Strategic Randomization in Markovian Stopping Games

• Applicant: Professor Dr. Sören Christensen, since 10/2025
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 553381018

In this project, a new theory for dealing with Markovian stopping games is developed. This class of problems lies at the intersection of game theory and stochastic control theory, and the underlying question can be formulated as follows: In a competitive situation, how should players stop a stochastic process such that the expected payoff is maximized? The problem is structured in such a way that the payoff depends not only on the player's own decision, but also on the stopping decisions of the other players, so that it is a problem of dynamic game theory. Stopping games form one of the fundamental classes of dynamic games with a variety of applications, e.g., in market entry problems, in contests, and in time-inconsistent problems. Nevertheless, some fundamental questions remain to be answered. While for classical problems of optimal stopping the theory is so far developed that there are standard methods for solving concrete problems, this is not the case for stopping games. There are rather general existence theorems for equilibria in randomized stopping times. However, the size of this class makes it difficult to find explicit equilibria, and the path dependence of general randomized stopping times implies that subgame perfection cannot be guaranteed for such equilibria. As a result even for very specific stopping games, often only a case-by-case treatment is possible due to a lack of sufficient theoretical foundation. This is especially true in situations where the players have to perform strategic randomization. The main goal of this project is to provide a framework that enables the fruitful analysis of subgame perfect equilibria of general Markovian stopping games in both discrete and continuous time. A key feature of the project will be the division of the work programme into games in discrete and continuous time. The main rational behind this division is that ideas in discrete time are often easier to develop, but for many applications models in continuous time are of primary importance. The framework should achieve the following goals: - The framework should allow to treat as many classical and novel examples as possible. - The framework should be flexible enough to guarantee the existence of equilibria for general classes of games. - The framework should be manageable enough to be able to concretely solve problems. The solution can be explicit or numerical, depending on the problem, but should go beyond a mere abstract characterization. In particular, the resulting stopping times should be described by an object that is as simple and interpretable as possible.

• DFG Programme: Research Grants
• Ehemalige Antragstellerin: Dr. Berenice Anne Neumann, until 10/2025