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

Dropout Behavior in R&D Races with Learning

We examine a game-theoretic model of a two-firm R&D race in which expenditures on R&D and the concomitant increase in experience/learning enable the firms to increase their probability of discovering an invention. The learning process is stochastic. It generates a unique subgame-perfect equilibrium for identical firms with the characteristic that the leader never drops out, but the follower drops out if the leader gains a significant lead. The leader can find it optimal to drop out if the firms value the invention differently or have different R&D efficiencies. Thus, our analysis generates results between vigorous competition and natural monopoly.

Repeated Gambles, Learning, and Risk Aversion

We analyze a decision problem with repeated gambles and find that under some seemingly reasonable risk-averse utility functions, recommended behavior for the initial decision can be highly risk-taking and counterintuitive. Further analysis reveals that the derived utility function for the return on the first gamble is discontinuous because gains or losses carry with them positive or negative signals regarding future prospects. A variant of the basic model without a discontinuity in derived utility has essentially the same implications. The issues raised in this paper present no conceptual difficulties for the standard expected utility theory; in principle, we can model the grand world and understand fully all implications of grand-world utility functions. In practice, however, this ideal may not always be attainable and as a result we may be faced with serious modeling and assessment problems.decision analysis, sequential: learning and risk taking, philosophy of modeling: small world and grand world, utility/preference, theory: derived utility