Mathematical Sciences: Abstract Gambling Theory, Stochastic Games, and Statistical Inference

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9423009: Sudderth Abstract. Research is planned in abstract gambling theory (a particular formulation of stochastic control), stochastic games, and the foundations of Bayesian statistics. Part of the research aims for a better understanding of a new algorithm which can be used to calculate the optimal reward function in gambling theory and also to calculate the value function for a large class of two-person, zero-sum stochastic games. Research is also planned on a class of many-person, noncooperative games that can be used to study questions in the theory of money and financial institutions. Finally, research is planned on certain problems in the foundations of statistical inference. Research is planned on fundamental questions about how to make optimal decisions through time in the presence of uncertainty. Abstract gambling theory treats problems in which a single decision maker seeks to control a process so as to reach a desired objective. In stochastic games, two or more decision act to control a process and may have opposing interests. The mathematical theory of such problems is quite technical, but solutions are of interest in many areas including business, economics and operations research.