MULTI-EQUILIBRIUM SOLUTIONS IN GAME-CONTROL PROBLEMS OF TIMING

Abstract: The paper addresses the issue of optimal investments in innovations. As an example, investments in the construction of gas pipelines are considered. Rational decisions in choosing the commercialization times (stopping times) can be associated with Nash equilibria in a game between the projects. In this game, the total benefits gained during the pipelines ’ life periods act as payoffs and commercialization times as strategies. The goal of this paper is to characterize multi-equilibria in the game of timing. The case of two players is studied in detail. A key point in the analysis is the observation that all player’s best response commercialization times concentrate at two instants that are fixed in advance. This reduces decisionmaking to choosing between two fixed investment policies, fast and slow, with the prescribed commercialization times. A description of a computational algorithm that finds all the Nash equilibria composed of fast and slow scenarios concludes the paper. Copyright c © 2005 IFA