1 Inductive Reasoning and Bounded Rationality (The El Farol Problem) by W. Brian Arthur Stanford University and Santa Fe Institute Published in Amer. Econ. Review (Papers and Proceedings), 84, 406, Given at the American Economic Association Annual Meetings, 1994 Session: Complexity in Economic Theory, chaired by Paul Krugman. Citibank Professor, Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM
3 Inductive Reasoning and Bounded Rationality By W. BRIAN ARTHUR * The type of rationality we assume in economics perfect, logical, deductive rationality is extremely useful in generating solutions to theoretical problems. But it demands much of human behavior much more in fact than it can usually deliver. If we were to imagine the vast collection of decision problems economic agents might conceivably deal with as a sea or an ocean, with the easier problems on top and more complicated ones at increasing depth, then deductive rationality would describe human behavior accurately only within a few feet of the surface. For example, the game Tic-Tac-Toe is simple, and we can readily find a perfectly rational, minimax solution to it. But we do not find rational solutions at the depth of Checkers; and certainly not at the still modest depths of Chess and Go. There are two reasons for perfect or deductive rationality to break down under complication. The obvious one is that beyond a certain complicatedness, our logical apparatus ceases to cope our rationality is bounded. The other is that in interactive situations of complication, agents can not rely upon the other agents they are dealing with to behave under perfect rationality, and so they are forced to guess their behavior. This lands them in a world of subjective beliefs, and subjective beliefs about subjective beliefs. Objective, well-defined, shared assumptions then cease to apply. In turn, rational, deductive reasoning deriving a conclusion by perfect logical processes from well-defined premises itself cannot apply. The problem becomes ill-defined. As economists, of course, we are well aware of this. The question is not whether perfect rationality works, but rather what to put in its place. How do we model bounded rationality in economics? Many ideas have been suggested in the small but growing literature on bounded rationality; but there is not yet much convergence among them. In the behavioral sciences this is not the case. Modern psychologists are in reasonable agreement that in situations that are complicated or ill-defined, humans use characteristic and predictable methods of reasoning.
4 2 These methods are not deductive, but inductive. In this paper I will argue that as economists we need to pay great attention to inductive reasoning; that it makes excellent sense as an intellectual process; and that it is not hard to model. In the main part of this paper, I will present a decision problem the bar problem in which inductive reasoning is assumed and modeled, and its implications are examined. The system that emerges under inductive reasoning will have connections both with evolution and complexity. I. Thinking Inductively How do humans reason in situations that are complicated or ill-defined? Modern psychology tells us that as humans we are only moderately good at deductive logic, and we make only moderate use of it. But we are superb at seeing or recognizing or matching patterns behaviors that confer obvious evolutionary benefits. In problems of complication then, we look for patterns; and we simplify the problem by using these to construct temporary internal models or hypotheses or schemata to work with. 1 We carry out localized deductions based on our current hypotheses and act on them. And, as feedback from the environment comes in, we may strengthen or weaken our beliefs in our current hypotheses, discarding some when they cease to perform, and replacing them as needed with new ones. In other words, where we cannot fully reason or lack full definition of the problem, we use simple models to fill the gaps in our understanding. Such behavior is inductive. We can see inductive behavior at work in Chess playing. Players typically study the current configuration of the board, and recall their opponent s play in past games, to discern patterns (De Groot, 1965). They use these to form hypotheses or internal models about each others' intended strategies, maybe even holding several in their minds at one time: He s using a Caro-Kann defense. This looks a bit like the 1936 Botvinnik-Vidmar game. He is trying to build up his mid-board pawn formation. They make local deductions based on these analyzing the possible implications of moves several moves deep. And as play unfolds they hold onto hypotheses or mental models that prove plausible, or toss them aside if not, generating new ones to put in their
5 3 place. In other words, they use a sequence of pattern recognition, hypothesis formation, deduction using currently-held hypotheses, and replacement of hypotheses as needed. This type of behavior may not be familiar in economics. But we can recognize its advantages. It enables us to deal with complication: we construct plausible, simpler models that we can cope with. It enables us to deal with ill-definedness: where we have insufficient definition, our working models fill the gap. It is not antithetical to reason, or to science for that matter. In fact, it is the way science itself operates and progresses. Modeling Induction. If humans indeed reason in this way, how can we model this? In a typical problem that plays out over time, we might set up a collection of agents, probably heterogeneous, and assume they can form mental models, or hypotheses, or subjective beliefs. These beliefs might come in the form of simple mathematical expressions that can be used to describe or predict some variable or action; or of complicated expectational models of the type common in economics; or of statistical hypotheses; or of condition/prediction rules ( If situation Q is observed/predict outcome or action D ). These will normally be subjective, that is, they will differ among the agents. An agent may hold one in mind at a time, or several simultaneously. Each agent will normally keep track of the performance of a private collection of such belief-models. When it comes time to make choices, he acts upon his currently most credible (or possibly most profitable) one. The others he keeps at the back of his mind, so to speak. Alternatively, he may act upon a combination of several. (However, humans tend to hold in mind many hypotheses and act on the most plausible one (Feldman, 1962).) Once actions are taken the aggregative picture is updated, and agents update the track record of all their hypotheses. This is a system in which learning takes place. Agents learn which of their hypotheses work, and from time to time they may discard poorly performing hypotheses and generate new ideas to put in their place. Agents linger with their currently most believable hypothesis or belief model, but drop it when it no longer functions well, in favor of a better one. This causes a built-in hysteresis. A belief model is clung to not because it is correct there is no way to
6 4 know this but rather because it has worked in the past, and must cumulate a record of failure before it is worth discarding. In general, there may be a constant, slow turnover of hypotheses acted upon. We could speak of this as a system of temporarily fulfilled expectations beliefs or models or hypotheses that are temporarily fulfilled (though not perfectly), that give way to different beliefs or hypotheses when they cease to be fulfilled. If the reader finds this system unfamiliar, he or she might think of it as generalizing the standard economic learning framework which typically has agents sharing one expectational model with unknown parameters, acting upon their currently most plausible values. Here, by contrast, agents differ, and each uses several subjective models instead of a continuum of one commonly held one. This is a richer world, and we might ask whether, in a particular context, it converges to some standard equilibrium of beliefs; or whether it remains open-ended, always discovering new hypotheses, new ideas. It is also a world that is evolutionary or more accurately co-evolutionary. Just as species, to survive and reproduce, must prove themselves by competing and being adapted within an environment created by other species, in this world hypotheses, to be accurate and therefore acted upon, must prove themselves by competing and being adapted within an environment created by other agents hypotheses. The set of ideas or hypotheses that are acted upon at any stage therefore coevolves. 2 A key question remains. Where do the hypotheses or mental models come from? How are they generated? Behaviorally, this is a deep question in psychology, having to do with cognition, object representation, and pattern recognition. I will not go into it here. But there are some simple and practical options for modeling. Sometimes we might endow our agents with focal models patterns or hypotheses that are obvious, simple and easily dealt with mentally. We might generate a bank of these and distribute them among the agents. Other times, given a suitable model-space, we might allow the genetic algorithm or some similar intelligent search device to generate ever smarter models. Whatever option is taken, it is important to be clear that the framework described above is independent of the specific hypotheses or beliefs used,
7 5 just as the consumer theory framework is independent of particular products chosen among. Of course, to use the framework in a particular problem, some system of generating beliefs must be adopted. III. The Bar Problem Consider now a problem I will construct to illustrate inductive reasoning and how it might be modeled. N people decide independently each week whether to go to a bar that offers entertainment on a certain night. For concreteness, let us set N at 100. Space is limited, and the evening is enjoyable if things are not too crowded specifically, if fewer than 60% of the possible 100 are present. There is no way to tell the numbers coming for sure in advance, therefore a person or agent: goes deems it worth going if he expects fewer than 60 to show up, or stays home if he expects more than 60 to go. (There is no need that utility differ much above and below 60.) Choices are unaffected by previous visits; there is no collusion or prior communication among the agents; and the only information available is the numbers who came in past weeks. (The problem was inspired by the bar El Farol in Santa Fe which offers Irish music on Thursday nights; but the reader may recognize it as applying to noontime lunch-room crowding, and to other coordination problems with limits to desired coordination.) Of interest is the dynamics of the numbers attending from week to week. Notice two interesting features of this problem. First, if there were an obvious model that all agents could use to forecast attendance and base their decisions on, then a deductive solution would be possible. But this is not the case here. Given the numbers attending in the recent past, a large number of expectational models might be reasonable and defensible. Thus, not knowing which model other agents might choose, a reference agent cannot choose his in a well-defined way. There is no deductively rational solution no correct expectational model. From the agents viewpoint, the problem is ill-defined and they are propelled into a world of induction. Second, and diabolically, any commonalty of expectations gets broken up: If all believe few will go, all will go. But this would invalidate that belief. Similarly, if all believe most will go, nobody will go, invalidating that belief. Expectations will be forced to differ.
8 6 At this stage, I invite the reader to pause and ponder how attendance might behave dynamically over time. Will it converge, and if so to what? Will it become chaotic? How might predictions be arrived at? A Dynamic Model. To answer this, let us construct a model along the lines of the framework sketched above. Assume the 100 agents can individually each form several predictors or hypotheses, in the form of functions that map the past d weeks attendance figures into next week s. For example, recent attendance might be: And particular hypotheses or predictors might be: predict next week s number to be the same as last week s  a mirror image around 50 of last week s  67  a (rounded) average of the last four weeks  the trend in last 8 weeks, bounded by 0, 100  the same as 2 weeks ago (2-period cycle detector)  the same as 5 weeks ago (5-period cycle detector)  etc. Assume each agent possesses and keeps track of a individualized set of k such focal predictors. He decides to go or stay according to the currently most accurate predictor in his set. (I will call this his active predictor). Once decisions are made, each agent learns the new attendance figure, and updates the accuracies of his monitored predictors. Notice that in this bar problem, the set of hypotheses currently most credible and acted upon by the agents the set of active hypotheses determines the attendance. But the attendance history determines the set of active hypotheses. To use John Holland s term, we can think of these active hypotheses as forming an ecology. Of interest is how this ecology evolves over time.
9 7 Computer Experiments. For most sets of hypotheses, analytically this appears to be a difficult question. So in what follows I will proceed by computer experiments. In the experiments, to generate hypotheses, I first create an alphabet soup of predictors, in the form of several dozen focal predictors replicated many times. I then randomly ladle out k (6 or 12 or 23, say) of these to each of 100 agents. Each agent then possesses k predictors or hypotheses or ideas he can draw upon. We need not worry that useless predictors will muddy behavior. If predictors do not work they will not be used; if they do work they will come to the fore. Given starting conditions and the fixed set of predictors available to each agent, the future accuracies of all predictors are predetermined. The dynamics in this case are deterministic Numbers Attending Time FIGURE 1. BAR ATTENDANCE IN THE FIRST 100 WEEKS. The results of the experiments are interesting (Fig.1). Where cycle-detector predictors are present, cycles are quickly arbitraged away so there are no persistent cycles. (If several people expect many to go because many went three weeks ago, they will stay home.) More interestingly, mean attendance converges always to 60. In fact, the predictors self-organize into an equilibrium pattern or ecology in which of the active predictors, those most accurate and therefore acted
10 8 upon, on average 40% are forecasting above 60, 60% below 60. This emergent ecology is almost organic in nature. For, while the population of active predictors splits into this 60/40 average ratio, it keeps changing in membership forever. This is something like a forest whose contours do not change, but whose individual trees do. These results appear throughout the experiments, robust to changes in types of predictors created and in numbers assigned. How do the predictors self-organize so that 60 emerges as average attendance and forecasts split into a 60/40 ratio? One explanation might be that 60 is a natural attractor in this bar problem; in fact if we view it as a pure game of predicting, a mixed strategy of forecasting above 60 with probability 0.4 and below it with probability 0.6 is Nash. But still this does not explain how the agents approximate any such outcome, given their realistic, subjective reasoning. To get some understanding of how this happens, suppose 70% of their predictors forecasted above 60 for a longish time. Then on average only 30 people would show up. But this would validate predictors that forecasted close to 30, restoring the ecological balance among predictions, so to speak. Eventually the 40% 60% combination would assert itself. (Making this argument mathematically exact appears to be non-trivial.) It is important to be clear that we do not need any forecasting balance in the predictors that are set up. Many could have a tendency to predict high, but aggregate behavior calls the equilibrium predicting ratio to the fore. Of course, the result would fail if all predictors could only predict below 60 then all 100 agents would always show up. Predictors need to "cover" the available prediction space to some modest degree. The reader might ponder what would happen if all agents shared the same set of predictors. It might be objected that I lumbered the agents in these experiments with fixed sets of clunky predictive models. If they could form more open-ended, intelligent predictions, different behavior might emerge. We could certainly test this using a more sophisticated procedure, say genetic programming (Koza, 1992). This continually generates new hypotheses new predictive expressions that adapt intelligently and often become more complicated as time progresses. But I would be surprised if this changes the above results in any qualitative way.
11 9 III. Conclusion The inductive-reasoning system I have described above consists of a multitude of elements in the form of belief-models or hypotheses that adapt to the aggregate environment they jointly create. Thus it qualifies as an adaptive complex system. After some initial learning time, the hypotheses or mental models in use are mutually co-adapted. Thus we can think of a consistent set of mental models as a set of hypotheses that work well with each other under some criterion that have a high degree of mutual adaptedness. Sometimes there is a unique such set, it corresponds to a standard rational expectations equilibrium, and beliefs gravitate into it. More often there is a high, possibly very high, multiplicity of such sets. In this case we might expect inductive reasoning systems in the economy whether in stock-market speculating, in negotiating, in poker games, in oligopoly pricing, in positioning products in the market to cycle through or temporarily lock into psychological patterns that may be non-recurrent, pathdependent, and increasingly complicated. The possibilities are rich. Economists have long been uneasy with the assumption of perfect, deductive rationality in decision contexts that are complicated and potentially ill-defined. The level at which humans can apply perfect rationality is surprisingly modest. Yet it has not been clear how to deal with imperfect or bounded rationality. From the reasoning given above, I believe that as humans in these contexts we use inductive reasoning: we induce a variety of working hypotheses, act upon the most credible, and replace hypotheses with new ones if they cease to work. Such reasoning can be modeled in a variety of ways. Usually this leads to a rich psychological world in which agents ideas or mental models compete for survival against other agents ideas or mental models a world that is both evolutionary and complex.
12 10 Footnotes * Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, NM 87501, and Stanford University. I thank particularly John Holland whose work inspired many of the ideas here. I also thank Kenneth Arrow, David Lane, David Rumelhart, Roger Shepard, Glen Swindle, and colleagues at Santa Fe and Stanford for discussions. A lengthier version is given in Arthur (1992). For parallel work on bounded rationality and induction, but applied to macroeconomics, see Sargent (1994). 1 For accounts in psychological literature, see Bower and Hilgard (1981), Holland et al. (1986), Rumelhart (1980), and Schank and Abelson (1977). Not all decision problems of course work this way. Most of our mundane actions like walking or driving are subconsciously directed, and for these pattern-cognition maps directly in action. Here connectionist models work better. 2 A similar statement holds for strategies in evolutionary game theory; but there, instead of a large number of private, subjective expectational models, a small number of strategies compete.
13 11 REFERENCES Arthur, W. Brian, On Learning and Adaptation in the Economy, Santa Fe Institute Paper , Bower, Gordon H. and Hilgard, Ernest R., Theories of Learning, Englewood Cliffs: Prentice Hall, De Groot Adriann, Thought and Choice in Chess, in the series Psychological Studies, 4, Paris: Mouton & Co., Feldman, Julian Computer Simulation of Cognitive Processes, in Harold Borko (ed.), Computer Applications in the Behavioral Sciences, Prentice Hall, Holland, John H., Keith J. Holyoak, Richard E. Nisbett and Paul R. Thagard, Induction. Cambridge, Mass: MIT Press, Koza, John. Genetic Programming. Cambridge, Mass: MIT Press, Rumelhart, David, Schemata: the Building Blocks of Cognition, in R. Spiro, B. Bruce, and W. Brewer (eds.), Theoretical Issues in Reading Comprehension. Hillsdale, N.J.: Lawrence Erlbaum, Sargent, Thomas, J. Bounded Rationality in Macroeconomics. Oxford University Press, Schank R. and R.P. Abelson, Scripts, Plans, Goals, and Understanding: An Inquiry into Human Knowledge Structures. Hillsdale, N.J.: Lawrence Erlbaum, 1977.
American Economic Association Inductive Reasoning and Bounded Rationality Author(s): W. Brian Arthur Source: The American Economic Review, Vol. 84, No. 2, Papers and Proceedings of the Hundred and Sixth
Undergraduate Psychology Major Learning Goals and Outcomes i Goal 1: Knowledge Base of Psychology Demonstrate familiarity with the major concepts, theoretical perspectives, empirical findings, and historical
Week 7 - Game Theory and Industrial Organisation The Cournot and Bertrand models are the two basic templates for models of oligopoly; industry structures with a small number of firms. There are a number
IS MORE INFORMATION BETTER? THE EFFECT OF TRADERS IRRATIONAL BEHAVIOR ON AN ARTIFICIAL STOCK MARKET Wei T. Yue Alok R. Chaturvedi Shailendra Mehta Krannert Graduate School of Management Purdue University
Rafael Witten Yuze Huang Haithem Turki Playing Strong Poker 1. Why Poker? Chess, checkers and Othello have been conquered by machine learning - chess computers are vastly superior to humans and checkers
Australian Journal of Educational Technology Tracks for learning: Metacognition and learning technologies Julie Gordon University of Wollongong Research into metacognition suggests that learners need to
When does ignorance make us smart? Additional factors guiding heuristic inference. C. Philip Beaman (email@example.com) Rachel McCloy (firstname.lastname@example.org) Philip T. Smith (email@example.com)
Michael Lacewing Philosophical argument At the heart of philosophy is philosophical argument. Arguments are different from assertions. Assertions are simply stated; arguments always involve giving reasons.
The Classes P and NP We now shift gears slightly and restrict our attention to the examination of two families of problems which are very important to computer scientists. These families constitute the
Cognitive Science 32 (2008) 155 161 Copyright C 2008 Cognitive Science Society, Inc. All rights reserved. ISSN: 0364-0213 print / 1551-6709 online DOI: 10.1080/03640210701802113 Is a Single-Bladed Knife
Principles of Programming Languages Prof: S. Arun Kumar Department of Computer Science and Engineering Indian Institute of Technology Delhi Lecture no 7 Lecture Title: Syntactic Classes Welcome to lecture
Laboratory work in AI: First steps in Poker Playing Agents and Opponent Modeling Avram Golbert 01574669 firstname.lastname@example.org Abstract: While Artificial Intelligence research has shown great success in deterministic
LEARNING OUTCOMES FOR THE PSYCHOLOGY MAJOR Goal 1. Knowledge Base of Psychology Demonstrate familiarity with the major concepts, theoretical perspectives, empirical findings, and historical trends in psychology.
Prof. Dr. Thomas Lux / Markus Demary Summer Term 2007 Seminar Distributed Economic Activity and Collective Phenomena The seminar will cover advanced topics related to the collective outcome of distributed
What is Evolutionary Game Theory? Origins: Genetics and Biology Explain strategic aspects in evolution of species due to the possibility that individual fitness may depend on population frequency Basic
Psychology Learning Goals and Outcomes UNDERGRADUATE PSYCHOLOGY MAJOR LEARNING GOALS AND OUTCOMES: A Report (March 2002) American Psychological Association, Task Force Members: Jane S. Halonen, Drew C.
Introduction to Artificial Intelligence What is Artificial Intelligence? One definition: AI is the study of how to make computers do things that people generally do better Many approaches and issues, e.g.:
Asset Pricing Under Endogenous Expectations in an Artificial Stock Market by W. Brian Arthur, John H. Holland, Blake LeBaron, Richard Palmer, and Paul Tayler * Dec 12, 1996 * All authors are affiliated
SIMULATION MODEL VERIFICATION AND VALIDATION: INCREASING THE USERS CONFIDENCE Stewart Robinson Operations and Information Management Group Aston Business School Aston University Birmingham, B4 7ET, UNITED
25 Measuring the Performance of an Agent The rational agent that we are aiming at should be successful in the task it is performing To assess the success we need to have a performance measure What is rational
CHAPTER7 Savvy software agents can encourage the use of second-order theory of mind by negotiators Abstract In social settings, people often rely on their ability to reason about unobservable mental content
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture - 17 Shannon-Fano-Elias Coding and Introduction to Arithmetic Coding
COMP 424 - Artificial Intelligence Lecture 7: Game Playing Instructor: Joelle Pineau (email@example.com) Class web page: www.cs.mcgill.ca/~jpineau/comp424 Unless otherwise noted, all material posted
SPADA, Nina. Foreign Language Teaching: an interview with Nina Spada. ReVEL, vol. 2, n. 2, 2004. ISSN 1678-8931 [www.revel.inf.br/eng]. FOREIGN LANGUAGE TEACHING AN INTERVIEW WITH NINA SPADA Nina Spada
An Investigation into Visualization and Verbalization Learning Preferences in the Online Environment Dr. David Seiler, Assistant Professor, Department of Adult and Career Education, Valdosta State University,
Artificial Intelligence Adversarial Search Andrea Torsello Games Vs. Planning Problems In many problems you re are pitted against an opponent certain operators are beyond your control: you cannot control
Gaming the Law of Large Numbers Thomas Hoffman and Bart Snapp July 3, 2012 Many of us view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas.
Two-State Options John Norstad firstname.lastname@example.org http://www.norstad.org January 12, 1999 Updated: November 3, 2011 Abstract How options are priced when the underlying asset has only two possible
Five Myths of Active Portfolio Management Most active managers are skilled. Jonathan B. Berk 1 This research was supported by a grant from the National Science Foundation. 1 Jonathan B. Berk Haas School
Assessment of the project International Marketing Offensive for Smart Phones in China 1. Assessment of the project itself In November 2014 we started preparing our project which was an international marketing
How to Learn Good Cue Orders: When Social Learning Benefits Simple Heuristics Rocio Garcia-Retamero (email@example.com) Center for Adaptive Behavior and Cognition, Max Plank Institute for Human
Confidence Intervals on Effect Size David C. Howell University of Vermont Recent years have seen a large increase in the use of confidence intervals and effect size measures such as Cohen s d in reporting
Chap 3 CAPM, Arbitrage, and Linear Factor Models 1 Asset Pricing Model a logical extension of portfolio selection theory is to consider the equilibrium asset pricing consequences of investors individually
Game Theory and Algorithms Lecture 0: Extensive Games: Critiques and Extensions March 3, 0 Summary: We discuss a game called the centipede game, a simple extensive game where the prediction made by backwards
Research Methodology source: Best and Kahn (2006) and Litosseliti (2010) Human beings are the unique product of their own creation and evolution. In contrast to other forms of animal life, their highly
cis20.2 design and implementation of software applications 2 spring 2010 lecture # IV.1 introduction to intelligent systems AI is the science of making machines do things that would require intelligence
136 JOURNAL OF EMERGING TECHNOLOGIES IN WEB INTELLIGENCE, VOL. 5, NO. 2, MAY 2013 Prediction of Stock Performance Using Analytical Techniques Carol Hargreaves Institute of Systems Science National University
Frankfurt am Main, 14. April 2010 Sophie Ahlswede Deutsche Bank AG/DB Research P.O. Box 60262 Frankfurt, Germany e-mail: firstname.lastname@example.org Tel. +49 (0)69 910 31832 Deutsche Bank response to the public
Direct Marketing of Insurance Integration of Marketing, Pricing and Underwriting As insurers move to direct distribution and database marketing, new approaches to the business, integrating the marketing,
Three Challenges Facing Modern Macroeconomics White paper submitted to the National Science Foundation Kenneth Rogoff, Professor of Economics, Harvard University, September 21, 2010 Abstract: Three Challenges
Metacognition and Mathematical Problem Solving: Helping Students to Ask The Right Questions Shirley Gartmann and Melissa Freiberg The acquisition of problem solving, reasoning and critical thinking skills
Chapter 3 Prediction Markets, Fair Games and Martingales Prediction markets...... are speculative markets created for the purpose of making predictions. The current market prices can then be interpreted
Lecture Notes in Quantitative Biology Exploratory Data Analysis -- Introduction Chapter 19.1 Revised 25 November 1997 ReCap: Correlation Exploratory Data Analysis What is it? Exploratory vs confirmatory
Some History 0 Virtual Worlds Exploratory Project 0 Nosh Contractor, Northwestern 0 Jaideep Srivastava, Minnesota 0 Dmitri Williams, University of Southern California 0 Scott Poole, University of Illinois
DM842 Computer Game Programming: AI Lecture 9 Tactical Analysis Board Games Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark Outline 1. Tactical Pathfinding
Fall 2012 Q530 Programming for Cognitive Science Aimed at little or no programming experience. Improve your confidence and skills at: Writing code. Reading code. Understand the abilities and limitations
Skepticism about the external world & the problem of other minds So far in this course we have, broadly speaking, discussed two different sorts of issues: issues connected with the nature of persons (a
Perspectives on Computer Intelligence Can computers think? In attempt to make sense of this question Alan Turing, John Searle and Daniel Dennett put fourth varying arguments in the discussion surrounding
Five Myths of Active Portfolio Management Most active managers are skilled. Jonathan B. Berk Proponents of efficient markets argue that it is impossible to beat the market consistently. In support of their
INSTRUCTIONAL DESIGN FOR DEVELOPING EXPERTISE Rebecca L. Fiedler, Ph.D. Kaner, Fiedler & Associates, LLC AN EXPERT IS... someone widely recognized as a reliable source of technique or skill whose faculty
CS 683 Learning, Games, and Electronic Markets Spring 2007 Notes from Week 1: Algorithms for sequential prediction Instructor: Robert Kleinberg 22-26 Jan 2007 1 Introduction In this course we will be looking
Review Bayesianism and Reliability Models and Simulations in Philosophy April 14th, 2014 Last Class: Difference between individual and social epistemology Why simulations are particularly useful for social
The Real Business Cycle model Spring 2013 1 Historical introduction Modern business cycle theory really got started with Great Depression Keynes: The General Theory of Employment, Interest and Money Keynesian
DEFINING, TEACHING AND ASSESSING LIFELONG LEARNING SKILLS Nikos J. Mourtos Abstract - Lifelong learning skills have always been important in any education and work setting. However, ABET EC recently put
How Not to Win a Million Dollars: A Counterexample to a Conjecture of L. Breiman Thomas P. Hayes arxiv:1112.0829v1 [math.pr] 5 Dec 2011 Abstract Consider a gambling game in which we are allowed to repeatedly
The behaviour of players in games with a mixed strategy Nash equilibrium: Evidence from a stylised Poker experiment. Department of Economics, University of Essex Katherine Drakeford Registration Number:
Induction Margaret M. Fleck 10 October 011 These notes cover mathematical induction and recursive definition 1 Introduction to induction At the start of the term, we saw the following formula for computing
Piaget's Stages Piaget's Stages of Cognitive Development Kay C. Wood, Harlan Smith, Daurice Grossniklaus Department of Educational Psychology and Instructional Technology, University of Georgia Contents
The QOOL Algorithm for fast Online Optimization of Multiple Degree of Freedom Robot Locomotion Daniel Marbach January 31th, 2005 Swiss Federal Institute of Technology at Lausanne Daniel.Marbach@epfl.ch
University Press Scholarship Online You are looking at 1-10 of 77 items for: keywords : general equilibrium Strategic Interaction and Markets Jean J. Gabszewicz Published in print: 2000 Published Online:
EMERGING FRONTIERS AND FUTURE DIRECTIONS FOR PREDICTIVE ANALYTICS, VERSION 4.0 ELINOR L. VELASQUEZ Dedicated to the children and the young people. Abstract. This is an outline of a new field in predictive
Lecture 1: Introduction to Reinforcement Learning David Silver Outline 1 Admin 2 About Reinforcement Learning 3 The Reinforcement Learning Problem 4 Inside An RL Agent 5 Problems within Reinforcement Learning
LECTURE 10: GAMES IN EXTENSIVE FORM Sequential Move Games 2 so far, we have only dealt with simultaneous games (players make the decisions at the same time, or simply without knowing what the action of
Computational Scientific Discovery and Cognitive Science Theories Peter D Sozou University of Liverpool and LSE Joint work with: Mark Addis Birmingham City University and LSE Fernand Gobet University of
LEARNING THEORIES Ausubel's Learning Theory David Paul Ausubel was an American psychologist whose most significant contribution to the fields of educational psychology, cognitive science, and science education.
STEM TEACHING TOOL #30 Integrating Science Practices Into Assessment Tasks The Next Generation Science Standards call for the development of three-dimensional science proficiency, that is, students integrated
The Analogy Item Format and the Miller Analogies Test assessment report Don Meagher, EdD Senior Research Director Post-Secondary Education Two views of analogies Analogies : Admission Testing :: Manual
NEURAL NETWORKS IN DATA MINING 1 DR. YASHPAL SINGH, 2 ALOK SINGH CHAUHAN 1 Reader, Bundelkhand Institute of Engineering & Technology, Jhansi, India 2 Lecturer, United Institute of Management, Allahabad,
A Guide to Curriculum Development: Purposes, Practices, Procedures The purpose of this guide is to provide some general instructions to school districts as staff begin to develop or revise their curriculum
THE THREE-HAT PROBLEM BRIAN BENSON AND YANG WANG 1. Introduction Many classical puzzles involve hats. The general setting for these puzzles is a game in which several players are each given a hat to wear.
G u i d e l i n e s f o r K12 Global C l i m a t e Change Education Adapted by: by the National Wildlife Federation from the Environmental Education Guidelines for Excellence of the North American Association
MASTER OF SCIENCE FINANCIAL ECONOMICS ABAC SCHOOL OF MANAGEMENT ASSUMPTION UNIVERSITY OF THAILAND ECO 5001 Mathematics for Finance and Economics The uses of mathematical argument in extending the range,
Lecture 8 The Subjective Theory of Betting on Theories Patrick Maher Philosophy 517 Spring 2007 Introduction The subjective theory of probability holds that the laws of probability are laws that rational
Ph. D. Program in Education Specialization: Educational Leadership School of Education College of Human Sciences Iowa State University The purpose of the doctoral program in Educational Leadership is to
6.42/8.62J Mathematics for Computer Science Srini Devadas and Eric Lehman May 3, 25 Lecture otes Expected Value I The expectation or expected value of a random variable is a single number that tells you
Practical Research Planning and Design Tenth Edition Paul D. Leedy Jeanne Ellis Ormrod 2013, 2010, 2005, 2001, 1997 Pearson Education, Inc. All rights reserved. Chapter 1 The Nature and Tools of Research
Problem Solving, Reasoning, & Decision Making Dr. Director Center for University Teaching, Learning, and Assessment Associate Professor School of Psychological and Behavioral Sciences EXP 4507 Spring 2012
Subject area: Ethics Title: Injustice causes revolt. Discuss. 1 Injustice causes revolt. Discuss. When we explain phenomena we rely on the assertion of facts. The sun rises because the earth turns on its
What is learning? Learning is a very general term denoting the way in which agents: Acquire and organize knowledge (by building, modifying and organizing internal representations of some external reality);
Online Appendix to Stochastic Imitative Game Dynamics with Committed Agents William H. Sandholm January 6, 22 O.. Imitative protocols, mean dynamics, and equilibrium selection In this section, we consider
A Critique of Cosmological Natural Selection Gordon McCabe March 7, 2004 Abstract Mathematical physicist Lee Smolin has proposed a theory of Cosmological natural selection which, he argues, explains the
ARTIFICIAL INTELLIGENCE AND NEURAL NETWORKS WHAT IS AN ARTIFICIAL INTELLIGENCE? It is the science and engineering of making intelligent machines, especially intelligent computer programs. It is related
1 of 11 5/24/02 3:50 PM Data Mining and KDD: A Shifting Mosaic By Joseph M. Firestone, Ph.D. White Paper No. Two March 12, 1997 The Idea of Data Mining Data Mining is an idea based on a simple analogy.
October 14, 2007 Prologue Modern mathematics is a rich and complex tapestry of ideas that have evolved over thousands of years. Unlike computer science or biology, where the concept of truth is in a constant
AN INTRODUCTION TO GAME THEORY 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. MARTIN J. OSBORNE University of Toronto
Game Theory 1. Introduction Dmitry Potapov CERN What is Game Theory? Game theory is about interactions among agents that are self-interested I ll use agent and player synonymously Self-interested: Each