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Singular Control Games: Strategic Issues in Real Options and Dynamic Oligopoly under Knightian Uncertainty

Subject Area Economic Theory
Mathematics
Term from 2011 to 2018
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 199871851
 
Final Report Year 2018

Final Report Abstract

Decisions of firms often have to be made under uncertainty and in competitive environments, with long-ranging consequences, for example if they are hardly reversible due to physical or legal frictions. Irreversible investment problems occur in real life when the cost of an investment decision cannot be recovered by liquidating the investment. In most cases physical investment is irreversible since it is industry-specific and, hence, very little can be recovered by selling it off. The project has substantially improved our understanding of oligopolistic markets in continuous time. At the more foundational level, we have developed a theory of subgames and subgame perfect equilibria for stochastic timing games in continuous time. These results were used to study various particular market structures. As a further preparation for our applications to games, we have obtained new results for individual optimal entry and investment decisions when entry or investment cost are irreversible. An important contribution of our project characterizes Nash equilibria in non–zero sum games of optimal stopping. Our methods allow to develop public good games in continuous time. A new method has been developed to characterize the equilibria of such games. We are able to give sufficient conditions for uniqueness. We also quantify the usual free-rider effect in such settings. We also explore the issue of Knightian uncertainty in continuous-time real option games. It is shown that Knightian uncertainty can have substantially different effects than mere risks in such markets.

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