Changing market structures in intertemporal optimization

Optimal control (unilateral decision maker) and differential game theory (several decision makers) are established tools to analyze dynamic processes in economics and related fields. Both theories rely on the assumption that the model framework (i.e. number of players, form of collaboration between the players, etc.) does not change over time. However, many real phenomena demonstrate the opposite, e.g. 1. Monopolistic market changes to competition (and vice versa) 2. Entry/exit of competitors to/from the market 3. Begin/end of a collaboration of players. While such behaviour is extensively studied in static and two period models (see Tirole 1988 for an overview), this has not been done in continuous time. We plan to work on a systematic analysis of models of this type. For that reason we have to link an optimal control model and a differential game (example a), two differential games with a different number of players (example b) and a non-cooperative differential game with a differential game with cooperating players (example c). The models will be analyzed with various assumptions concerning the switching time (exogenous, endogenous, stochastic), the commitment structure (open-loop and feedback) and the initial states (e.g. different initial capital stocks of new market entrants). Since linking models in the above proposed way has not been done so far (except very few examples), we have to deal with new mathematical challenges. With the analysis of such models it is possible to learn the optimal behaviour before the change in the market structure. Comparing the results to the situation without switch, provides important economic insights that go beyond the knowledge from static and two-period models. It is possible to deal with questions like, weather it is optimal to increase (decrease) the capital stock before competition gets tougher (weaker)? How should a firm influence the competitors decisions already before the switching time? Should a firm influence the switching time or is this too costly?

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