, by inclusion of strategic considerations modelled in a game theoretic setting. We show that the firm's best response mapping satisfies a dynamic programming recursion (even when the one period reward function is unbounded) providing management with a familiar tool to solve its problem. Best response behavior is characterized by a monotone sequence of pairs of threshold numbers which give rise to a "cone-shaped" continuation region. The continuation region is shown to shift up (down) with increases in the expected level of substitute (complementary) competition making the firm less (more) likely to adopt the innovation. Finally, the existence of a Nash equilibrium in cone-shaped strategies is established.innovation, competition, game theory, search

A Bayesian Approach to Managing Learning-Curve Uncertainty

This paper introduces a Bayesian decision theoretic model of optimal production in the presence of learning-curve uncertainty. The well-known learning-curve model is extended to allow for random variation in the learning process with uncertainty regarding some parameter of the variation. A production run generates excess value (above its current revenue) for a Bayesian manager in two ways: it pushes the firm further along the learning curve, increasing the likelihood of lower costs for future runs; and it provides information, through the observed costs, that reduces the uncertainty regarding the rate at which costs are decreasing. We provide conditions under which one of the classical deterministic learning-curve results---namely, that optimal production exceeds the myopic level---carries over to the extended framework. We demonstrate that another classical deterministic learning-curve result---namely, that optimal production increases with cumulative production---does not hold in the Bayesian setting.learning curve, stochastic learning, Bayesian analysis, dynamic programming model