Nash Equilibrium Search for the Best Alternative

In a recent paper, Weitzman (1979) described a policy of “optimal search for the best alternative.“ The present paper is concerned with the development and characterization of a policy of “Nash equilibrium search for the best alternative.“ Specifically, it is shown that, under certain monotonicity assumptions, and under the assumption that firms have incomplete information regarding the results of rivals' search behavior, a Nash equilibrium search policy exists and has the same form as Weitzman's optimal search policy

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 i's development costs may result in an increase in the firm's development activity

Uncertain innovation and the persistence of monopoly: A reply

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Plea bargaining and prosecutorial discretion

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 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

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 (t) only. Consequently, the closed-loop equilibrium is also an equilibrium in open-loop strategies

Patent Races with a Sequence of Innovations

The theoretical literature on patent races has been an interesting and fast-evolving one, moving from largely heuristic discussion to quite rigorous analysis within the space of the past two decades. This literature has been characterized by a pattern of interesting results which are subsequently reversed under alternative behavioral and/or structural assumptions. This sensitivity of key results to mutually exclusive but perhaps equally plausible modeling assumptions has kept conclusions and policy recommendations in a constant state of revision. All of these papers have been concerned with a single innovation produced by a number of identical agents. This paper generalizes this literature in two important ways. First, we consider a market in which one firm is the current patent-holder the incumbent, while the remaining firms are non-incumbents; firms are entirely symmetric in every other sense. Second, 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

A Note on Rational Threats and Competitive Equilibrium

Many economic problems can be modeled as n-person non-zero sum games. In such situations, there are gains to be had by coordination of strategies. Assuming there are no restrictions on side-payments, the players then bargain over the division of the gains. This note establishes that, for a restricted class of economic problems, the threat equilibrium in the bargaining game coincides with the perfectly competitive equilibrium

A dynamic game of R and D: Patent protection and competitive behavior

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