Subgame-Perfect Equilibria in Stochastic Timing Games

28 Pages Posted: 19 Sep 2014 Last revised: 8 Nov 2014

See all articles by Frank Riedel

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Jan-Henrik Steg

Bielefeld University - Center for Mathematical Economics

Date Written: September 16, 2014

Abstract

We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies - in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications.

Keywords: timing games, stochastic games, mixed strategies, subgame-perfect equilibrium in continuous time, optimal stopping

JEL Classification: C61, C73, D21, L12

Suggested Citation

Riedel, Frank and Steg, Jan-Henrik, Subgame-Perfect Equilibria in Stochastic Timing Games (September 16, 2014). Institute of Mathematical Economics Working Paper No. 524, Available at SSRN: https://ssrn.com/abstract=2497602 or http://dx.doi.org/10.2139/ssrn.2497602

Frank Riedel (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Jan-Henrik Steg

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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