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academicearth
Introduction to Game Theory

By Benjamin Polak - Yale

Course Index

• 1.Introduction to Game Theory
• 2.Putting Yourselves into Other People's Shoes
• 3.Iterative Deletion and the Median-Voter Theorem
• 4.Best Responses in Soccer and Business Partnerships
• 5.Nash Equilibrium
• 6.Nash Equilibrium: Dating and Cournot
• 7.Nash Equilibrium: Shopping, Standing and Voting on a Line
• 8.Nash Equilibrium: Location, Segregation and Randomization
• 9.Mixed Strategies in Theory and Tennis
• 10.Mixed Strategies in Baseball, Dating and Paying Your Taxes
• 11.Evolutionary Stability: Cooperation, Mutation, and Equilibrium
• 12.Evolutionary Stability: Social Convention, Aggression, and Cycles
• 13.Sequential Games: Moral Hazard, Incentives, and Hungry Lions
• 14.Backward Induction: Commitment, Spies, and First-Mover Advantages
• 15.Backward Induction: Chess, Strategies, and Credible Threats
• 16.Backward Induction: Reputation and Duels
• 17.Backward Induction: Ultimatums and Bargaining
• 18.Imperfect Information: Information Sets and Sub-Game Perfection
• 19.Subgame Perfect Equilibrium: Matchmaking and Strategic Investments
• 20.Subgame Perfect Equilibrium: Wars of Attrition
• 21.Repeated Games: Cooperation vs the End Game
• 22.Repeated Games: Cheating, Punishment, and Outsourcing
• 23.Asymmetric Information: Silence, Signaling and Suffering Education
• 24.Asymmetric Information: Auctions and the Winner's Curse

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buffalo
Recent Advances in Game Theory and Political Science

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canterbury
History of Game Theory

A Chronology of Game Theory
byPaul Walker
October 2005
| Ancient | 1700 | 1800 | 1900 | 1950 | 1960 | 1970 | 1980 | 1990 | Nobel Prize | 2nd Nobel Prize |

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dklevine
What is Game Theory?

by David K. Levine, Department of Economics, UCLA
...

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Game theory (W3)

The Good, the Bad, and the Ugly
Review contributed by Phil Mellinger

I think that the final scene in this Clint Eastwood movie is the most outstanding example of game theory. Three men in a triangle -- each with a gun, a rock at the center of the three. It is up to each man to evaluate his situation. All are excellent shots. Who do they shoot?

Clint has supposedly put a message on a rock that holds the key to everything, but do the other two trust Clint to have actually written the correct answer? As the other two evaluate the situation, they realize they can't trust Clint to have written the answer on the rock - therefore they can't shoot Clint who likely still has the answer. That means the other two can only shoot each other, but only one will likely hit before the other.

What they don't know is that Clint has given one an unloaded gun... Clint can ignore this one. The one Clint has to worry about with the loaded gun will try to kill the one with the unloaded gun. Neither will fire at Clint. Clint will fire at the one with the loaded gun. As the camera passes from one face to the other the audience is meant to figure out what each would do.

The guy with the loaded gun shoots at the guy with the unloaded gun - Clint shoots the guy with the loaded gun. Game over. As with the hangings in the movie, he has dangled Duco out as bait while Clint takes the money.

The game is decided before it starts.

Clint sets up a situation where each evaluates their possible moves, but in reality, Clint has already won the game. Its a brilliant example of people making the best decisions based on the information available to them... and somebody manipulating the information available to them.

Phil Mellinger, 2002

How Game Theory Works
by Tom Scheve

Inside this Article

• 1.Introduction to How Game Theory Works
• 3.Games
• 4.Using a Game Tree
• 5.One-shot Games vs. Repeated Games
• 6.Game Theory and the Cold War
• 7.Other Games and Applications
• 8.Criticisms of Game Theory
• 9.Lots More Information

• 052043 2005-07-15 16:03 131 Re: peeties and more dice slang
• 032709 2003-07-09 15:15 49 Re: Farkling/farggling
• 032711 2003-07-09 14:14 49 Re: Farkling/farggling
• 014496 2001-04-12 19:26 31 Re: THEORY OF GAMES, 1944
• 014483 2001-04-12 11:26 19 Re: game theory
• 014459 2001-04-11 11:48 31 Re: THEORY OF GAMES, 1944
• 014456 2001-04-11 08:42 63 Re: THEORY OF GAMES, 1944
• 014457 2001-04-11 08:28 176 Re: THEORY OF GAMES, 1944
• 014443 2001-04-10 18:40 41 Re: THEORY OF GAMES, 1944
• 014441 2001-04-10 14:39 41 Re: THEORY OF GAMES, 1944
• 014433 2001-04-10 10:28 83 Re: THEORY OF GAMES, 1944
• 014430 2001-04-10 09:28 16 Re: THEORY OF GAMES, 1944
• 014429 2001-04-10 09:10 134 Re: THEORY OF GAMES, 1944
• 014423 2001-04-09 22:35 88 Re: THEORY OF GAMES, 1944
• 014411 2001-04-09 12:38 32 Re: THEORY OF GAMES, 1944
• 014410 2001-04-09 12:00 73 THEORY OF GAMES, 1944
• 014412 2001-04-09 11:33 135 Re: THEORY OF GAMES, 1944
• 014392 2001-04-08 22:46 39 Re: Game Theory
• 014390 2001-04-08 20:55 33 Re: Game Theory
• 014385 2001-04-08 16:19 35 Re: Game Theory
• 014382 2001-04-08 15:48 34 Re: Game Theory
• 014378 2001-04-07 19:54 34 Game Theory
• 014242 2001-04-02 20:19 25 Re: Win-Win (1963)
• 014224 2001-04-02 09:12 83 Re: Win-Win (1963)

Mathematical Programming and Operations Research

• Game Theory [173]

Game Theory

First published Sat Jan 25, 1997; substantive revision Wed May 5, 2010

Game theory is the study of the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents. The meaning of this statement will not be clear to the non-expert until each of the italicized words and phrases has been explained and featured in some examples. Doing this will be the main business of this article. First, however, we provide some historical and philosophical context in order to motivate the reader for the technical work ahead.

• 1. Philosophical and Historical Motivation
• 2. Basic Elements and Assumptions of Game Theory?2.1 Utility
• 2.2 Games and Information
• 2.3 Trees and Matrices
• 2.5 Solution Concepts and Equilibria
• 2.6 Subgame Perfection
• 2.7 On Interpreting Payoffs: Morality and Efficiency in Games
• 2.8 Trembling Hands
• 3. Uncertainty, Risk and Sequential Equilibria?3.1 Beliefs
• 4. Repeated Games and Coordination
• 5. Commitment
• 6. Evolutionary Game Theory
• 7. Game Theory and Behavioral Evidence?7.1 Game Theory in the Laboratory
• 7.2 Neuroeconomics and Game Theory
• 7.3 Game Theoretic Models of Human Nature
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

Rational Choice & Game Theories

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gametheory
Glossary of game theory terms
Game theory Glossary

• A: absolute auctionall-pay auctionassurance game (technical)asynchronyauctionauction theoryauctionsAntoine Augustin Cournot
• B: backward inductionbattle of the sexes (informal)battle of the sexes (technical)Bayes RuleBayes TheoremBayes, ThomasBernoulli, Danielbest reply dynamicbidbid riggingbidderbidder's choice Auctionbidding incrementbidding ringblind auctionBorel, Emilebusiness strategybutton auction
• C: cardinal payoffsChicken, Game of (technical)Chinese auctioncollusion in auctionscombinatorial auctioncombinatorial bidcombinatorial game theorycommon knowledgecomplete informationconstant sum gamecooperative gamecoordination game, pure (technical)Cournot, Antoine AugustinCournot learning
• D: Daniel BernoulliDeadlock game (technical)discriminatory auctiondominant strategydominant strategy, strictlydominant strategy, weaklydominated strategydynamic gameDutch auction
• E: Edgeworth, FrancisEmile BorelEnglish auctionefficiencyequilibriumequilibrium refinementevolutionary game theoryexperimental economicsextensive form
• F: fictitious playfirst price auctionfixed price auctionFrancis Edgeworthfree riderfree rider problem
• G: gamegame of assurance (technical)game of chicken (technical)game of Nimgame treegrim trigger strategy
• H: Hawk-Dove game (technical)heuristicHicks, JohnHicks optimalhistory of game theory
• I: incentiveinformation, completeinformation, imperfectinformation, perfectiterated gameimperfect information
• J: Japanese auctionJohn HicksJohn NashJohn von NeumannJulia Robinson
• K: Kakutani, Shizuoknowledge, commonknowledge, mutual
• L: learning, Cournot
• M: matching pennies (technical)minimum bidmixed strategymixed strategy, totallyMorgenstern, Oskarmultiple item auctionmultiunit auctionmutual knowledge
• N: Nash, JohnNash equilibriumNash equilibrium, subgame perfectnaturenature playerNeumann, John vonNimNim Gamenon-cooperative gamenon-credible threatnormal form
• O: ordinal payoffsordinally symmetric game (technical)Oskar Morgensternoutcome
• P: Pareto, Vilfredo Pareto coordination game (technical) Pareto dominated Pareto efficient Pareto optimal payoff payoffs Perfect Information player player, naturepositive sum gameprincipal agent procurement auction proxy bidder pure coordination game (technical) pure strategy
• Q:
• R: rationalityrefinementrepeated gamereserve pricereverse auctionringRobinson, JuliaRock Paper Scissors (technical)rollback
• S: schedule bidsealed bid auctionsecond price auctionsequential gameShizuo Kakutanisimultaenous gamesingle unit auctionstag hunt game (technical)static gamestraight auctionstrategic formstrategic managementstrategystrategy, mixedstrategy, purestrictly dominant strategysubgamesubgame perfectsymmetric game
• T: Thomas Bayesthreat, noncredibletit for tattotally mixed strategytrigger strategy
• U: uniform price auctionutility
• V: variable sum gameVickrey auctionVickrey, WilliamVilfredo Pareto Volunteer's Dilemma (technical) von Neumann, John
• W: weakly dominant strategyWilliam Vickrey
• X:
• Y: Yankee auction
• Z: zero sum game

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harvard
Game Theory, Experimental Economics, and Market Design Page

Al Roth's

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Prisoners' Dilemma (W3)

prisoner’s dilemma (game theory)
...

You Have Found The Prisoners' Dilemma

A fiendish cyberspace wizard has locked you and Serendip into a diabolical game with the following rules:
...

Mathematics and Biology
...
... The nice guys finish first, to the favorite puzzle [Costi] of game theory - the Prisoner's Dilemma. As described in Pinker:

Partners in crime are held in separate cells, and the prosecutor offers each one a deal. If you rat on your partner and he stays mum, you go free and he gets ten years. If you both stay mum, you both get six months. If you both rat, you both get five years. The partners cannot communicate, and neither knows what the other will do. Each one thinks: If my partner rats and I stay mum, I'll do ten years; if he rats and I rat, too, I'll do five years. If he stays mum and I stay mum, I'll do six months; if he stays mum and I rat, I'll go free. Regardless of what he does, then, I'm better off betraying him. Each is compelled to turn in his partner, and they both serve five years-far worse than if each had trusted the other. But neither could take the chance because of the punishment he would incur if the other didn't. Social psychologists, mathematicians, economists, moral philosophers, and nuclear strategists have fretted over the paradox for decades. There is no solution.

There is no solution for a single trial. But, repeated trials allow players - partners in crime - to observe and study each other's behavior and develop a better paying strategy. Dawkins describes two competitions organized by Robert Axelrod that showed superiority of a simple strategy Tit for Tat: start mum, then do what your opponent did on the previous trial. In general, strategies were divided into two classes: nice and nasty. An adherent of a nice strategy never rats first, a nasty fellow does. It so happened that, on the whole, nice strategies outperformed the nasty ones.
...

prisoner's dilemma, noun

(in game theory) a scenario in which the outcome of one person's decision is determined by the simultaneous decisions of the other participants, resulting in a bad outcome for all of them if all act in their own self-interest.
...

A favourite example in GAME THEORY, which shows why co-operation is difficult to achieve even when it is mutually beneficial.
...

Prisoners' Dilemma (informal)

Prisoner's Dilemma (technical)

"Prisoner's Dilemma" will be familiar to many people from the extended treatment Richard Dawkins gives it in his classic popular science work The Selfish Gene. It is a fairly simple problem which has, since it first came to prominence in the 1950s, exercised and exasperated the minds of people drawn from such diverse fields as political science, economics, social psychology and philosophy.

What is the Dilemma?

The basic problem at the heart of the dilemma is the question, 'How can co-operation emerge among rational, self-interested individuals without there being any form of central authority imposed on them?'. In other words, it can be seen as an attempt to find a secular, rational alternative to old-fashioned 'top-down' moral codes such as those of religious doctrines.

The term is used to refer to any situation in which there appears to be a conflict between the rational individual's self-interest and the common good. The basic premise underpinning the Prisoner's Dilemma is the Darwinian insight that human beings are essentially selfish creatures genetically programmed to place their own survival above all other considerations. However, an individual who works against the 'common good' can in fact be undermining the very foundations on which his/her own self-interest can thrive. An example of this being the continued short-sighted waste of the planet's resources by us as individuals, without taking the wider view that, since everyone else is doing the same, there may soon be little left of the planet for us to live on.
...

The Prisoner's Dilemma

One of the best ways to understand some basic game theory principles is to look at a classic game theory example: the prisoner's dilemma. This game examines how two players interact based on an understanding of motives and strategies. The prisoner's dilemma is a game that concerns two players -- both suspects in a crime. They're arrested and brought to a police station. If both suspects protect each other by staying quiet (called cooperation in game theory terms), the police have only enough evidence to put each in jail for five years.

However, each suspect is offered a deal. If either one confesses (defection from a cooperative relationship), and the other suspect doesn't, the defector will be rewarded with freedom, while the tight-lipped suspect will get 20 years in jail. If both confess, both get 10 years in jail.
...

What Is the Prisoner's Dilemma and How Does It Work?

The prisoner's dilemma is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome.
...
Understanding the Prisoner's Dilemma
...
Examples of the Prisoner's Dilemma
...
Escape from the Prisoner's Dilemma
...
What Is the Likely Outcome of a Prisoner's Dilemma?
...
What Are Some Ways to Combat the Prisoner's Dilemma?
...
Can the Prisoner's Dilemma Be Useful to Society?
...
What Is the Tragedy of the Commons?
...
The Bottom Line
...
Trading is a Journey, and We're With You at Every Step
...

prisoner's dilemma (classic problem)

Definition: Two prisoners are questioned separately about a crime they committed. Each may give evidence against the other or may say nothing. If both say nothing, they get a minor reprimand and go free because of lack of evidence. If one gives evidence and the other says nothing, the first goes free and the second is severely punished. If both give evidence, both are severely punished. The overall (globally) best strategy is for both to say nothing. However not knowing (or trusting) what the other will do, each prisoner's (locally) best strategy is to give evidence, which is the worst possible outcome.

In general, a situation where local optimization leads to the worst possible outcome globally.
...

The PRISONER'S DILEMMA was posed by A. W. Tucker in 1950, when addressing an audience of psychologists at Stanford University, where he was a visiting professor. The OED entry includes an account it received from Tucker, "The Prisoner's Dilemma is my brain child. I concocted it at Stanford in early 1950 as a catchy example to enliven a semi-popular talk on Game Theory... My example became known by the 'grapevine', but I did not publish it." It is discussed in the 1957 book by Luce & Raiffa Games & Decisions.

2.4 The Prisoner’s Dilemma as an Example of Strategic-Form vs. Extensive-Form Representation

Prisoner’s Dilemma (Steven Kuhn)

The Prisoners' Dilemma

Cooperation is usually analysed in game theory by means of a non-zero-sum game called the "Prisoner's Dilemma" (Axelrod, 1984). The two players in the game can choose between two moves, either "cooperate" or "defect". The idea is that each player gains when both cooperate, but if only one of them cooperates, the other one, who defects, will gain more. If both defect, both lose (or gain very little) but not as much as the "cheated" cooperator whose cooperation is not returned. The whole game situation and its different outcomes can be summarized by table 1, where hypothetical "points" are given as an example of how the differences in result might be quantified.
...

Prisoner's Dilemma

A problem in game theory first discussed by A. Tucker. Suppose each of two prisoners A and B, who are not allowed to communicate with each other, is offered to be set free if he implicates the other. If neither implicates the other, both will receive the usual sentence. However, if the prisoners implicate each other, then both are presumed guilty and granted harsh sentences.
...

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temple
Game Theory

An Introduction to Game Theory
with Economic Applications
by
Andrew J. Buck

• 1. A First Look
• A First Homework
• Cigarette Advertising
• 2. Strategic Form Games
• 3. Dominance Solvability
• Bertrand Duopoly
• 4. Nash Equilibrium
• Multiple Equilibria by Roger McCain
• Min-max
• Felix and Oscar: An Example of a Player's Best Response
• The Pizza Wars: An Example
• The Cola Wars: An example of a coordination problem
• Homework: IEDS - Nash - - Oil Wells
• 5. Tragedy of the Commons
• 6. Mixed Strategies
• Reason 1
• Reason 2
• Reason 3
• Solving Mixed Strategy Games
• Rock - Paper-Scissors
• Len Guienie and Al Dente go after the spaghetti market
• Frank and Kathy Lee go out
• 7. Mixed Strategy Applications
• Monopoly
• Bankruptcy
• Mixed Strategy Homework: A Day at the Beach
• Publishing: Lex E. Kahn v. Thea Soraus
• Market Niches
• Classic Strategic Form Games
• 8. Extensive Form Games
• Information and Extensive Form Games
• Backward Induction
• Commitment:
• The Proposal
• Kidnapped
• Netsoft versus Macroscape
• Kuhn's Theorem on Solvability
• Iterative Elimination and Backward Induction
• Poison Pills
• An Application: R&D
• Extensive Form Game Homework: Bush versus Gore
• The Duel: Hamilton versus Burr
• Career Decisions
• Normal Form and Extensive Form
• Credibility and Subgames
• 9. Sub-game Perfect Equilibrium
• Buck's Bolts: An Example
• George and Gina: An Example
• Treasury Bill Auctions: A Dynamic Game with Imperfect Information
• Subgame perfect equilibrium homework: Market Entry
• 10. Bilateral Trade: A Static Game in Strategic Form with Complete Information
• 11. Involuntary Unemployment: A Dynamic Game with Uncertainty
• 12. Time Consistent Monetary Policy: Making Credible Commitments
• 13. Static Games with Incomplete Information Part 1
• and Part 2
• Homework: Trade Relations
• Rob R. Baron and Bea Ware
• 14. Auctions
• Glossary
• 1st Pay
• 2nd Pay
• All Pay
• Selling State Liquor Stores
• Homework: Equivalence of Auctions
• All-pay Auction
• Other reading: Mester
• Lucking-Reiley
• 15. Dynamic Games with Incomplete Information
• Homework: The Value of Pedigree: Angie O'Plastie and Amanda Reckonwith
• Good Cars and Bad Cars
• 16. The Market for Lemons

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translationdirectory
Game Theory Glossary

Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. This is a glossary of some terms of the subject.

Definitions of a game

• Notational conventions
• Real numbers
• The set of players
• Strategy space
• Player i's strategy space
• A strategy for player i
• complements
• Outcome space
• Payoffs
• Normal form game
• A game in normal form is a function:
• Extensive form game
• Cooperative game
• Simple game

Glossary

• Acceptable game
• Allocation of goods
• Best reply
• Coalition
• Condorcet winner
• Dictator
• Dominated outcome
• Dominated strategy
• Dummy
• Effectiveness
• Finite game
• Grand coalition
• Mixed strategy
• Mixed Nash Equilibrium
• Pareto efficiency
• Preference profile
• Pure Nash Equilibrium
• Say
• Value
• Veto
• Weakly acceptable game
• Zero sum game

Published - February 2011

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umass
Game Theory Evolving

A Problem-centered Introduction to Evolutionary Game Theory
Second Edition (2009)
Herbert Gintis

For contractual reasons, only the first several pages of each chapter are available for download

• Introductory Material
• Preface
• Chapter 1: Game Theory: Probability Theory
• Chapter 2: Bayesian Decision Theory
• Chapter 3: Game Theory: Basic Concepts
• Chapter 4: Eliminating Dominated Strategies
• Chapter 5: Pure Strategy Nash Equilibria
• Chapter 6: Mixed Strategy Nash Equilibria
• Chapter 7: Principal-agent Models
• Chapter 8: Signaling Gameds
• Chapter 9: Evolutionarily Stable Strategies
• Chapter 10: Repeated Games
• Chapter 11: Dynamical Systems
• Chapter 12: Evolutionary Dynamics
• Chapter 13: Markov Economies and Stochastic Dynamical Systems
• Chapter 14: Table of Symbols
• Chapter 15: Answers
• Game Theory Evolving (First Edition, 2000)
• Errata for First Printing of Game Theory Evolving (2000)

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Majer, Ondrej (Herausgeber)
Pietarinen, Ahti-Veikko (Herausgeber)
Tulenheimo, Tero (Herausgeber)
Games: Unifying Logic, Language, and Philosophy
Logic, Epistemology, and the Unity of Science

Kurzbeschreibung
This volume presents mathematical game theory as an interface between logic and philosophy. It provides a discussion of various aspects of this interaction, covering new technical results and examining the philosophical insights that these have yielded. Organized in four sections it offers a balanced mix of papers dedicated to the major trends in the field: the dialogical approach to logic, Hintikka-style game-theoretic semantics, game-theoretic models of various domains (including computation and natural language) and logical analysis of game-theoretic situations. This volume will be of interest to any philosopher concerned with logic and language. It is also relevant to the work of argumentation theorists, linguists, economists, computer scientists and all those concerned with the foundational aspects of these disciplines.

Games: Unifying Logic, Language, and Philosophy
Series: Logic, Epistemology, and the Unity of Science , Vol. 15
Majer, Ondrej; Pietarinen, Ahti-Veikko; Tulenheimo, Tero (Eds.)
2009, XXIV, 380 p., Hardcover
ISBN: 978-1-4020-9373-9

Written for: Logicians, philosophers, mathematicians, linguists, computer scientists
Keywords: Computation | Dialogue | Game theory | Logic | Semantics