# Game Theory

(Non-cooperative) Game Theory studies strategic conflicts. As such, it can model many fundamental situations of economic life, and beyond. Well-known examples of such situations include auctions, elections, bargaining, sports competitions, competition between firms, lobbying, political debate, and even international conflict. Almost all members of the Center for Mathematical Economics work on game theory in one form or another. More specifically our main interests lie in the following subfields of game theory. |

## Ambiguity in Games

Strategic decisions of firms often have to be made under uncertainty and moreover imply long-ranging consequences, for example if they are hardly reversible due to physical or legal frictions. In this project we address these aspects with new methods. On the one hand we apply the most recent findings concerning model uncertainty ("Knightian Ambiguity") to such decisions. On the other hand we develop a theory of dynamic oligopoly games with irreversible capacity choices in continuous time. For such games, there exists no satisfying game theory, since a mathematically consistent game theoretic equilibrium concept (which allows for feedback) has not been successfully established so far. We use a new method for solving singular control problems, which has been (co-)developed by the principle investigator, to establish such a game theory. We will analyse in particular oligopoly games under Knightian uncertainty. For instance, we want to clarify the question whether the value of the option to wait disappears already with two firms. A first paper on the topic appears in Theory and Decision (Frank Riedel and Linda Sass). This research is jointly funded by the DFG and ANR.## Differential Games

Many economic problems are characterized by the interplay of strategic interaction and intertemporal effects of actions. Differential games are a very suitable tool to analyze behavior in such situations, and have been heavily used in areas like Industrial Organization and Resource Economics. Our research focuses on investment behavior of firms in dynamic oligopolies with product innovation. In particular we study how oligopolists in established markets should react to the anticipated and actual extension of the relevant product range due to product innovation, and how the effort to develop new products is affected by the position of a firm on the established market (see also the DFG project 'Dynamic Oligopolistic Competition between Innovating Firms').## Evolutionary Game Theory

(Games and Economic Behavior 2009)Does learning / evolution lead to behavior in the long-run that resembles that of highly rational players? Examples of work on this topic include Kuzmics (2004, Games and Economic Behavior); Kuzmics, (2011, Games and Economic Behavior); Balkenborg, Hofbauer, and Kuzmics (2013, Theoretical Economics).

If nature could freely choose individuals? preferences, what preferences would she choose? Examples of work on this topic includes Herold and Kuzmics (2009, Games and Economic Behavior).