Topics in Abstract Gambling Theory, Stochastic Games, and Predictive Inference

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9703285 Sudderth Basic research is proposed in four areas:(1)abstract gambling theory, (2)two- person, zero-sum stochastic games, (3)strategic market games, and (4)predictive inference in statistics. The first three areas all involve agents controlling stochastic processes either alone or jointly. Abstract gambling theory is a particular formulation of one-person stochastic control theory, whereas two-person, zero-sum stochastic games have two controllers with opposing interests. Strategic market games typically have many agents and are used to model features of an economy such as price formation and loan markets. In the fourth area, predictive inference, research is proposed on two criteria that seem natural to require of any statistical prediction. Most of the proposed research is on questions of how one or more individuals should act when faced by a series of successive choices that must be made with considerable uncertainty about their consequences. An example is the problem of how much of one's income should be spent on current consumption and how much should be saved (or invested) for the future. This problem, when formulated for a single individual, fits into the framework of abstract gambling theory. If two individuals are in direct competition for resources, the problem can be viewed as a two-person stochastic game. Finally, if the problem involves all the individuals in a large economy, it can be viewed as a many-person, strategic market game in which the individuals as a group determine, or at least influence, prices and interest rates. If a central bank is added to the game as another player that has the power to set interest rates, the question arises as to how the bank should set interest rates so as to minimize inflation or improve the general welfare. This is likely to be a difficult problem for our models just as it is in the real world.