Observation,Measurement, and Computation in Finite Games

Limitations in agents ability to observe, measure and compute are studied. A formulation in terms of induced changes in the players subjective perception of the game makes it possible to study these phenomena on a common footing with objective variation in the game. We study a model where payoffs undergo continuous variation and players reason about the process from limited local information. Specifically, finite games, and statements about them, are interpreted within sheaf models, which incorporate both variation and a logic of limited observation. Nashs theorem on the existence of equilibrium is not valid unless special observational properties hold, although closely related statements are valid. The possibility of learning to play a mixed strategy Nash equilibrium from observation of past play is also examined within the framework.I thank the referee and associate editor for their comments and suggestions. I also received very helpful suggestions from Josh Epstein. All remaining errors are my own.Received: April 2000 / Revised: December 2003     

中国经济市场化与集约化进程现状及关联分析

本文通过对给各地市场化、集约化的测定及关联分析 ,为各地决策部门提供可靠的参考     

Students' Accuracy of Measurement Estimation: Context,Units, and Logical Thinking

This study examined students' accuracy of measurement estimation for linear distances, different units of measure, task context, and the relationship between accuracy estimation and logical thinking. Middle school students completed a series of tasks that included estimating the length of various objects in different contexts and completed a test of logical thinking ability. Results found that the students were not able to give accurate estimations for the lengths of familiar objects. Students were also less accurate in estimating in metric units as compared to English or novel units. Estimation accuracy was dependent on the task context. There were significant differences in estimation accuracy for two‐ versus three‐dimensional estimation tasks. There were no significant differences for estimating objects with different orientations or embedded objects. For the tasks requiring the students to estimate in English units, the embedded task and the three‐dimensional tasks were correlated with logical thinking. For estimation tasks with novel units, three‐dimensional and two‐dimensional estimation tasks were significantly correlated with the logical thinking. In order to interact effectively with our environment it is essential to possess an intuitive grasp of both dimension and scale and to be able to manipulate such information. Estimation, approximating and measuring are all components of such intuition ( Forrester, Latham, & Shire, 1990 , p. 283).     

熵—证券投资组合风险的一种新的度量方法

本文在研究马科维茨 ( Markowitz)证券投资组合模型的基础上 ,分析了该模型用方差度量风险的缺陷 ,进而提出用熵作为风险的度量方法 ,改进马科维茨 ( Markowitz)证券投资组合模型 ,并建立新的证券投资组合优化模型     

The Measurement of Time: Children's Construction of Transitivity,Unit Iteration,and Conservation of Speed

One hundred twenty children in kindergarten and grades 2, 4, and 6 were individually interviewed with five Piagetian tasks to determine the grade level at which most have constructed transitive reasoning, unit iteration, and the conservation of speed. The responses were categorized as “successful,”“unsuccessful,” or “transitional.” By combining the “successful” and “transitional” categories, it was found that the children reasoned transitively by second grade (70.0%) and demonstrated unit iteration and conservation of speed by sixth grade (70.0% and 83.3%, respectively). It was concluded that the construction of the logic necessary to make sense of the measurement of time is generally not complete before sixth grade.