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 rival's strategic behavior.

The theoretical literature on innovation has been concerned with a single innovation produced by a number of identical agents. By contrast, we consider a market in which one firm is the current incumbent, while the remaining firms are challengers. Moreover, we consider a sequence of innovations, so that success does not imply that the successful firm reaps monopoly profits forever after, but only until the next, better innovation is developed. We begin with a fully optimizing behavioral model and derive the equivalent of the Schumpeterian “process of creative destruction.” That is, a firm enjoys temporary monopoly power but is soon overthrown by a more inventive challenger. The essential point to grasp is that in dealing with capitalism we are dealing with an evolutionary process…The fundamental impulse that sets and keeps the capitalist engine in motion comes from the new consumers' goods, the new methods of production or transportation, the new markets, the new forms of industrial organization that capitalist enterprise creates [Schumpeter, 1942, pp. 82–83].

A theory of dynamic optimal resource allocation to R and D in an n-firm industry is developed using differential games. This technique represents a synthesis of the analytic methods previously applied to the problem: static game theory and optimal control. The use of particular functional forms allows the computation and detailed discussion of the Nash equilibrium in investment rules.

[A model of plea bargaining with asymmetric information is presented. The prosecutor's private information is the strength of the case; the defendant's is is his guilt or innocence. In equilibrium, some cases are dismissed because they are too likely to involve an innocent defendant. In the remaining cases, the prosecutor's sentence offer reveals the strength of the case. A particular restriction on prosecutorial discretion is shown to be welfare-enhancing for some parameter configurations.]

[This paper demonstrates that price dispersion can exist even within the context of a very simple model. Identical buyers with elastic demand curves sample sequentially from a known price distribution, at a fixed cost per observation. Firms are assumed to be perfectly informed of buyers' reservation prices and demand functions. Given the firms' distribution of marginal costs, firms' behavior as monopolistic competitors results in their offering a distribution of prices which is consistent with expected utility maximization by buyers and with expected profit maximization by sellers.]

This paper demonstrates that price dispersion can exist even within the context of a very simple model. Identical buyers with elastic demand curves sample sequentially from a known price distribution, at a fixed cost per observation. Firms are assumed to be perfectly informed of buyers' reservation prices and demand functions. Given the firms' distribution of marginal costs, firms' behavior as monopolistic competitors results in their offering a distribution of prices which is consistent with expected utility maximization by buyers and with expected profit maximization by sellers.

Jennifer F. Reinganum, Louis L. Wilde; A Note on Enforcement Uncertainty and Taxpayer Compliance*, The Quarterly Journal of Economics, Volume 103, Issue 4,