Jennifer F. Reinganum

The timing of innovation: Research, development, and diffusion

Publisher Summary The analysis of the timing of innovation posits a particular innovation and examines the way the expected benefits, the cost of research and development, and interactions among competing firms combine to determine the pattern of expenditure across firms and over time, the date of introduction, and the identity of the innovating firm. In the case of a sequence of innovations, the expected lifetime of a given innovation and the pattern of technological leadership are also determined endogenously. Given that an innovation has been perfected, the extent and timing of its dissemination into use may be examined. This may depend upon a number of factors, including the existence of rival firms and institutions, which may facilitate or retard the dissemination of innovations. The chapter discusses the issues of innovation production in the context of symmetric noncooperative models. The chapter investigates the extent of dissemination of the innovation, where this dissemination is achieved through licensing.

On the diffusion of new technology: A game theoretic approach

This paper is an attempt at a rigorous (albeit not exceedingly general) analysis of the diffusion of new technology. In particular, consider an industry composed of two firms, each using the current best-practice technology. The firms are assumed to be operating at Nash equilibrium output levels, generating a market price (given demand) and profit allocations. When a cost-reducing innovation is announced, each firm must determine when (if ever) to adopt it, based in part upon the discounted cost of implementing the new technology, and in part upon the behavior of the rival firm. If either firm adopts before the other, it can expect to make substantial profits at the expense of the other firm. On the other hand, the discounted sum of purchase price and adjustment costs may decline with the lengthening of the adjustment period as various quasi-fixed factors become more easily variable. Therefore, although waiting costs the firm more in terms of foregone profits, it may save money on the cost of purchasing the new technology. Thus the firm must weigh the costs and benefits of delaying adoption, as well as take account of its rivals strategic behavior.

Settlement, Litigation, and the Allocation of Litigation Costs

This article examines a model of settlement and litigation in which the plaintiff makes a settlement demand based upon his true level of damages; the defendant infers the plaintiffs true damage level and decides whether to go to trial. When both parties share common beliefs about the likelihood of judgment in favor of the plaintiff (but not necessarily about the expected award) and when the plaintiff retains the entire settlement, then the system for allocating litigation costs does not affect the equilibrium probability of trial. If either of these two assumptions is violated, then the litigation cost allocation system becomes an important determinant of the equilibrium probability of trial.

Imperfect Competition and Quality Signaling

We examine the interplay of imperfect competition and incomplete information in the context of price competition among firms producing horizontally and vertically differentiated substitute products. Incomplete information about vertical quality (consumer satisfaction) signalled via price softens price competition. Low-quality firms always prefer the incomplete information game to the full-information analog. Moreover, for high-value markets with a sufficiently high proportion of high-quality firms, these firms also prefer incomplete information to full information. We find that an increase in the loss to consumers associated with the low-quality product may perversely benefit low-quality firms; we consider applications to tort reform and professional licensing. Copyright (c)2008, RAND.

Technology adoption under imperfect information

This article presents a static game theoretic model of a firms decision to adopt a technological innovation of uncertain profitability. Given the levels of adoption costs, discount rates, and expectations regarding the profitability of the innovation, we determine the (Nash equilibrium) range of initial production costs for which each firm prefers to adopt the innovation. We show that if initial costs are sufficiently dissimilar, then it is the high-cost firm which adopts the new technology, while the low-cost firm eschews adoption. An increase in a firms adoption cost (or equivalently, a decrease in the firms discount rate) makes that firm no more likely to adopt the new technology, while the rival firm may be more or less likely to adopt, depending upon the initial values of the parameters.

A Class of Differential Games Where the Closed-Loop and Open-Loop Nash Equilibria Coincide

It is well known that, in general, Nash equilibria in open-loop strategies do not coincide with those in closed-loop strategies. This note identifies a class of differential games in which the Nash equilibrium in closed-loop strategies is degenerate, in the sense that it depends on time only. Consequently, the closed-loop equilibrium is also an equilibrium in open-loop strategies.

A two-stage model of research and development with endogenous second-mover advantages

This paper describes a simple two-stage model of research and development, in which the ‘winner’ of the research stage has the option of moving first in the development stage. Some unexpected results emerge: in equilibrium, the leader in the development stage invests less than each follower, and is consequently least likely to collect the patent. Moreover, the leader receives a lower expected payoff than each of the followers. Thus there are endogenous second-mover advantages. Using a game of timing (in which the identity of the Stackelberg leader is determined) to link the two stages, I find that firms face quite different incentives in the research stage. Although the leader invests less than each follower in the research stage as well, the leader enjoys higher expected revenue from the complete (two-stage) game than does each follower. The equilibrium is inefficient because there is a lag between the time at which research is completed and the time at which development is begun, and because aggregate investment is inefficiently (asymmetrically) distributed across firms.

Communicating Quality: A Unified Model of Disclosure and Signaling

Firms communicate product quality attributes to consumers through a variety of channels, such as pricing, advertising, releases of research reports and test results, or warranties and returns policies. The conceptualization of the economics of such communication is that it takes on one of two alternative forms when quality is exogenous: 1) disclosure of quality through a credible direct claim; 2) signaling of quality via producer actions that influence buyersO beliefs about quality. In general, these two literatures have ignored one-another. In this paper we argue that disclosure and signaling are two sides of a coin and that firms should be viewed as choosing which means of communication they will employ. Moreover, we show that integration of these two alternatives leads to a number of new implications about disclosure, signaling, firm preferences over type, and the social efficiency of the channel of communication employed.

Settlement negotiations with two-sided asymmetric information: Model duality, information distribution, and efficiency

We analyze a settlement and litigation game in which both parties possess private information relevant to the value of a claim. The plaintiff knows the level of damages, while the defendant knows the probability he will be held liable for those damages. We consider two alternatives: (1) the plaintiff proposes a settlement, which the defendant accepts or rejects; and (2) the defendant proposes a settlement, which the plaintiff accepts or rejects. Despite the extensive symmetry of the model, these alternatives will generally result in different equilibrium expected frequencies of trial, and therefore different social efficiencies.

Strategic Search Theory

This paper combines the “theory of search”—the application of optimal stopping rules to decision-making under uncertainty—with concepts from the theory of games in order to analyze new product development. A development trial is envisioned as a random drawing of a production cost level, and a strategy is a rule describing conditions under which no further development is desired—a stopping rule. Nash equilibrium in stopping rules is shown to exist and possess the reservation property. The possibility of multiple equilibria implies that the usual comparative statics results need not hold in equilibrium—e.g., an increase in firm is development costs may result in an increase in the firms development activity.