Mathematical and computational models of language evolution
|
|
|
- Christiana Robinson
- 5 years ago
- Views:
Transcription
1 Mathematical and computational models of language evolution Gerhard Jäger Institute of Linguistics, Tübingen University DGfS Summer School August 19, 2013 Gerhard Jäger (UTübingen) Language Evolution / 46
2 EGT and pragmatics Horn strategies: prototypical meanings tend to go with simple expressions and less prototypical meanings with complex expressions. (1) a. John went to church/jail. (prototypical interpretation) b. John went to the church/jail. (literal interpretation) (2) a. I am going to marry you. (no indirect speech act) b. I will marry you. (indirect speech act) (3) a. I need a new driller/cooker. b. I need a new drill/cook. Gerhard Jäger (UTübingen) Language Evolution / 46
3 Horn strategies simple game: players: speaker and hearer two forms: f 0 (short) and f 1 (long) two meanings: m 0 (frequent) and m 1 (rare) speaker strategies: mappings from meanings to forms hearer strategies: mappings from forms to meanings Gerhard Jäger (UTübingen) Language Evolution / 46
4 Speaker strategies S 1 : m 0 f 0, m 1 f 1 : Horn strategy S 2 : m 0 f 1, m 1 f 0 : anti-horn strategy S 3 : m 0 f 0, m 1 f 0 : Smolensky strategy S 4 : m 0 f 1, m 1 f 1 : anti-smolensky strategy Gerhard Jäger (UTübingen) Language Evolution / 46
5 Hearer strategies H 1 : f 0 m 0, f 1 m 1 : Horn strategy' H 2 : f 0 m 1, f 1 m 0 : anti-horn strategy H 3 : f 0 m 0, f 1 m 0 : Smolensky strategy H 4 : f 0 m 1, f 1 m 1 : anti-smolensky strategy Gerhard Jäger (UTübingen) Language Evolution / 46
6 Utility of Horn games whether communication works depends both on speaker strategy S and hearer strategy H two factors for functionality of communication communicative success (hearer economy) { 1 i H(S(m)) = m δ m (S, H) = 0 else least eort (speaker economy) cost(f)... measure of complexity of expression Gerhard Jäger (UTübingen) Language Evolution / 46
7 Utility of Horn games u s/h (S, H) = m p m (δ m (S, H) cost(s(m))) p... probability distribution over meanings Gerhard Jäger (UTübingen) Language Evolution / 46
8 Utility of Horn game Let's make up some numbers: p(m 0 ) =.75 p(m 1 ) =.25 cost(f 0 ) =.1 cost(f 1 ) =.2 Gerhard Jäger (UTübingen) Language Evolution / 46
9 Utility of Horn game H 1 H 2 H 3 H 4 S S S S Gerhard Jäger (UTübingen) Language Evolution / 46
10 Utility of Horn game H 1 H 2 H 3 H 4 S S S S Gerhard Jäger (UTübingen) Language Evolution / 46
11 The problem of equilibrium selection both Horn and anti-horn are evolutionarily stable EGT explains the aversion of natural languages against synonymy and ambiguity preference for Horn not directly explainable in standard EGT Gerhard Jäger (UTübingen) Language Evolution / 46
12 The problem of equilibrium selection rationalistic considerations favor Horn over anti-horn: Horn strategy is Pareto ecient (nobody can do better in absolute terms) Horn strategy risk dominates anti-horn (if you know the population is in an equilibrium but you do not know in which one, going for Horn is less risky than anti-horn) replicator dynamics favors Horn over anti-horn: complete random state evolves to Horn/Horn basin of attraction of Horn is about 20 times as large as basin of attraction of anti-horn (numerical approximationdoes anybody know how to do this analytically?) Gerhard Jäger (UTübingen) Language Evolution / 46
13 Dynamics starting from random state S1 S2 S3 S H1 H2 H3 H4 Gerhard Jäger (UTübingen) Language Evolution / 46
14 The evolution of dierential case marking Gerhard Jäger (UTübingen) Language Evolution / 46
15 Ways of argument identication transitivity may lead to ambiguity die Frau, die Maria kennt the woman that Maria knows the woman that knows Maria three ways out 1 word order 2 agreement 3 case Gerhard Jäger (UTübingen) Language Evolution / 46
16 die Frau, die er kennt die Frau, die ihn kennt the woman that he knows the woman that knows him Gerhard Jäger (UTübingen) Language Evolution / 46
17 Suppose one argument is a pronoun and one is a noun (or a phrase) {I, BOOK, KNOW} both conversants have an interest in successful communication case marking (accusative or ergative) is usually more costly than zero-marking (nominative) speaker wants to avoid costs Gerhard Jäger (UTübingen) Language Evolution / 46
18 speaker strategies always case mark the object (accusative) always case mark the agent (ergative) case mark the object if it is a pronoun. hearer strategies ergative is agent and accusative object pronoun is agent pronoun is object pronoun is agent unless it is accusative. Gerhard Jäger (UTübingen) Language Evolution / 46
19 Statistical patterns of language use four possible clause types O/p O/n A/p he knows it he knows the book A/n the man knows it the man knows the book statistical distribution (from a corpus of spoken English) O/p O/n A/p pp = 198 pn = 716 A/n np = 16 nn = 75 pn np Gerhard Jäger (UTübingen) Language Evolution / 46
20 functionality of speaker strategies and hearer strategies depends on various factors: How often will the hearer get the message right? How many case markers does the speaker need per clause on average? Gerhard Jäger (UTübingen) Language Evolution / 46
21 speaker strategies that will be considered agent is pronoun agent is noun object is pronoun object is noun e(rgative) e(rgative) a(ccusative) a(ccusative) e e a z(ero) e e z a e e z z e z a a z e z z z z a a z z a z z z z a z z z z Gerhard Jäger (UTübingen) Language Evolution / 46
22 hearer strategies: strict rule: ergative means agent, and accusative means object elsewhere rules: 1 SO: The rst phrase is always the agent. 2 pa: Pronouns are agents, and nouns are objects. 3 po: Pronouns are objects, and nouns are agents. 4 OS: The rst phrase is always the object. Gerhard Jäger (UTübingen) Language Evolution / 46
23 The game of case strategy space and utility function are known probability of meaning types can be estimated from corpus study hard to estimate how the complexity of a case morpheme compares to its benet for disambiguation from the speaker perspective parameterized utility function u(s, H) = m p m (δ m (S, H) k cost(s(m))) Gerhard Jäger (UTübingen) Language Evolution / 46
24 Utility of case marking let us assume k =.1 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
25 Utility of case marking let us assume k =.1 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
26 Utility of case marking only one evolutionarily stable state: zeaz/pa (split ergative) very common among Australian aborigines languages Gerhard Jäger (UTübingen) Language Evolution / 46
27 Non-strict Nash equilibria Why are non-strict Nash Equilibria unstable? Dynamics without mutation Gerhard Jäger (UTübingen) Language Evolution / 46
28 Non-strict Nash equilibria Why are non-strict Nash Equilibria unstable? Dynamics with mutation Gerhard Jäger (UTübingen) Language Evolution / 46
29 Utility of case marking If speakers get lazier... k = 0.45 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
30 Utility of case marking If speakers get lazier... k = 0.45 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
31 Utility of case marking... and lazier... k = 0.53 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
32 Utility of case marking... and lazier... k = 0.53 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
33 Utility of case marking... and lazier... k = 0.7 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
34 Utility of case marking... and lazier... k = 0.7 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
35 Utility of case marking... k = 1 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
36 Utility of case marking... k = 1 Speaker Hearer strategies strategies SO pa po OS eezz zzaa ezaz zeza zeaz ezzz zezz zzaz zzza zzzz Gerhard Jäger (UTübingen) Language Evolution / 46
37 Taking stock zeaz/pa split ergative zzaz/pa dierential object marking zezz/pa dierential subject marking ezzz/po inverse DOM zzza/po inverse DSM zzzz/pa no case marking zzza/po zzzz/pa Gerhard Jäger (UTübingen) Language Evolution / 46
38 Taking stock zeaz/pa split ergative Australian languages zzaz/pa dierential object marking zezz/pa dierential subject marking ezzz/po inverse DOM zzza/po inverse DSM zzzz/pa no case marking zzza/po zzzz/pa Gerhard Jäger (UTübingen) Language Evolution / 46
39 Taking stock zeaz/pa split ergative Australian languages zzaz/pa dierential object marking English, Dutch,... zezz/pa dierential subject marking ezzz/po inverse DOM zzza/po inverse DSM zzzz/pa no case marking zzza/po zzzz/pa Gerhard Jäger (UTübingen) Language Evolution / 46
40 Taking stock zeaz/pa split ergative Australian languages zzaz/pa dierential object marking English, Dutch,... zezz/pa dierential subject marking several caucasian languages zzzz/pa no case marking ezzz/po inverse DOM zzza/po inverse DSM zzza/po zzzz/pa Gerhard Jäger (UTübingen) Language Evolution / 46
41 Taking stock zeaz/pa split ergative Australian languages zzaz/pa dierential object marking English, Dutch,... zezz/pa dierential subject marking several caucasian languages zzzz/pa no case marking Chinese, Thai ezzz/po inverse DOM zzza/po inverse DSM zzza/po zzzz/pa Gerhard Jäger (UTübingen) Language Evolution / 46
42 Taking stock zeaz/pa split ergative Australian languages zzaz/pa dierential object marking English, Dutch,... zezz/pa dierential subject marking several caucasian languages zzzz/pa no case marking Chinese, Thai ezzz/po inverse DOM zzza/po inverse DSM Nganasan zzza/po zzzz/pa Gerhard Jäger (UTübingen) Language Evolution / 46
43 Taking stock only very few languages are not evolutionary stable in this sense zzaa: Hungarian, ezza: Parachi, Yazguljami (Iranian languages), eeaa: Wangkumara curious asymmetry: if there are two competing stable states, one is common and the other one rare similar pattern as with Horn vs. anti-horn Gerhard Jäger (UTübingen) Language Evolution / 46
44 Alle equilibria are stable, but some equilibria are more stable than others. Stochastic EGT Gerhard Jäger (UTübingen) Language Evolution / 46
45 Random mutation and stability idealizations of standard Evolutionary Game Theory populations are (practically) innite mutations rate is constant and low better model (Young 1993; Kandori, Mailath and Rob 1993) nite population mutation is noisy Gerhard Jäger (UTübingen) Language Evolution / 46
46 Consequences of nite population model every mutation barrier will occasionally be taken no absolute stability if multiple Strict Nash Equilibria coexist, system will oscillate between them some equilibria are more stable than others system will spend most of the time in most robustly stable state stochastically stable states Gerhard Jäger (UTübingen) Language Evolution / 46
47 A particular model discrete time/nite population version of replicator dynamics mutations occur rarely (most generations have no mutants at all) if mutation occurs, each individual in this generation has same probability to be a mutant mutation frequency and mutation rate equal for both populations each strategy is equally likely for a mutant (within its population) Gerhard Jäger (UTübingen) Language Evolution / 46
48 The formulas x i t y i t = x i (ũ i ũ A ) + j = y i (ũ i ũ B ) + j Z ji Z ij n Z ji Z ij n Gerhard Jäger (UTübingen) Language Evolution / 46
49 The formulas x i t y i t = x i (ũ i ũ A ) + j = y i (ũ i ũ B ) + j Z ji Z ij n Z ji Z ij n x i : frequency of speaker strategy i Gerhard Jäger (UTübingen) Language Evolution / 46
50 The formulas x i t y i t = x i (ũ i ũ A ) + j = y i (ũ i ũ B ) + j Z ji Z ij n Z ji Z ij n x i : frequency of speaker strategy i y i : frequency of hearer strategy i Gerhard Jäger (UTübingen) Language Evolution / 46
51 The formulas x i t y i t = x i (ũ i ũ A ) + j = y i (ũ i ũ B ) + j Z ji Z ij n Z ji Z ij n x i : frequency of speaker strategy i y i : frequency of hearer strategy i ũ i : expected utility of strategy i Gerhard Jäger (UTübingen) Language Evolution / 46
52 The formulas x i t y i t = x i (ũ i ũ A ) + j = y i (ũ i ũ B ) + j Z ji Z ij n Z ji Z ij n x i : frequency of speaker strategy i y i : frequency of hearer strategy i ũ i : expected utility of strategy i ũ R : average utility of entire R-population Gerhard Jäger (UTübingen) Language Evolution / 46
53 The formulas x i t y i t = x i (ũ i ũ A ) + j = y i (ũ i ũ B ) + j Z ji Z ij n Z ji Z ij n x i : frequency of speaker strategy i y i : frequency of hearer strategy i ũ i : expected utility of strategy i ũ R : average utility of entire R-population Z ij : random variable; distributed according to the binomial distribution b(p ij, x i n ) p ij : probability that an i-individual mutates to strategy j Gerhard Jäger (UTübingen) Language Evolution / 46
54 The formulas x i t y i t = x i (ũ i ũ A ) + j = y i (ũ i ũ B ) + j Z ji Z ij n Z ji Z ij n x i : frequency of speaker strategy i y i : frequency of hearer strategy i ũ i : expected utility of strategy i ũ R : average utility of entire R-population Z ij : random variable; distributed according to the binomial distribution b(p ij, x i n ) p ij : probability that an i-individual mutates to strategy j n: population size Gerhard Jäger (UTübingen) Language Evolution / 46
55 A simulation Horn anti-horn Gerhard Jäger (UTübingen) Language Evolution / 46
56 Stochastic stability punctuated equilibria long periods of dynamic stability alternate with short transition periods in the long run, more time in Horn state (67% vs. 26% in anti-horn) simulation suggests that Horn is stable while anti-horn is not can this be proved? Gerhard Jäger (UTübingen) Language Evolution / 46
57 Analytic considerations Simple recipes for nding stochastically stable state in 2 2 games not easily extrapolated to larger games basic idea: calculate the height of the invasion barrier of each ESS the ESSs with maximal invasion barrier is stochastically stable Gerhard Jäger (UTübingen) Language Evolution / 46
58 Analytic considerations invasion barrier = amount of mutations necessary to push the system into the basin of attraction of another ESS Horn anti-horn: 50% anti-horn Horn: 47.5% Hence: Horn strategy is the only stochastically stable state Gerhard Jäger (UTübingen) Language Evolution / 46
59 Stochastic evolution of case marking k = 0.45 competition between zzaz/pa and ezzz/po evolution of speaker population: zzaz ezzz Gerhard Jäger (UTübingen) Language Evolution / 46
60 Stochastic evolution of case marking k = 0.45 competition between zzaz/pa and ezzz/po evolution of hearer population: AO OA Gerhard Jäger (UTübingen) Language Evolution / 46
61 Analysis invasion barriers: dierential object marking: 45.2% inverse dierential subject marking: 2.06% Dierential object marking is stochastically stable; inverse dierential subject marking is not. likewise, dierential subject marking is stochastically stable while inverse dierential object marking is not. Gerhard Jäger (UTübingen) Language Evolution / 46
62 Stochastically stable states zeaz/pa split ergative Australian languages zzaz/pa dierential object marking English, Dutch,... zezz/pa dierential subject marking several caucasian languages zzzz/pa no case marking Chinese, Thai Gerhard Jäger (UTübingen) Language Evolution / 46
63 Conclusion out of 4 16 = 64 possible case marking patterns only four are stochastically stable vast majority of all languages that t into this categorization are stochastically stable precise numbers are hard to come by though linguistic universals can be result of evolutionary pressure in the sense of cultural evolution Gerhard Jäger (UTübingen) Language Evolution / 46
Evolutionary Game Theory and Linguistics
Gerhard.Jaeger@uni-bielefeld.de February 21, 2007 University of Tübingen Conceptualization of language evolution prerequisites for evolutionary dynamics replication variation selection Linguemes any piece
Wright-Fisher Process. (as applied to costly signaling)
Wright-Fisher Process (as applied to costly signaling) 1 Today: 1) new model of evolution/learning (Wright-Fisher) 2) evolution/learning costly signaling (We will come back to evidence for costly signaling
BLUFF WITH AI. Advisor Dr. Christopher Pollett. By TINA PHILIP. Committee Members Dr. Philip Heller Dr. Robert Chun
BLUFF WITH AI Advisor Dr. Christopher Pollett Committee Members Dr. Philip Heller Dr. Robert Chun By TINA PHILIP Agenda Project Goal Problem Statement Related Work Game Rules and Terminology Game Flow
Cognitive Radios Games: Overview and Perspectives
Cognitive Radios Games: Overview and Yezekael Hayel University of Avignon, France Supélec 06/18/07 1 / 39 Summary 1 Introduction 2 3 4 5 2 / 39 Summary Introduction Cognitive Radio Technologies Game Theory
Computing Nash Equilibrium; Maxmin
Computing Nash Equilibrium; Maxmin Lecture 5 Computing Nash Equilibrium; Maxmin Lecture 5, Slide 1 Lecture Overview 1 Recap 2 Computing Mixed Nash Equilibria 3 Fun Game 4 Maxmin and Minmax Computing Nash
Mixed Strategies; Maxmin
Mixed Strategies; Maxmin CPSC 532A Lecture 4 January 28, 2008 Mixed Strategies; Maxmin CPSC 532A Lecture 4, Slide 1 Lecture Overview 1 Recap 2 Mixed Strategies 3 Fun Game 4 Maxmin and Minmax Mixed Strategies;
INSTRUCTIONS: all the calculations on the separate piece of paper which you do not hand in. GOOD LUCK!
INSTRUCTIONS: 1) You should hand in ONLY THE ANSWERS ASKED FOR written clearly on this EXAM PAPER. You should do all the calculations on the separate piece of paper which you do not hand in. 2) Problems
Wire Layer Geometry Optimization using Stochastic Wire Sampling
Wire Layer Geometry Optimization using Stochastic Wire Sampling Raymond A. Wildman*, Joshua I. Kramer, Daniel S. Weile, and Philip Christie Department University of Delaware Introduction Is it possible
Note: A player has, at most, one strictly dominant strategy. When a player has a dominant strategy, that strategy is a compelling choice.
Game Theoretic Solutions Def: A strategy s i 2 S i is strictly dominated for player i if there exists another strategy, s 0 i 2 S i such that, for all s i 2 S i,wehave ¼ i (s 0 i ;s i) >¼ i (s i ;s i ):
Self-Organising, Open and Cooperative P2P Societies From Tags to Networks
Self-Organising, Open and Cooperative P2P Societies From Tags to Networks David Hales www.davidhales.com Department of Computer Science University of Bologna Italy Project funded by the Future and Emerging
Population Genetics. Joe Felsenstein. GENOME 453, Autumn Population Genetics p.1/70
Population Genetics Joe Felsenstein GENOME 453, Autumn 2013 Population Genetics p.1/70 Godfrey Harold Hardy (1877-1947) Wilhelm Weinberg (1862-1937) Population Genetics p.2/70 A Hardy-Weinberg calculation
Game Theory two-person, zero-sum games
GAME THEORY Game Theory Mathematical theory that deals with the general features of competitive situations. Examples: parlor games, military battles, political campaigns, advertising and marketing campaigns,
Population Genetics. Joe Felsenstein. GENOME 453, Autumn Population Genetics p.1/74
Population Genetics Joe Felsenstein GENOME 453, Autumn 2011 Population Genetics p.1/74 Godfrey Harold Hardy (1877-1947) Wilhelm Weinberg (1862-1937) Population Genetics p.2/74 A Hardy-Weinberg calculation
Introduction to Game Theory
Introduction to Game Theory Review for the Final Exam Dana Nau University of Maryland Nau: Game Theory 1 Basic concepts: 1. Introduction normal form, utilities/payoffs, pure strategies, mixed strategies
Exercises for Introduction to Game Theory SOLUTIONS
Exercises for Introduction to Game Theory SOLUTIONS Heinrich H. Nax & Bary S. R. Pradelski March 19, 2018 Due: March 26, 2018 1 Cooperative game theory Exercise 1.1 Marginal contributions 1. If the value
BLUFF WITH AI. A Project. Presented to. The Faculty of the Department of Computer Science. San Jose State University. In Partial Fulfillment
BLUFF WITH AI A Project Presented to The Faculty of the Department of Computer Science San Jose State University In Partial Fulfillment Of the Requirements for the Degree Master of Science By Tina Philip
Cost-based pragmatic implicatures in an artificial language experiment
Cost-based pragmatic implicatures in an artificial language experiment Judith Degen, Michael Franke & Gerhard Jäger Rochester/Stanford Amsterdam Tübingen July 27, 2013 Workshop on Artificial Grammar Learning
Summary Overview of Topics in Econ 30200b: Decision theory: strong and weak domination by randomized strategies, domination theorem, expected utility
Summary Overview of Topics in Econ 30200b: Decision theory: strong and weak domination by randomized strategies, domination theorem, expected utility theorem (consistent decisions under uncertainty should
Lecture #3: Networks. Kyumars Sheykh Esmaili
Lecture #3: Game Theory and Social Networks Kyumars Sheykh Esmaili Outline Games Modeling Network Traffic Using Game Theory Games Exam or Presentation Game You need to choose between exam or presentation:
OPINION FORMATION IN TIME-VARYING SOCIAL NETWORK: THE CASE OF NAMING GAME
OPINION FORMATION IN TIME-VARYING SOCIAL NETWORK: THE CASE OF NAMING GAME ANIMESH MUKHERJEE DEPARTMENT OF COMPUTER SCIENCE & ENGG. INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR Naming Game in complex networks
Robustness against Longer Memory Strategies in Evolutionary Games.
Robustness against Longer Memory Strategies in Evolutionary Games. Eizo Akiyama 1 Players as finite state automata In our daily life, we have to make our decisions with our restricted abilities (bounded
EconS Sequential Move Games
EconS 425 - Sequential Move Games Eric Dunaway Washington State University eric.dunaway@wsu.edu Industrial Organization Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 57 Introduction Today, we
Luciano Andreozzi. A note on Critical Masses, Network Externalities and Converters.
January 2004 Luciano Andreozzi A note on Critical Masses, Network Externalities and Converters. Abstract Witt [9] demonstrates that superior technological standards have smaller critical mass, so that
Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Game Theory
Resource Allocation and Decision Analysis (ECON 8) Spring 4 Foundations of Game Theory Reading: Game Theory (ECON 8 Coursepak, Page 95) Definitions and Concepts: Game Theory study of decision making settings
Game Theory: Introduction. Game Theory. Game Theory: Applications. Game Theory: Overview
Game Theory: Introduction Game Theory Game theory A means of modeling strategic behavior Agents act to maximize own welfare Agents understand their actions affect actions of other agents ECON 370: Microeconomic
ECON 2100 Principles of Microeconomics (Summer 2016) Game Theory and Oligopoly
ECON 2100 Principles of Microeconomics (Summer 2016) Game Theory and Oligopoly Relevant readings from the textbook: Mankiw, Ch. 17 Oligopoly Suggested problems from the textbook: Chapter 17 Questions for
FLORIDA LANGUAGE MATHEMATICS READING SCIENCE
Instructional Areas FLORIDA LANGUAGE MATHEMATICS READING SCIENCE Tests Standards Growth: Language 2-12 FL 2014 Growth: Math K-2 FL 2014 Growth: Math 2-5 FL 2014 Growth: Math 6+ FL 2014 Growth: Reading
Game Theory Lecturer: Ji Liu Thanks for Jerry Zhu's slides
Game Theory ecturer: Ji iu Thanks for Jerry Zhu's slides [based on slides from Andrew Moore http://www.cs.cmu.edu/~awm/tutorials] slide 1 Overview Matrix normal form Chance games Games with hidden information
Games. Episode 6 Part III: Dynamics. Baochun Li Professor Department of Electrical and Computer Engineering University of Toronto
Games Episode 6 Part III: Dynamics Baochun Li Professor Department of Electrical and Computer Engineering University of Toronto Dynamics Motivation for a new chapter 2 Dynamics Motivation for a new chapter
LANGUAGE MATHEMATICS READING SCIENCE
Instructional Areas AERO LANGUAGE MATHEMATICS READING SCIENCE Tests Growth: Language 2-12 AERO 2012/2015 Growth: Math K-2 CCSS Intl 2010 Growth: Math 2-5 AERO 2015 Growth: Math 6+ AERO 2015 Growth: Reading
Analyzing Games: Mixed Strategies
Analyzing Games: Mixed Strategies CPSC 532A Lecture 5 September 26, 2006 Analyzing Games: Mixed Strategies CPSC 532A Lecture 5, Slide 1 Lecture Overview Recap Mixed Strategies Fun Game Analyzing Games:
Calculators will not be permitted on the exam. The numbers on the exam will be suitable for calculating by hand.
Midterm #: practice MATH Intro to Number Theory midterm: Thursday, Nov 7 Please print your name: Calculators will not be permitted on the exam. The numbers on the exam will be suitable for calculating
Student Name. Student ID
Final Exam CMPT 882: Computational Game Theory Simon Fraser University Spring 2010 Instructor: Oliver Schulte Student Name Student ID Instructions. This exam is worth 30% of your final mark in this course.
LANGUAGE MATHEMATICS READING SCIENCE
Instructional Areas MARYLAND LANGUAGE MATHEMATICS READING SCIENCE Tests Standards Growth: Language 2-12 MD 2011 Growth: Math K-2 MD 2011 Growth: Math 2-5 MD 2011 Growth: Math 6+ MD 2011 Growth: Reading
Reading Robert Gibbons, A Primer in Game Theory, Harvester Wheatsheaf 1992.
Reading Robert Gibbons, A Primer in Game Theory, Harvester Wheatsheaf 1992. Additional readings could be assigned from time to time. They are an integral part of the class and you are expected to read
CSCI 699: Topics in Learning and Game Theory Fall 2017 Lecture 3: Intro to Game Theory. Instructor: Shaddin Dughmi
CSCI 699: Topics in Learning and Game Theory Fall 217 Lecture 3: Intro to Game Theory Instructor: Shaddin Dughmi Outline 1 Introduction 2 Games of Complete Information 3 Games of Incomplete Information
Leandro Chaves Rêgo. Unawareness in Extensive Form Games. Joint work with: Joseph Halpern (Cornell) Statistics Department, UFPE, Brazil.
Unawareness in Extensive Form Games Leandro Chaves Rêgo Statistics Department, UFPE, Brazil Joint work with: Joseph Halpern (Cornell) January 2014 Motivation Problem: Most work on game theory assumes that:
COORDINATION GAMES. Nash Equilibria, Schelling Points and the Prisoner s Dilemma. Owain Evans, MIT Paradox, Monday 25 February 2013.
COORDINATION GAMES Nash Equilibria, Schelling Points and the Prisoner s Dilemma Owain Evans, MIT Paradox, Monday 25 February 2013. 2 Newcomb s Paradox $1,000? Box A Box B Image by MIT OpenCourseWare. 3
Chapter 30: Game Theory
Chapter 30: Game Theory 30.1: Introduction We have now covered the two extremes perfect competition and monopoly/monopsony. In the first of these all agents are so small (or think that they are so small)
Problem 1 (15 points: Graded by Shahin) Recall the network structure of our in-class trading experiment shown in Figure 1
Solutions for Homework 2 Networked Life, Fall 204 Prof Michael Kearns Due as hardcopy at the start of class, Tuesday December 9 Problem (5 points: Graded by Shahin) Recall the network structure of our
UPenn NETS 412: Algorithmic Game Theory Game Theory Practice. Clyde Silent Confess Silent 1, 1 10, 0 Confess 0, 10 5, 5
Problem 1 UPenn NETS 412: Algorithmic Game Theory Game Theory Practice Bonnie Clyde Silent Confess Silent 1, 1 10, 0 Confess 0, 10 5, 5 This game is called Prisoner s Dilemma. Bonnie and Clyde have been
Effect of Information Exchange in a Social Network on Investment: a study of Herd Effect in Group Parrondo Games
Effect of Information Exchange in a Social Network on Investment: a study of Herd Effect in Group Parrondo Games Ho Fai MA, Ka Wai CHEUNG, Ga Ching LUI, Degang Wu, Kwok Yip Szeto 1 Department of Phyiscs,
Population Initialization Techniques for RHEA in GVGP
Population Initialization Techniques for RHEA in GVGP Raluca D. Gaina, Simon M. Lucas, Diego Perez-Liebana Introduction Rolling Horizon Evolutionary Algorithms (RHEA) show promise in General Video Game
Contents Modeling of Socio-Economic Systems Agent-Based Modeling
Contents 1 Modeling of Socio-Economic Systems... 1 1.1 Introduction... 1 1.2 Particular Difficulties of Modeling Socio-Economic Systems... 2 1.3 Modeling Approaches... 4 1.3.1 Qualitative Descriptions...
CHAPTER 6: Tense in Embedded Clauses of Speech Verbs
CHAPTER 6: Tense in Embedded Clauses of Speech Verbs 6.0 Introduction This chapter examines the behavior of tense in embedded clauses of indirect speech. In particular, this chapter investigates the special
Chapter 3: Complex systems and the structure of Emergence. Hamzah Asyrani Sulaiman
Chapter 3: Complex systems and the structure of Emergence Hamzah Asyrani Sulaiman In this chapter, we will explore the relationship between emergence, the structure of game mechanics, and gameplay in more
U strictly dominates D for player A, and L strictly dominates R for player B. This leaves (U, L) as a Strict Dominant Strategy Equilibrium.
Problem Set 3 (Game Theory) Do five of nine. 1. Games in Strategic Form Underline all best responses, then perform iterated deletion of strictly dominated strategies. In each case, do you get a unique
Chapter 3 Learning in Two-Player Matrix Games
Chapter 3 Learning in Two-Player Matrix Games 3.1 Matrix Games In this chapter, we will examine the two-player stage game or the matrix game problem. Now, we have two players each learning how to play
Game Theory and Algorithms Lecture 3: Weak Dominance and Truthfulness
Game Theory and Algorithms Lecture 3: Weak Dominance and Truthfulness March 1, 2011 Summary: We introduce the notion of a (weakly) dominant strategy: one which is always a best response, no matter what
INTRODUCTION TO GAME THEORY
1 / 45 INTRODUCTION TO GAME THEORY Heinrich H. Nax hnax@ethz.ch & Bary S. R. Pradelski bpradelski@ethz.ch February 20, 2017: Lecture 1 2 / 45 A game Rules: 1 Players: All of you: https://scienceexperiment.online/beautygame/vote
Domination Rationalizability Correlated Equilibrium Computing CE Computational problems in domination. Game Theory Week 3. Kevin Leyton-Brown
Game Theory Week 3 Kevin Leyton-Brown Game Theory Week 3 Kevin Leyton-Brown, Slide 1 Lecture Overview 1 Domination 2 Rationalizability 3 Correlated Equilibrium 4 Computing CE 5 Computational problems in
Economics II: Micro Winter 2009 Exercise session 4 Aslanyan: VŠE
Economics II: Micro Winter 2009 Exercise session 4 slanyan: VŠE 1 Review Game of strategy: player is engaged in a game of strategy if that individual s payo (utility) is determined not by that individual
Game Theory Refresher. Muriel Niederle. February 3, A set of players (here for simplicity only 2 players, all generalized to N players).
Game Theory Refresher Muriel Niederle February 3, 2009 1. Definition of a Game We start by rst de ning what a game is. A game consists of: A set of players (here for simplicity only 2 players, all generalized
Dynamics and Coevolution in Multi Level Strategic interaction Games. (CoNGas)
Dynamics and Coevolution in Multi Level Strategic interaction Games (CoNGas) Francesco De Pellegrini CREATE-NET Obj. ICT-2011 9.7 DyM-CS 15/06/2012 Abstract Many real world systems possess a rich multi-level
EconS Game Theory - Part 1
EconS 305 - Game Theory - Part 1 Eric Dunaway Washington State University eric.dunaway@wsu.edu November 8, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 28 November 8, 2015 1 / 60 Introduction Today, we
SF2972: Game theory. Introduction to matching
SF2972: Game theory Introduction to matching The 2012 Nobel Memorial Prize in Economic Sciences: awarded to Alvin E. Roth and Lloyd S. Shapley for the theory of stable allocations and the practice of market
Resource Allocation Challenges in Future Wireless Networks
Resource Allocation Challenges in Future Wireless Networks Mohamad Assaad Dept of Telecommunications, Supelec - France Mar. 2014 Outline 1 General Introduction 2 Fully Decentralized Allocation 3 Future
REPORT DOCUMENTATION PAGE
REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions,
Introduction to (Networked) Game Theory. Networked Life NETS 112 Fall 2014 Prof. Michael Kearns
Introduction to (Networked) Game Theory Networked Life NETS 112 Fall 2014 Prof. Michael Kearns percent who will actually attend 100% Attendance Dynamics: Concave equilibrium: 100% percent expected to attend
STAT Statistics I Midterm Exam One. Good Luck!
STAT 515 - Statistics I Midterm Exam One Name: Instruction: You can use a calculator that has no connection to the Internet. Books, notes, cellphones, and computers are NOT allowed in the test. There are
Arpita Biswas. Speaker. PhD Student (Google Fellow) Game Theory Lab, Dept. of CSA, Indian Institute of Science, Bangalore
Speaker Arpita Biswas PhD Student (Google Fellow) Game Theory Lab, Dept. of CSA, Indian Institute of Science, Bangalore Email address: arpita.biswas@live.in OUTLINE Game Theory Basic Concepts and Results
Terry College of Business - ECON 7950
Terry College of Business - ECON 7950 Lecture 5: More on the Hold-Up Problem + Mixed Strategy Equilibria Primary reference: Dixit and Skeath, Games of Strategy, Ch. 5. The Hold Up Problem Let there be
LECTURE 26: GAME THEORY 1
15-382 COLLECTIVE INTELLIGENCE S18 LECTURE 26: GAME THEORY 1 INSTRUCTOR: GIANNI A. DI CARO ICE-CREAM WARS http://youtu.be/jilgxenbk_8 2 GAME THEORY Game theory is the formal study of conflict and cooperation
Describe the variable as Categorical or Quantitative. If quantitative, is it discrete or continuous?
MATH 2311 Test Review 1 7 multiple choice questions, worth 56 points. (Test 1) 3 free response questions, worth 44 points. (Test 1 FR) Terms and Vocabulary; Sample vs. Population Discrete vs. Continuous
Basic Probability & Statistics Exam 2 { Part I { Sections (Chapter 4, Chapter 5) March 19, 2009
NAME: INSTRUCTOR: Dr. Bathi Kasturiarachi Math 30011 Spring 2009 Basic Probability & Statistics Exam 2 { Part I { Sections (Chapter 4, Chapter 5) March 19, 2009 Read through the entire test before beginning.
1 Simultaneous move games of complete information 1
1 Simultaneous move games of complete information 1 One of the most basic types of games is a game between 2 or more players when all players choose strategies simultaneously. While the word simultaneously
ON THE EVOLUTION OF TRUTH. 1. Introduction
ON THE EVOLUTION OF TRUTH JEFFREY A. BARRETT Abstract. This paper is concerned with how a simple metalanguage might coevolve with a simple descriptive base language in the context of interacting Skyrms-Lewis
COMPSCI 223: Computational Microeconomics - Practice Final
COMPSCI 223: Computational Microeconomics - Practice Final 1 Problem 1: True or False (24 points). Label each of the following statements as true or false. You are not required to give any explanation.
final examination on May 31 Topics from the latter part of the course (covered in homework assignments 4-7) include:
The final examination on May 31 may test topics from any part of the course, but the emphasis will be on topic after the first three homework assignments, which were covered in the midterm. Topics from
Game Theory: introduction and applications to computer networks
Game Theory: introduction and applications to computer networks Lecture 3: two-person non zero-sum games Giovanni Neglia INRIA EPI Maestro 6 January 2010 Slides are based on a previous course with D. Figueiredo
Combinations. April 14, 2006
Combinations April 14, 2006 Combinations (cont'd), April 14, 2006 Inclusion-Exclusion Principle Theorem. Let P be a probability distribution on a sample space Ω, and let {A 1, A 2,..., A n } be a nite
Chapter 2 The Market. The Classical Approach
Chapter 2 The Market The economic theory of markets has been central to economic growth since the days of Adam Smith. There have been three major phases of this theory: the classical theory, the neoclassical
Game Theory: The Basics. Theory of Games and Economics Behavior John Von Neumann and Oskar Morgenstern (1943)
Game Theory: The Basics The following is based on Games of Strategy, Dixit and Skeath, 1999. Topic 8 Game Theory Page 1 Theory of Games and Economics Behavior John Von Neumann and Oskar Morgenstern (1943)
HORIZON HIGH SCHOOL- English Composition, Grammar and Poetry
HORIZON HIGH SCHOOL- English Composition, Grammar and Poetry Materials Creating Poetry, John Drury A Poetry Handbook, Mary Oliver English Warriner, John E. Various Poems drawn from many sources Weeks 1
Distributed Optimization and Games
Distributed Optimization and Games Introduction to Game Theory Giovanni Neglia INRIA EPI Maestro 18 January 2017 What is Game Theory About? Mathematical/Logical analysis of situations of conflict and cooperation
Optimization of Time of Day Plan Scheduling Using a Multi-Objective Evolutionary Algorithm
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Civil Engineering Faculty Publications Civil Engineering 1-2005 Optimization of Time of Day Plan Scheduling Using a Multi-Objective
Introduction to Game Theory I
Nicola Dimitri University of Siena (Italy) Rome March-April 2014 Introduction to Game Theory 1/3 Game Theory (GT) is a tool-box useful to understand how rational people choose in situations of Strategic
Community Radio. National Listener Survey Wave #1 FACT SHEET ACT. July Prepared for:
Community Radio National Listener Survey 20 Wave #1 F SHEET July 20 Prepared for: *Speak Languages Other Than English At Home McNair Ingenuity Research Pty Ltd ACN. 096 437 991 Level 4, 270 Pacific Highway,
GAME THEORY: ANALYSIS OF STRATEGIC THINKING Exercises on Multistage Games with Chance Moves, Randomized Strategies and Asymmetric Information
GAME THEORY: ANALYSIS OF STRATEGIC THINKING Exercises on Multistage Games with Chance Moves, Randomized Strategies and Asymmetric Information Pierpaolo Battigalli Bocconi University A.Y. 2006-2007 Abstract
Introduction to Experiments on Game Theory
Introduction to Experiments on Game Theory Syngjoo Choi Spring 2010 Experimental Economics (ECON3020) Game theory 1 Spring 2010 1 / 23 Game Theory A game is a mathematical notion of a strategic interaction
Community Radio. National Listener Survey Wave #1 FACT SHEET NON-METRO QLD. July Prepared for:
Community Radio National Listener Survey 2016 Wave #1 FACT SHEET July 2016 Prepared for: *Speak Languages Other Than English At Home McNair Ingenuity Research Pty Ltd ACN. 096 437 991 Level 4, 270 Pacific
Reinforcement Learning in Games Autonomous Learning Systems Seminar
Reinforcement Learning in Games Autonomous Learning Systems Seminar Matthias Zöllner Intelligent Autonomous Systems TU-Darmstadt zoellner@rbg.informatik.tu-darmstadt.de Betreuer: Gerhard Neumann Abstract
ECON 282 Final Practice Problems
ECON 282 Final Practice Problems S. Lu Multiple Choice Questions Note: The presence of these practice questions does not imply that there will be any multiple choice questions on the final exam. 1. How
Population Games and Evolutionary Dynamics
Population Games and Evolutionary Dynamics William H. Sandholm September 9, 2009 1 3 Chaos under the replicator dynamic 4 ii CONTENTS IN BRIEF Preface xv 1 Introduction 1 I Population Games 19 2 Population
Hypergeometric Probability Distribution
Hypergeometric Probability Distribution Example problem: Suppose 30 people have been summoned for jury selection, and that 12 people will be chosen entirely at random (not how the real process works!).
Online Resource to The evolution of sanctioning institutions: an experimental approach to the social contract
Online Resource to The evolution of sanctioning institutions: an experimental approach to the social contract Boyu Zhang, Cong Li, Hannelore De Silva, Peter Bednarik and Karl Sigmund * The experiment took
Non-overlapping permutation patterns
PU. M. A. Vol. 22 (2011), No.2, pp. 99 105 Non-overlapping permutation patterns Miklós Bóna Department of Mathematics University of Florida 358 Little Hall, PO Box 118105 Gainesville, FL 326118105 (USA)
How good is simple reversal sort? Cycle decompositions. Cycle decompositions. Estimating reversal distance by cycle decomposition
How good is simple reversal sort? p Not so good actually p It has to do at most n-1 reversals with permutation of length n p The algorithm can return a distance that is as large as (n 1)/2 times the correct
Simultaneous Move Games
Simultaneous Move Games These notes essentially correspond to parts of chapters 7 and 8 of Mas-Colell, Whinston, and Green. Most of this material should be a review from BPHD 8100. 1 Introduction Up to
Case 1: If Denver is the first city visited, then the outcome looks like: ( D ).
2.37. (a) Think of each city as an object. Each one is distinct. Therefore, there are 6! = 720 different itineraries. (b) Envision the process of selecting an itinerary as a random experiment with sample
Mixed strategy Nash equilibrium
Mixed strategy Nash equilibrium Felix Munoz-Garcia Strategy and Game Theory - Washington State University Looking back... So far we have been able to nd the NE of a relatively large class of games with
Modeling language change for the worse
Modeling language change for the worse Some considerations from an evolutionary perspective Gerhard Jäger Tübingen University Workshop Language change for the worse Munich, May 28, 2017 Gerhard Jäger (Tübingen)
Distributed social dilemma with competitive meta-players
Intl. Trans. in Op. Res. 8 (21) 75±88 Distributed social dilemma with competitive meta-players Tomohisa Yamashita, Keiji Suzuki and Azuma Ohuchi Graduate School of Engineering, Hokkaido University, Kita
ESSENTIALS OF GAME THEORY
ESSENTIALS OF GAME THEORY 1 CHAPTER 1 Games in Normal Form Game theory studies what happens when self-interested agents interact. What does it mean to say that agents are self-interested? It does not necessarily
Optimization, Wisconsin Institutes of Discovery, and Conservation: Is there a link?
Optimization, Wisconsin Institutes of Discovery, and Conservation: Is there a link? Michael C. Ferris University of Wisconsin, Madison Conservation seminar, Madison: March 10, 2010 Collaboration with Jeff
SF2972: Game theory. Plan. The top trading cycle (TTC) algorithm: reference
SF2972: Game theory The 2012 Nobel prize in economics : awarded to Alvin E. Roth and Lloyd S. Shapley for the theory of stable allocations and the practice of market design The related branch of game theory
Study Singular They in Contemporary English. Bich Ngoc Do
Study Singular They in Contemporary English Bich Ngoc Do Content 1. Introduction 2. Similar Works 3. Data Collection 4. Statistical Analysis 5. Conclusion 1. Introduction Gender in English O Male-oriented
Introduction to (Networked) Game Theory. Networked Life NETS 112 Fall 2016 Prof. Michael Kearns
Introduction to (Networked) Game Theory Networked Life NETS 112 Fall 2016 Prof. Michael Kearns Game Theory for Fun and Profit The Beauty Contest Game Write your name and an integer between 0 and 100 Let
Prisoner 2 Confess Remain Silent Confess (-5, -5) (0, -20) Remain Silent (-20, 0) (-1, -1)
Session 14 Two-person non-zero-sum games of perfect information The analysis of zero-sum games is relatively straightforward because for a player to maximize its utility is equivalent to minimizing the
Pattern Avoidance in Unimodal and V-unimodal Permutations
Pattern Avoidance in Unimodal and V-unimodal Permutations Dido Salazar-Torres May 16, 2009 Abstract A characterization of unimodal, [321]-avoiding permutations and an enumeration shall be given.there is