Singular Control Games: Strategic Issues in Real Options and Dynamic Oligopoly under Knightian Uncertainty
Mathematics
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.
Publications
- (2018) Fear of the Market or Fear of the Competitor? Ambiguity in a Real Options Game. Operations Research 66 (6) 1744–1759
Hellmann, Tobias; Thijssen, Jacco J. J.
(See online at https://doi.org/10.1287/opre.2018.1762) - Continuous-time Public Good Contribution under Uncertainty: a Stochastic Control Approach, Applied Mathematics and Optimization 75(3) (2017), pp. 429–470
G. Ferrari, F. Riedel, J.H. Steg
(See online at https://doi.org/10.1007/s00245-016-9337-5) - Optimal Boundary Surface for Irreversible Investment with Stochastic Costs, Mathematics of Operations Research 42(4) (2017), pp. 1135–1161
T. De Angelis, S. Federico, G. Ferrari
(See online at https://doi.org/10.1287/moor.2016.0841) - Optimal Entry to an Irreversible Investment Plan with Non Convex Costs, Mathematics and Financial Economics 11(4) (2017), pp. 423–454
T. De Angelis, G. Ferrari, R. Martyr, J. Moriarty
(See online at https://doi.org/10.1007/s11579-017-0187-y) - Subgame-perfect Equilibria in Stochastic Timing Games, Journal of Mathematical Economics 72 (2017), pp. 36–50
F. Riedel, J.-H. Steg
(See online at https://doi.org/10.1016/j.jmateco.2017.06.006) - Nash Equilibria of Threshold Type for Two-player Nonzero-sum Games of Stopping, The Annals of Applied Probability 28(1) (2018), pp. 112–147
T. De Angelis, G. Ferrari, J. Moriarty
(See online at https://doi.org/10.1214/17-AAP1301)
