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

提出了四个方面的基础研究：(1)抽象赌博理论；(2)二人零和随机博弈；(3)战略市场博弈；(4)统计学中的预测推理。前三个领域都涉及个体单独或联合控制随机过程。摘要赌博理论是一人随机控制理论的一种特殊表述，而两人零和随机博弈有两个利益相反的控制者。战略市场博弈通常有许多代理人，用于模拟经济的特征，如价格形成和贷款市场。在第四个领域，预测推理，研究提出了两个标准，这似乎是任何统计预测的自然要求。大多数提议的研究都是关于一个或多个个体在面对一系列连续的选择时应该如何行动，这些选择必须在其后果相当不确定的情况下做出。一个例子是，一个人的收入有多少应该花在当前的消费上，有多少应该为未来储蓄（或投资）。这个问题，如果是针对单个个体的，就符合抽象赌博理论的框架。如果两个人直接竞争资源，这个问题可以看作是一个两人随机博弈。最后，如果问题涉及到一个大型经济体中的所有个人，它可以被视为一个多人的战略市场博弈，在这个博弈中，个人作为一个群体决定或至少影响价格和利率。如果中央银行作为另一个有权设定利率的参与者加入到游戏中，那么问题就出现了，银行应该如何设定利率以使通货膨胀最小化或提高总体福利。这对我们的模型来说可能是一个难题，就像在现实世界中一样。

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.