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Chapter 21: Differential Game-Theoretical Analysis and Industrial Policy
21 Diﬀerential game-theoretical analysis and industrial policy Roberto Cellini and Luca Lambertini 1 Introduction Even if industrial organization (IO) generally deals with dynamic issues, the most widely used theoretical models are in fact static. This holds for the vast majority of the existing models involving strategic interdependence among agents, and taking a game-theoretical approach. At most, they are multi-stage games, in which the dynamics is implicitly summarized by the backward induction process, or they are repeated static games (as is the case for the various folk theorems employed to investigate collusive behaviour or entry deterrence). A proper dynamic approach in presence of strategic interdependence among ﬁrms requires the adoption of diﬀerential game theory tools. Diﬀerential games are a special class of dynamic games: speciﬁcally, they are games in which a set of state variables is introduced, to describe the state of a dynamic system at any particular instant, and its evolution over continuous time.1 In the previous chapter of this Handbook, Lambertini has discussed why diﬀerential games have received relatively scant attention from economics and speciﬁcally from IO so far. In this chapter we show that, once a proper diﬀerential game approach is taken, relevant results may drastically change as compared to the results deriving from a static game approach. More speciﬁcally, we focus on a few particular issues, and discuss how a proper dynamic approach aﬀects the resulting industrial policy prescriptions. We focus on ﬁve speciﬁc problems: (i) the...
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