Elena Parilina - Theory and Applications of Dynamic Games: A Course on Noncooperative and Cooperative Games Played over Event Trees (Theory and Decision Library C, 51)

Dynamic games theory provides paradigms to analyze repeated strategic interactions in both discrete time (multistage games) and continuous time (differential games). The uncertainty in the parameter values, which is fully expected in any intertemporal problem, can be modeled by various stochastic processes, with each having its pros and cons. For multistage games, we believe that an event tree is a natural approach to representing this uncertainty for two main reasons. First, it mimics how decision makers deal with uncertain parameter values. Indeed, they most likely consider only a few anchor points, e.g., that the next periods inflation rate could be low, medium, or high. Similarly, if the price of oil influences certain choices to be made, e.g., to invest or not in a thermal power plant, the decision maker will consider sufficiently distinct prices, and rarely a continuum of values. Second, event trees lead to computable and implementable models, and are easily prone to sensitivity analyses, which helps in assessing the robustness of the results with respect to the parameter values.

This book deals with multistage games with uncertain parameters where the stochastic process is described by an event tree. We refer to this class of games as dynamic games played over event trees (DGPETs).

An example: For a brief sample of a DGPET model, consider a region served by a few electricity producers (players) who compete or cooperate over time in one or more market segments, e.g., residential, commercial, and industrial markets. In a long-term model, each firm must plan its energy production schedule and investments in different production technologies (solar, thermal, hydro, etc.), while facing some uncertainties in demand or supply, or both. For instance, future demands depend on the not perfectly predictable state of the economy, and the cost of operating a thermal power plant varies greatly with the uncertain price of fuel. In the parlance of dynamic games, the quantities committed by a firm to each market segment and the investments in the different technologies at each period are the players control variables. The installed mix of production capacities and (if relevant) the capacity of interconnections to export markets are the state variables.