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In this talk, the lack of a unified decision-theoretic understanding of complex dynamics and uncertainty in game theory is addressed. Combining the theory of decision trees and a Harsanyian notion of exogenous uncertainty, the concept of stochastic decision forests is introduced. Generalising classical theory, a consistent model of a game's "rules" is built: the stochastic extensive form. In this formulation, a well-posed theory based on stochastic processes obtains if and only if the time half-axis is essentially well-ordered. This is insufficient for many applications. Therefore, a relaxed game-theoretic model of "extensive form characteristics" is introduced. The problem of instantaneous reaction and information about it is tackled by introducing vertically extended continuous time, for which a suitable stochastic analysis is developed. This theory admits natural notions of information sets, subgames, and equilibrium, and applies to stochastic differential and timing games, addressing open issues in the literature.

Biography: E. Emanuel Rapsch is a mathematician who successfully defended his doctoral dissertation in Mathematics at Technische Universität Berlin, having previously studied at Oxford, Berlin, Lyon (ENS), and Freiburg, and earned an MSc in Mathematics in Lyon. His research spans game and decision theory, stochastic control theory, financial mathematics, and environmental economics. He is currently a member of the "Stochastik und Finanzmathematik" group at TU Berlin under Prof Peter Bank, and also teaches courses in probability theory, financial mathematics, and analysis.