# Backward Induction and Common Knowledge of Rationality ..

The end result is that the expectations of firms (or, moregenerally, the subjective probability distribution of outcomes) tend to bedistributed, for some information set, about the prediction of the theory (orthe objective probability distribution of outcomes).To see how the hypothesis works imagine an economic variable, Y, whose value isdetermined by its own lagged value, by the lagged value of two other variables,X and Z, and by a random variable U.

## Common Knowledge of Rationality in Extensive Games …

### the strength of the common knowledge hypothesis.

To show that this hypothesis is rational I willoutline the theory itself and then I will show how it can withstand boththeoretical and empirical criticisms.

### strict re nement of common knowledge of rationality in terms ..

The basic grammatical unit recognized at this time was the morpheme, though many linguists did not use the term itself. Language was thought to be (among other things perhaps) a repertory of morphemes. A sentence consisted of a sequence of morphemes. Intermediate between the morpheme and the sentence, however, was the word. A word, like a sentence, was a sequence of one or more morphemes, but the processes by which morphemes combined to form words were different from those by which sentences were formed. Within the word at least two types of morphemes could be distinguished, often called roots and affixes. In an English word such as , for example, was regarded as the root, and the remaining two parts, - and -, were affixes.

### and so more desirable in a hypothesis.

Data and Decisions teaches you how to use data and quantitative reasoning to make sound decisions in complex and uncertain environments. The course draws on probability, statistics, and decision theory. Probabilities provide a foundation for understanding uncertainties, such as the risks faced by investors, insurers, and capacity planners. We will discuss the mechanics of probability (manipulating some probabilities to get others) and how to use probabilities to make decisions about uncertain events. Statistics allows managers to use small amounts of information to answer big questions. For example, statistics can help predict whether a new product will succeed or what revenue will be next quarter. The third topic, decision analysis, uses probability and statistics to plan actions, such as whether to test a new drug, buy an option, or explore for oil. In addition to improving your quantitative reasoning skills, this class seeks to prepare you for later classes that draw on this material, including finance, economics, marketing, and operations. At the end we will discuss how this material relates to machine learning and artificial intelligence.