Iterative Processes of Decision Making: A Bayesian Game Theoretic Framework

对我们大多数人来说，知道一些总比什么都不知道好，做出明智的决定总比不知情的决定好。斯基姆斯教授正在研究的问题是，在考虑决策的过程中，如何最好地做出决策，从而产生新的信息，使我们能够做出更明智的决策。在这个动态的审议过程中，决策者开始时根本不确定什么是最佳行动方案；但是，通过从审议过程中反馈信息，采取各种行动的可能性会不断发展，直到最终决定变得清晰。这样的研究侧重于决策理论和博弈论中的问题，但它们对政策科学中的问题也有重要影响——例如，在关于军备竞赛中最佳行动方案的辩论中。此外，这些结果对科学推理理论具有重要意义，即科学如何从特定的实例或事件发展到准确描述我们周围世界的可概括的理论。Skryms教授专门研究了审议动力学和贝叶斯博弈论之间的关系。审议动力学显示了博弈论的主要解决方案概念，即纳什均衡，是如何建立在个人理性决策理论的预期效用原则之上的。期望效用激发动态协商，纳什均衡对应于在共同知识的理想条件下博弈参与者联合协商动态的固定点。Skyrms教授将研究审议动力学中不动点的稳定性，并利用这一框架来阐明当前关于纳什均衡概念在正常形式和广泛形式博弈中的改进讨论。他还将研究削弱前面所要求的关于优柔寡断的初始状态和所有游戏参与者都是贝叶斯审议者这一事实的强大常识假设的结果。他将表明，这些假设的最小削弱可能会对游戏的可能理性解决方案产生巨大影响，这对模拟现实生活中的决策很重要。

It is a basic tenant for most of us that it is better to know something rather than nothing and to make informed decisions rather than uninformed ones. Professor Skyrms is examining the problem of how best to make decisions in a situation where the very process of deliberating about the decision generates new information which will allow us to make more informed decisions. In this dynamic deliberational process, decision makers start in a state where they are not at all certain what the best course of action should be; but by feeding back information from the deliberational process, the probabilities of doing various acts evolve until the final decision becomes clear. Such a study is focussed on questions in decision theory and game theory, but they have an important bearing upon issues in the policy sciences--for example, in debates about the best course of action in the arms race. Further, these results have important implications for the theory of scientific inference, that is on how science moves from particular instances or events to a generalizable theory which accurately describes the world about us. Professor Skryms is specifically examining the relationships of deliberational dynamics and Bayesian Game theory. Deliberational dynamics shows how the dominant solution concept of Game Theory, that of a Nash equilibrium, can be grounded on the expected utility principle of the theory of individual rational decision. Expected utility motivates dynamic deliberation, and a Nash equilibrium corresponds to a fixed point of the joint deliberational dynamics of the players of the game in question under ideal conditions of common knowledge. Professor Skyrms will investigate the stability of fixed points in the deliberational dynamics, and use this framework to throw light on the current discussions of refinements of the Nash equilibrium concept in both normal form and extensive form games. He will also investigate the results of weakening the strong common knowledge assumptions required in the foregoing with regard to both the initial state of indecision and the fact that all players of the game are Bayesian deliberators. He will show that minimal weakening of these assumptions can have dramatic effects on the possible rational solutions for games that are important in modeling real life decisions.