DOCSLIB.ORG

Index, 3Rd Edition. Games and Information "41D" Indicates That The

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Out-of-equilibrium 143, 155n Index, 3rd edition. Games and Information Posterior 55 Prior 54 "41d" indicates that the concept is defined on page 41, Updating 55 "33n" that the entry is in an endnote, and "54p" that the entry is in Benoit-Krishna game 134p a homework problem. Articles and books are indexed separately, Bertrand equilibrium 35n, 343, 367n, 370p in the bibliography. Best reply 19d Best response 19d, 82 This index was prepared by the author, not by a research Bid-ask spread 226 assistant or by the publisher. Bilateral Trading games I, II, III, and IV 309, 321n Bimatrix game 34n Biology 106n, 125, 133n, 289n Action combination 13d Blackboxing 100 Action set 13d Boiling in oil contract 175, 182n Action 13d Boundary 32 Additively separable 130 Bounded set 70 Advantages Bourgeois strategy 128 first-mover 29 Boxed Pigs game 25, 35 last-mover 300 Branch 40d second-mover 37p Bridge card game 85n Adverse selection 161, 211-39 Broadway Game Advertising 289n, 291p I 174 Affiliated variables 338n II 178 Affine transformation 76 Brouwer fixed-point theorem 404 Agent 162d Budget-balancing constraint 202, 207n, 262 Almost always 396, 404-06 Buyout, entry for 386, 392p Almost perfect information 63dn Alternating Offers game 299, 320 Calculus 394, 399, 400 Annuity 395, Capacity constraints 368n, 387, 345 Anonymity condition 271 Cardinal utility 34n, 76 Argmax 394 Certain information 47d Assessment 140 Chainstore paradox 110, 129 Assurance game 35n Cheap talk 75 Asymmetric information 49d,50 Chatterjee-Samuelson mechanism 315 Auctions 323-339 Chicken game 71, 85n categories 324 Closed set 70, 394, 395 common-value 324, 331 Civic Duty game 78 descending 327 Closed-loop 105n Dutch 327 Cloud 44 English 325 Coalition 319n first-price 325 Coalitionproofness 103 open-exit 325 Coarsening 45d private-value 324,330 Coase Conjecture 369n second-price 327,337 Coase Theorem 170 Auditing Game I, II, III 79, 86n Co-insurance 200 Authority 184p Colonel Blotto games 87n Axelrod tournament 151, 156n Combination 395 Combination, strategy 17d, 33n Backward induction 110 Commitment 29, 80, 117, 237p Bagehot model 226 Common knowledge 47d, 62n, 63nd, 158p Bank loans 153, 194, 231 In Entry Deterrence IV and V Bankruptcy constraint 186, 209p Common-value auction 324, 331 Bargaining 295-322, 165, 169 Communication 33, 75, 105, 32 Alternating Offers game 299, 320 Compact set 395 bargaining power 165, 169, 196 Comparative statics 357 Splitting a Pie game 296 Competition constraint 121, 213 take-it-or-leave-it offer 165 Competitive fringe 87n Battle of the Bismarck Sea game 21, 34n Complementary inputs 360 Battles of the Sexes game 28, 35n, 89p, 157p Complete information 50d, 51 Bayes's Rule 55d, 64p Complete robustness 146 Bayesian equilibrium 54 Completely mixed strategy 67d Beer-Quiche game 155n Concave function 395 Behavior strategy 84n Concordant beliefs 47d Beliefs Conditional likelihood 56 Constraints uniform 400 bankruptcy 186, 209p Dollar Auction game 336n competition 121, 213 Domain 396 incentive compatibility 121, 173, 213 Dominance-solvable 23d nonpooling 213 Dominance, stochastic 408 participation 173, 181n, 213, 233n Dominant diagonal condition 361 self selection 213 Dominant strategy 19d Continuous function 395 Dominant-strategy equilibrium 20d Continuous strategies 81, 100 Dominant-strategy mechanism 262 Continuous time 85n Dominated strategy 19d, 61 Continuum 395 Double auction mechanism 311 Continuum of players 69, 85, 303 Double-sided moral hazard 179n Continuum of equilibria 72, 207n, 296, 306 Dry Cleaners game 14 Contractible variable 170 Duelling games 74 Contraction mapping 395 Duopoly 30, 81, 87n, 156p, 340, 367n, 370p Contracts Durable monopoly 362, 369n boiling-in-oil 175, 182n Dutch auction 327, 336 first-best 172d, 246 Dynamic consistency 105n forcing 167 Dynamic game 90 linear 167 pooling 142, 145, 213d Edgeworth paradox 345 second-best 172d Education Game selling-the-store 178, 183p I 268 threshold 167 II-IV 271 Contribution games 77 V 277 Convex function 396 VI 278 Convex set 173, 396 VII 281 Cooperative games 21, 319n Efficiency wage 181n, 185, 205n, 210p, 230 Co-opting 205n Efficient rationing 367n Coordination games 29, 35n, 77 Elmer's Appetite 64p Copayment 200 Emotions 101, 132n Corner solution 72 End node (end point) 40d Correlated strategies 74 English auction 325 Correlated-value auction 324 Entry deterrence 372-392 Correspondence 396 Entry Deterrence game 106p, 134p Cournot model 30, 81, 87n, 156p, 340, 367n, 370p I 93 Cream skimming 224 II and III 139 Credible threat 94 IV and V 147, 158p Cumulative density function 400 Epsilon equilibrium 130n Customer Switching Costs game 123 Equilibrium 18d continua 72, 207n, 296, 306 Dangerous Coordination game 30 epsilon 130n Decision theory 14 existence 70, 225, 281 Decision tree 14 fully revealing 213, 246 Deductible 200 implausible 91, 143 Density 400 multiple 18 Derivatives, calculus 394, 399, 400 Pareto-dominant 28, 37p Descending auction 327 partially revealing 213 Determinants 399 Equilibrium concept 18d Deviation 33n coalitionproof 103 Differential games 87n dominant-strategy 20d Dimensionality condition 114, 131n evolutionarily stable strategies 125d, 135p Direct incentive-compatible mechanism 315 iterated dominance 23d, 118 Disagreement point 297 maximin 116 Discontinuity Nash 26d, 36p, 54, 100 Discoordination games 37p, 77 perfect bayesian 140d, 155 Discount factor 406 sequential 140d Discount rate 406 Stackelberg 30, 83, 87n, 106n Discounting 73, 299, 406-08 subgame perfect 91d, 137 in bargaining 301 trembling-hand-perfect 139 in the Folk Theorem 113 Equilibrium outcome 18 Distribution 400 Equilibrium path 89d exponential 400 Equilibrium refinement 28 lognormal 400 forward induction 158p Equilibrium strategy 18 Durable Monopoly 362 Evolutionary dynamics 128 Education I, II, III, IV, V, VI, VII 268, 271, 277, 278, 281 Evolutionarily stable strategy (ESS) 125d, 135p Entry for Buyout 386 Exemplifying theory 2 Expensive Talk 157p Existence of equilibrium 70, 225, 281 Follow the Leader I, II, III Exotic refinements 155n The Free Rider Problem in Takeovers 378 Expected externality mechanism 316, 321n General 2x2 game 75 Expected utility 48, 63n Government Procurement 255 Expensive Talk Game 157p Grab the Dollar 73, 135p Exponential distribution 400 Greenmail to Attract White Knights 381 Extensive form 40d, 94, 155n Hawk-Dove 127 Extrinsic uncertainty 74 The Hotelling Location Game 354 The Hotelling Pricing Game 350 Fairness 101, 298 Insurance Game I , II, III 197, 222 Fat-cat effect 390n The Iteration Path Game 25 Finer information partition 45d Lemons I, II, III, IV 215, 218 First-best Limit Pricing as Signal Jamming 285 contract 172d, 246 Matching Pennies 88p outcome 182p The Minimax Illustration Game 116 First-mover advantage 29 Modeller's Dilemma 27 First-order condition approach 173, 181n Nuisance Suits I, II, III 96 First-order stochastic dominance 408 Patent Race for a New Market 374 First-price auction 325 Patent Race for an Old Market 376 Fixed-dash theorem 403 Phd Admissions 144 Focal point 31-33, 36n, 89p The Png Settlement Game 59 Folk Theorem 112d, 120, 131n The Police Game 86n Follow the Leader game Predatory Pricing 383 I 39 Product Quality 119 II 49 Production Game I, II, III, IV, V, VI,VIa,VII 164, 169, III 51 211, 242 Forcing contract 167 Repossession Game I, II, III 194 Ford, Henry, wages 23 The Salesman Game 244 Forgiving strategy 152 Splitting a Pie 296 Forward induction 158p The Swiss Cheese Game 24 Free rider problem 378 Testing 232 Fully insured 197 Underpricing New Stock Issues 283 Fully revealing equilibrium 213, 246 The Utopian Exchange Economy Game 126 Function 396 The War of Attrition 72 Functional forms 400 The Welfare Game 67 Gang of Four 149 Game theory Generically 396, 404-06 history 1-2, 6-7n, 51 Good news 409 method 2 Government Procurement game 255 Game tree 15, 40d Grab the Dollar game 73, 135p Games--in general Greek alphabet 395 cooperative vs. noncooperative 21 Greenmail 380 zero- vs variable-sum 25d, 34n Grim strategy 111d, 135p Games--specific games Groves mechanism 261, 264n Alternating Offers 299, 320 Auditing Game I, II, III 79, 86n Harsanyi doctrine 53, 62 Battle of the Bismarck Sea21, 34n Harsanyi transformation 51, 63n Beer-Quiche 155n Hawk-Dove game 127 Benoit-Krishna 134p Hidden actions 161 Bilateral Trading I, II, III, IV 309, 321n Hidden knowledge 161, 179n, 241 Boxed Pigs 25, 35 Hold-up potential 193 Broadway Game I, II 174, 178 Hotelling models 350 Chicken 71, 85n Civic Duty 78 Imperfect information 47d, 63n Colonel Blotto 87n Imperfectly separating equilibrium 213 Cournot Game 81 Implicit function theorem 358 Customer Switching Costs 123 Implementing mechanism 241 Dangerous Coordination 30 Incentive compatibility 121, 173, 213 Discoordination 37p Incomplete information 50d, 51, 97 Dollar Auction 336n Incomplete information folk theorem 151d Individual rationality constraint 181n Minimax strategy 114d Infimum 394 Minimax Theorem 116 Infinite-horizon model 119, 130n Minimax value 114d Infinitely repeated game 119 Mixed extension 67d Information partition 45d Mixed strategy 66-81, 237p, 287 Information set 43d the payoff-equating method 71 Informational rents 248, 260 correlated strategies 74 Informed player 162 versus randomizing 80 Innovation 372, 390n Modeller's Dilemma game 27 Insurance 46, 99, 182n, 196, 222, 230, 235n, 237p Monitoring 86n, 207p, 208p Insurance Game Monotone likelihood ratio property 181n I and II 197 Monty Hall Problem 64p III 222 Moral hazard 132n, 161-210 Intensity rationing 345d, 367n Moral
Recommended publications
  • Game Theory Lecture Notes

    Game Theory Lecture Notes

    Game Theory: Penn State Math 486 Lecture Notes Version 2.1.1 Christopher Griffin « 2010-2021 Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License With Major Contributions By: James Fan George Kesidis and Other Contributions By: Arlan Stutler Sarthak Shah Contents List of Figuresv Preface xi 1. Using These Notes xi 2. An Overview of Game Theory xi Chapter 1. Probability Theory and Games Against the House1 1. Probability1 2. Random Variables and Expected Values6 3. Conditional Probability8 4. The Monty Hall Problem 11 Chapter 2. Game Trees and Extensive Form 15 1. Graphs and Trees 15 2. Game Trees with Complete Information and No Chance 18 3. Game Trees with Incomplete Information 22 4. Games of Chance 24 5. Pay-off Functions and Equilibria 26 Chapter 3. Normal and Strategic Form Games and Matrices 37 1. Normal and Strategic Form 37 2. Strategic Form Games 38 3. Review of Basic Matrix Properties 40 4. Special Matrices and Vectors 42 5. Strategy Vectors and Matrix Games 43 Chapter 4. Saddle Points, Mixed Strategies and the Minimax Theorem 45 1. Saddle Points 45 2. Zero-Sum Games without Saddle Points 48 3. Mixed Strategies 50 4. Mixed Strategies in Matrix Games 53 5. Dominated Strategies and Nash Equilibria 54 6. The Minimax Theorem 59 7. Finding Nash Equilibria in Simple Games 64 8. A Note on Nash Equilibria in General 66 Chapter 5. An Introduction to Optimization and the Karush-Kuhn-Tucker Conditions 69 1. A General Maximization Formulation 70 2. Some Geometry for Optimization 72 3.
  • Frequently Asked Questions in Mathematics

    Frequently Asked Questions in Mathematics

    Frequently Asked Questions in Mathematics The Sci.Math FAQ Team. Editor: Alex L´opez-Ortiz e-mail: [email protected] Contents 1 Introduction 4 1.1 Why a list of Frequently Asked Questions? . 4 1.2 Frequently Asked Questions in Mathematics? . 4 2 Fundamentals 5 2.1 Algebraic structures . 5 2.1.1 Monoids and Groups . 6 2.1.2 Rings . 7 2.1.3 Fields . 7 2.1.4 Ordering . 8 2.2 What are numbers? . 9 2.2.1 Introduction . 9 2.2.2 Construction of the Number System . 9 2.2.3 Construction of N ............................... 10 2.2.4 Construction of Z ................................ 10 2.2.5 Construction of Q ............................... 11 2.2.6 Construction of R ............................... 11 2.2.7 Construction of C ............................... 12 2.2.8 Rounding things up . 12 2.2.9 What’s next? . 12 3 Number Theory 14 3.1 Fermat’s Last Theorem . 14 3.1.1 History of Fermat’s Last Theorem . 14 3.1.2 What is the current status of FLT? . 14 3.1.3 Related Conjectures . 15 3.1.4 Did Fermat prove this theorem? . 16 3.2 Prime Numbers . 17 3.2.1 Largest known Mersenne prime . 17 3.2.2 Largest known prime . 17 3.2.3 Largest known twin primes . 18 3.2.4 Largest Fermat number with known factorization . 18 3.2.5 Algorithms to factor integer numbers . 18 3.2.6 Primality Testing . 19 3.2.7 List of record numbers . 20 3.2.8 What is the current status on Mersenne primes? .
  • Lecture Notes

    Lecture Notes

    GRADUATE GAME THEORY LECTURE NOTES BY OMER TAMUZ California Institute of Technology 2018 Acknowledgments These lecture notes are partially adapted from Osborne and Rubinstein [29], Maschler, Solan and Zamir [23], lecture notes by Federico Echenique, and slides by Daron Acemoglu and Asu Ozdaglar. I am indebted to Seo Young (Silvia) Kim and Zhuofang Li for their help in finding and correcting many errors. Any comments or suggestions are welcome. 2 Contents 1 Extensive form games with perfect information 7 1.1 Tic-Tac-Toe ........................................ 7 1.2 The Sweet Fifteen Game ................................ 7 1.3 Chess ............................................ 7 1.4 Definition of extensive form games with perfect information ........... 10 1.5 The ultimatum game .................................. 10 1.6 Equilibria ......................................... 11 1.7 The centipede game ................................... 11 1.8 Subgames and subgame perfect equilibria ...................... 13 1.9 The dollar auction .................................... 14 1.10 Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem ... 15 2 Strategic form games 17 2.1 Definition ......................................... 17 2.2 Nash equilibria ...................................... 17 2.3 Classical examples .................................... 17 2.4 Dominated strategies .................................. 22 2.5 Repeated elimination of dominated strategies ................... 22 2.6 Dominant strategies ..................................
  • The Monty Hall Problem in the Game Theory Class

    The Monty Hall Problem in the Game Theory Class

    The Monty Hall Problem in the Game Theory Class Sasha Gnedin∗ October 29, 2018 1 Introduction Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice? With these famous words the Parade Magazine columnist vos Savant opened an exciting chapter in mathematical didactics. The puzzle, which has be- come known as the Monty Hall Problem (MHP), has broken the records of popularity among the probability paradoxes. The book by Rosenhouse [9] and the Wikipedia entry on the MHP present the history and variations of the problem. arXiv:1107.0326v1 [math.HO] 1 Jul 2011 In the basic version of the MHP the rules of the game specify that the host must always reveal one of the unchosen doors to show that there is no prize there. Two remaining unrevealed doors may hide the prize, creating the illusion of symmetry and suggesting that the action does not matter. How- ever, the symmetry is fallacious, and switching is a better action, doubling the probability of winning. There are two main explanations of the paradox. One of them, simplistic, amounts to just counting the mutually exclusive cases: either you win with ∗[email protected] 1 switching or with holding the first choice.
  • Paper and Pencils for Everyone

    Paper and Pencils for Everyone

    (CM^2) Math Circle Lesson: Game Theory of Gomuku and (m,n,k-games) Overview: Learning Objectives/Goals: to expose students to (m,n,k-games) and learn the general history of the games through out Asian cultures. SWBAT… play variations of m,n,k-games of varying degrees of difficulty and complexity as well as identify various strategies of play for each of the variations as identified by pattern recognition through experience. Materials: Paper and pencils for everyone Vocabulary: Game – we will create a working definition for this…. Objective – the goal or point of the game, how to win Win – to do (achieve) what a certain game requires, beat an opponent Diplomacy – working with other players in a game Luck/Chance – using dice or cards or something else “random” Strategy – techniques for winning a game Agenda: Check in (10-15min.) Warm-up (10-15min.) Lesson and game (30-45min) Wrap-up and chill time (10min) Lesson: Warm up questions: Ask these questions after warm up to the youth in small groups. They may discuss the answers in the groups and report back to you as the instructor. Write down the answers to these questions and compile a working definition. Try to lead the youth so that they do not name a specific game but keep in mind various games that they know and use specific attributes of them to make generalizations. · What is a game? · Are there different types of games? · What make something a game and something else not a game? · What is a board game? · How is it different from other types of games? · Do you always know what your opponent (other player) is doing during the game, can they be sneaky? · Do all of games have the same qualities as the games definition that we just made? Why or why not? Game history: The earliest known board games are thought of to be either ‘Go’ from China (which we are about to learn a variation of), or Senet and Mehen from Egypt (a country in Africa) or Mancala.
  • Game, Set, and Match Carl W

    Game, Set, and Match Carl W

    Game, Set, and Match Carl W. Lee September 2016 Note: Some of the text below comes from Martin Gardner's articles in Scientific American and some from Mathematical Circles by Fomin, Genkin, and Itenberg. 1 1 Fifteen This is a two player game. Take a set of nine cards, numbered one (ace) through nine. They are spread out on the table, face up. Players alternately select a card to add their hands, which they keep face up in front of them. The goal is to achieve a subset of three cards in your hand so that the values of these three cards sum to exactly fifteen. (The ace counts as 1.) This is an example of a game that is isomorphic to (the \same as") a well-known game: Tic-Tac-Toe. Number the cells of a tic-tac-toe board with the integers from 1 to 9 arranged in the form of a magic square. 8 1 6 3 5 7 4 9 2 Then winning combinations correspond exactly to triples of numbers that sum to 15. This is a combinatorial two person game (but one that permits ties). There is no hidden information (e.g., cards that one player has that the other cannot see) and no random elements (e.g., rolling of dice). 2 2 Ones and Twos Ten 1's and ten 2's are written on a blackboard. In one turn, a player may erase (or cross out) any two numbers. If the two numbers erased are identical, they are replaced with a single 2.
  • Understanding Emotions in Electronic Auctions: Insights from Neurophysiology

    Understanding Emotions in Electronic Auctions: Insights from Neurophysiology

    Understanding Emotions in Electronic Auctions: Insights from Neurophysiology Marc T. P. Adam and Jan Krämer Abstract The design of electronic auction platforms is an important field of electronic commerce research. It requires not only a profound understanding of the role of human cognition in human bidding behavior but also of the role of human affect. In this chapter, we focus specifically on the emotional aspects of human bidding behavior and the results of empirical studies that have employed neurophysiological measurements in this regard. By synthesizing the results of these studies, we are able to provide a coherent picture of the role of affective processes in human bidding behavior along four distinct theoretical pathways. 1 Introduction Electronic auctions (i.e., electronic auction marketplaces) are information systems that facilitate and structure the exchange of products and services between several potential buyers and sellers. In practice, electronic auctions have been employed for a wide range of goods and services, such as commodities (e.g., Internet consumer auction markets, such as eBay.com), perishable goods (e.g., Dutch flower markets, such as by Royal FloraHolland), consumer services (e.g., procurement auction markets, such as myhammer.com), or property rights (e.g., financial double auction markets such as NASDAQ). In this vein, a large share of our private and commercial economic activity is being organized through electronic auctions today (Adam et al. 2017;Kuetal.2005). Previous research in information systems, economics, and psychology has shown that the design of electronic auctions has a tremendous impact on the auction M. T. P. Adam College of Engineering, Science and Environment, The University of Newcastle, Callaghan, Australia e-mail: [email protected] J.
  • Introduction to Probability 1 Monty Hall

    Introduction to Probability 1 Monty Hall

    Massachusetts Institute of Technology Course Notes, Week 12 6.042J/18.062J, Fall ’05: Mathematics for Computer Science November 21 Prof. Albert R. Meyer and Prof. Ronitt Rubinfeld revised November 29, 2005, 1285 minutes Introduction to Probability Probability is the last topic in this course and perhaps the most important. Many algo­ rithms rely on randomization. Investigating their correctness and performance requires probability theory. Moreover, many aspects of computer systems, such as memory man­ agement, branch prediction, packet routing, and load balancing are designed around probabilistic assumptions and analyses. Probability also comes up in information theory, cryptography, artificial intelligence, and game theory. Beyond these engineering applica­ tions, an understanding of probability gives insight into many everyday issues, such as polling, DNA testing, risk assessment, investing, and gambling. So probability is good stuff. 1 Monty Hall In the September 9, 1990 issue of Parade magazine, the columnist Marilyn vos Savant responded to this letter: Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what’s behind the doors, opens another door, say number 3, which has a goat. He says to you, ”Do you want to pick door number 2?” Is it to your advantage to switch your choice of doors? Craig. F. Whitaker Columbia, MD The letter roughly describes a situation faced by contestants on the 1970’s game show Let’s Make a Deal, hosted by Monty Hall and Carol Merrill.
  • The Monty Hall Problem

    The Monty Hall Problem

    The Monty Hall Problem Richard D. Gill Mathematical Institute, University of Leiden, Netherlands http://www.math.leidenuniv.nl/∼gill 17 March, 2011 Abstract A range of solutions to the Monty Hall problem is developed, with the aim of connecting popular (informal) solutions and the formal mathematical solutions of in- troductory text-books. Under Riemann's slogan of replacing calculations with ideas, we discover bridges between popular solutions and rigorous (formal) mathematical solutions by using various combinations of symmetry, symmetrization, independence, and Bayes' rule, as well as insights from game theory. The result is a collection of intuitive and informal logical arguments which can be converted step by step into formal mathematics. The Monty Hall problem can be used simultaneously to develop probabilistic intuition and to give a deeper understanding of the paradox, not just to provide a routine exercise in computation of conditional probabilities. Simple insights from game theory can be used to prove probability inequalities. Acknowledgement: this text is the result of an evolution through texts written for three internet encyclopedias (wikipedia.org, citizendium.org, statprob.com) and each time has benefitted from the contributions of many other editors. I thank them all, for all the original ideas in this paper. That leaves only the mistakes, for which I bear responsibility. 1 Introduction Imagine you are a guest in a TV game show. The host, a certain Mr. Monty Hall, shows you three large doors and tells you that behind one of the doors there is a car while behind the other two there are goats. You want to win the car.
  • Introduction to Game Theory I

    Introduction to Game Theory I

    Introduction to Game Theory I Presented To: 2014 Summer REU Penn State Department of Mathematics Presented By: Christopher Griffin [email protected] 1/34 Types of Game Theory GAME THEORY Classical Game Combinatorial Dynamic Game Evolutionary Other Topics in Theory Game Theory Theory Game Theory Game Theory No time, doesn't contain differential equations Notion of time, may contain differential equations Games with finite or Games with no Games with time. Modeling population Experimental / infinite strategy space, chance. dynamics under Behavioral Game but no time. Games with motion or competition Theory Generally two player a dynamic component. Games with probability strategic games Modeling the evolution Voting Theory (either induced by the played on boards. Examples: of strategies in a player or the game). Optimal play in a dog population. Examples: Moves change the fight. Chasing your Determining why Games with coalitions structure of a game brother across a room. Examples: altruism is present in or negotiations. board. The evolution of human society. behaviors in a group of Examples: Examples: animals. Determining if there's Poker, Strategic Chess, Checkers, Go, a fair voting system. Military Decision Nim. Equilibrium of human Making, Negotiations. behavior in social networks. 2/34 Games Against the House The games we often see on television fall into this category. TV Game Shows (that do not pit players against each other in knowledge tests) often require a single player (who is, in a sense, playing against The House) to make a decision that will affect only his life. Prize is Behind: 1 2 3 Choose Door: 1 2 3 1 2 3 1 2 3 Switch: Y N Y N Y N Y N Y N Y N Y N Y N Y N Win/Lose: L W W L W L W L L W W L W L W L L W The Monty Hall Problem Other games against the house: • Blackjack • The Price is Right 3/34 Assumptions of Multi-Player Games 1.
  • The Monty Hall Problem Yurixy Lopez Martinez a Project Presented for The

    The Monty Hall Problem Yurixy Lopez Martinez a Project Presented for The

    The Monty Hall Problem Yurixy Lopez Martinez A project presented for the degree of Bachelors of Arts, Mathematics Mathematics Department Whitman College Walla Walla, WA May 10, 2019 Abstract This paper begins by offering a detailed explanation of the solution to the Monty Hall Problem utilizing decision trees and mathematical concepts of conditional probability, mainly Bayes' Theorem. We will proceed to investigate the various versions of the problem that have risen throughout the years among scholars, mainly focusing on the benefits of a particular strategies. We will conclude by briefly discussing some applications of the Monty Hall Problem to other disciplines, mainly the probabilistic aspects. 1 Contents 1 Introduction 3 2 Monty Hall Problem 4 3 Why Switch? 5 4 Conditional Probability: Bayes' Theorem 7 5 Bayesian Monty 9 6 Variations of the Monty Hall Problem 10 6.1 Monty Chooses Randomly . 10 6.2 Highest-Ordered Selection . 11 6.3 Many doors . 14 6.3.1 Alternative Solution . 16 6.4 Many Doors, Many Cars . 17 6.5 Random Car Placement . 18 6.6 Two Contestants . 19 7 Applications of Monty Hall Problem 19 7.1 Philosophy . 20 7.2 Physics . 20 7.3 Economics . 21 7.4 Cognitive Science and Psychology . 21 8 Conclusion 21 9 Acknowledgements 22 2 1 Introduction The Monty Hall Problem is a recognized probability problem. The canonical, classical version of the problem is described as follows: A contestant is shown three identical doors. Behind one of them is a car. The other two conceal goats. The contestant is asked to choose, but not open, one of the doors.
  • The Monty Hall Problem As a Bayesian Game

    The Monty Hall Problem As a Bayesian Game

    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 25 May 2017 doi:10.20944/preprints201705.0187.v1 Peer-reviewed version available at Games 2017, 8, 31; doi:10.3390/g8030031 The Monty Hall Problem as a Bayesian Game Mark Whitmeyer∗ Department of Economics, University of Texas at Austin, Austin, TX 78712, USA Abstract This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty's motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty, and show that under certain conditions on p, the unique equilibrium is one where the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. Finally, we show that our formulation can explain the experimental results in Page (1998) [12]; that more people gradually choose switch as the number of doors in the problem increases. Keywords: Monty Hall; Equiprobability Bias; games of incomplete information; Bayes Nash Equilibrium JEL Classification: C60, C72, D81, D82 ∗Email: [email protected] 1 © 2017 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 25 May 2017 doi:10.20944/preprints201705.0187.v1 Peer-reviewed version available at Games 2017, 8, 31; doi:10.3390/g8030031 1 Introduction The \Monty Hall" problem is a famous scenario in decision theory.