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Game Theory Through Examples.

By: Series: Classroom Resource MaterialsPublisher: Washington : American Mathematical Society, 1925Copyright date: ©1925Description: 1 online resource (308 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781614441151
Subject(s): Genre/Form: Additional physical formats: Print version:: Game Theory Through ExamplesDDC classification:
  • 519.3
LOC classification:
  • QA269 -- .P757 2014eb
Online resources:
Contents:
front cover -- Game Theory Through Examples -- copyright page -- Contents -- Preface -- Theory 1: Introduction -- What's a Game? -- Game, Play, Move: Some Definitions -- Classification of Games -- Exercises -- Theory 2: Simultaneous Games -- Normal Form---Bimatrix Description -- Two Players -- Two Players, Zero-sum -- Three or More Players -- Symmetric Games -- Which Option to Choose -- Maximin Move and Security Level -- Dominated Moves -- Best Response -- Nash Equilibria -- Additional Topics -- Best Response Digraphs -- 2-Player Zero-sum Symmetric Games -- Exercises -- Project 1: Reacting fast or slow -- Example: Selecting a Class -- Three Players, Two Classes -- ``I like you both'' -- Disliking the Rival -- Outsider -- Larger Cases -- Assumptions -- Exercises -- Project 2 -- Project 3 -- Project 4 -- Example: Doctor Location Games -- Doctor Location -- An Example Graph -- No (Pure) Nash Equilibrium? -- How Good are the Nash Equilibria for the Public? -- Trees -- More than one Office (optional) -- Exercises -- Project 5: Doctor location on MOPs -- Project 6 -- Project 7 -- Example: Restaurant Location Games -- A First Graph -- A Second Graph -- Existence of Pure Nash Equilibria -- More than one Restaurant (optional) -- Exercises -- Using Excel -- Spreadsheet Programs like Excel -- Two-Person Simultaneous Games -- Three-Person Simultaneous Games -- Exercises -- Project 8: Simultaneous Quatro-Uno -- Project 9: Restaurant Location Games -- Project 10: 5 Knights -- Project 11: 5 Cardinals -- Example: Election I -- First Example -- Second Example -- The General Model -- Third Example -- The Eight Cases -- Voting Power Indices (optional) -- Exercises -- Theory 3: Sequential Games I: Perfect Information and no Randomness -- Extensive Form: Game Tree and Game Digraph -- Analyzing the Game: Backward Induction -- Finite Games -- The Procedure.
Zermelo's Theorem -- Additional Topics -- Reality Check -- Playing it Safe---Guaranteed Payoffs -- Two-person Zero-sum Games -- Breaking Ties -- Existing Games -- Greedy Strategies -- Exercises -- Project 12: TAKE SOME -- Project 13: WHO's NEXT(n) -- Project 14: LISA's GAME -- Project 15: 2-AUCTION -- Project 16: 3-AUCTION -- Example: Dividing A Few Items I -- Greedy Strategy -- Backward Induction -- Game Tree -- Game Digraph -- Example: Game Digraph for ABBAB -- An Abbreviated Analysis -- Why it Matters: Complexity (optional) -- Bottom-Up Analysis -- Interdependencies between the Items (optional) -- Exercises -- Example: Shubik Auction I -- Exercises -- Project 17: SHUBIK AUCTION -- Example: Sequential Doctor and Restaurant Location -- General Observations for Symmetric Games -- Doctor Location -- Constant-Sum Games -- Restaurant Location -- Nash Equilibria and First Mover Advantage for Symmetric Games -- Exercises -- Project 18 -- Project 19: Hostile versus Friendly Play -- Theory 4: Probability -- Terminology -- Computing Probabilities -- Equally Likely Simple Events -- Simple Events not Equally Likely -- Expected Value -- Multistep Experiments -- Probability Trees -- Conditional Probabilities -- Probability Digraphs -- Randomness in Simultaneous Games -- Counting without Counting -- Exercises -- Project 20: Tennis -- Project 21: Final Exam -- France 1654 -- Exercises -- Example: DMA Soccer I -- 1-Round 2-Step Experiment for Given Player Distributions -- Expected Goal Difference for the One-Round Game -- 3-Rounds Experiment for Given Player Distributions -- Static Three-round Game -- Static Nine-round DMA Soccer -- Exercises -- Project 22: DMA6* Soccer -- Project 23: DMA7* Soccer -- Example: Dividing A Few Items II -- Goals of Fairness and Efficiency -- Fairness -- Efficiency -- Three Additional Features -- Mechanism Design -- Some Games.
Selecting one by one Games -- Cut and Choose -- Random and Exchange -- Examples -- Comparison of the Games for Seven Items and Complete Information -- Opposing or Similar Preferences -- Incomplete Information -- Exercises -- Project 24: Dividing five items A -- Project 25: Dividing five items B -- Theory 5: Sequential Games with Randomness -- Extensive Form Extended -- Analyzing the Game: Backward Induction again -- Decision Theory: Alone against Nature -- Exercises -- Project 26: Job Interviews -- Project 27: 5 Envelopes -- Project 28: Oh-No or Oh-No6 -- Project 29: 3 4 version of Polyomino REC THE SQUARE with randomness -- Example: Sequential Quiz Show I -- Candidates with Little Knowledge -- More May be Less -- One Candidate Knows More -- Cindy Knows one Answer to be False -- Exercises -- Project 30: SEQUENTIAL QUIZ SHOW, clever Ann -- Project 31: SEQUENTIAL QUIZ SHOW, clever Beth -- Las Vegas 1962 -- Exercises -- Example: Mini Blackjack and Card Counting -- The Basic Game -- Playing against the House -- How Likely are the Distributions? -- Betting High and Low -- Reshuffling -- Exercises -- Project 32: 8 ROUNDS BLACK OR WHITE -- Project 33: x ROUNDS RED, GREEN, OR BLUE -- Project 34: MINI BLACKJACK -- Example: Duel -- One Bullet -- Analysis of One-bullet Variants with Increasing Probabilities without Computer Help -- Analysis of DUEL(1,1|m, 2m, 3m, …) -- Two or more Bullets -- A few Cases of DUEL(2,2|m, 2m, 3m,…) -- Exercises -- Project 35: Drunk Adam -- Project 36: How more dangerous weapons affect the state budget and the health of citizens -- Project 37: Selecting m between 0.04 and 0.13 -- Project 38: What duels are best for society? -- Santa Monica in the 50s -- Theory 6: Extensive Form of General Games -- Extensive Form and Information Sets -- No Backward Induction for Imperfect Information -- Subgames -- Multi-round Games.
Why Trees for Imperfect Information? -- Exercises -- Example: Shubik Auction II -- Possible Sudden End -- Imperfect and Incomplete Information -- The Auctioneer Enters the Game (optional) -- Exercises -- Project 39 -- Project 40 -- Project 41: SHUBIK AUCTION(45, 35, 6, p) -- Project 42: SHUBIK AUCTION(A, B, C, n, p) -- Theory 7: Normal Form and Strategies -- Pure Strategies -- Reduced Pure Strategies -- Normal Form -- Using Tools from Simultaneous Games for the Normal Form -- Subgame Perfectness -- Special Case of Sequential Games with Perfect Information -- Exercises -- Example: VNM POKER and KUHN POKER -- Description -- VNM POKER -- KUHN POKER -- Exercises -- Example: Waiting for Mr. Perfect -- The Last Round -- The Eight Pure Strategies -- Computing the Payoffs -- Domination -- The Reduced Normal Forms in the Three Cases -- The Case p2+2p3 1 -- The Case p2+2p3 = 1 -- Project 43 -- Project 44 -- Project 45 -- Project 46 -- Project 47 -- Project 48 -- Theory 8: Mixed Strategies -- Mixed Strategies -- Best Response -- Brown's Fictitious Play -- Mixed Maximin Strategy, Mixed Security Level, and Linear Programs -- Mixed Nash Equilibria -- Two-player Zero-sum Games -- Non-Zero-sum Games -- Computing Mixed Nash Equilibria -- Small Two-player Zero-sum Games (optional) -- Solving Small non Zero-sum Two-player Games by Solving Equations (optional) -- Exercises -- Project 49: Balanced 3-spinner duel with five options -- Project 50: Balanced 3-spinner duel -- Project 51: COLONEL BLOTTO(4, 9, 9) -- Project 52: Iterated COLONEL BLOTTO -- Project 53: Simultaneous Quatro-Uno -- Project 54 -- Project 55: 4-round Waiting for Mr. Perfect -- Princeton in 1950 -- Example: Airport Shuttle -- The Simple Model -- To the Airport -- From the Airport -- Combining Both -- Impatient Customers -- Exercises -- Example: Election II.
Left Over from Election I -- More Effort into Large Districts -- Defend Where Ahead or Attack Where Weak? -- Is Larger Better? -- ELECTION(7,8,13|-1,-1,2|x,x) -- Exercises -- Example: VNM POKER(2, r, m, n) -- The Case n m 2 - 1 r -- Best Responses -- Reading the Opponent (optional) -- Mixed Nash Equilibrium for n m 2-1 r -- Small Changes in the Parameters -- Exercises -- Theory 9: Behavioral Strategies -- Behavioral versus Mixed Strategies -- Calculating Mixed Strategies from Behavioral Strategies -- Calculating Behavioral Strategies from Mixed Strategies for a Game Tree with Perfect Recall -- Kuhn's Theorem -- Exercises -- Example: Multiple-Round Chicken -- Ordinary Chicken -- Two-round Chicken -- Generalized Backward Induction, using the Extensive Form -- Working with the Normal Form -- Connections between the two Approaches -- Three-round Chicken -- Exercises -- Project 56 -- Project 57 -- Project 58 -- Example: DMA Soccer II -- Multi-round Simultaneous Games -- Information Sets and Moves -- The Optimal Third Move in Selected Cases -- A Detailed Example: (2, 2) versus (3, 1) -- A Second Example: (1, 3) versus (2, 2) -- The Optimal Second Move for Seven Positions -- Couldn't We Analyze the Whole Game? -- How Good a Model is it? -- Example: Sequential Quiz Show II -- Fixed Coalitions -- Ann and Cindy Form a Coalition -- Ann and Beth Form a Coalition -- Beth and Cindy Form a Coalition -- Which Coalition Will Form? -- Fixed 50:50 Split -- Another Variant: Split can be Negotiated -- The Grand Coalition -- The Core -- The Shapley Value -- Exercises -- Project 59 -- Example: VNM POKER(4, 4, 3, 5) -- Mixed Nash Equilibria -- Performance of Pure Strategies against the Mixed Nash Equilibria -- Example: KUHN POKER(3, 4, 2, 3) -- From Behavioral Strategies to Mixed Strategies to Expectations -- From Mixed Strategies to Behavioral Strategies -- Exercises.
Example: End-of-Semester Poker Tournament.
Holdings
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Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
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Ebrary Ebrary Nepal Available EBKNP-N00033420
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Total holds: 0

front cover -- Game Theory Through Examples -- copyright page -- Contents -- Preface -- Theory 1: Introduction -- What's a Game? -- Game, Play, Move: Some Definitions -- Classification of Games -- Exercises -- Theory 2: Simultaneous Games -- Normal Form---Bimatrix Description -- Two Players -- Two Players, Zero-sum -- Three or More Players -- Symmetric Games -- Which Option to Choose -- Maximin Move and Security Level -- Dominated Moves -- Best Response -- Nash Equilibria -- Additional Topics -- Best Response Digraphs -- 2-Player Zero-sum Symmetric Games -- Exercises -- Project 1: Reacting fast or slow -- Example: Selecting a Class -- Three Players, Two Classes -- ``I like you both'' -- Disliking the Rival -- Outsider -- Larger Cases -- Assumptions -- Exercises -- Project 2 -- Project 3 -- Project 4 -- Example: Doctor Location Games -- Doctor Location -- An Example Graph -- No (Pure) Nash Equilibrium? -- How Good are the Nash Equilibria for the Public? -- Trees -- More than one Office (optional) -- Exercises -- Project 5: Doctor location on MOPs -- Project 6 -- Project 7 -- Example: Restaurant Location Games -- A First Graph -- A Second Graph -- Existence of Pure Nash Equilibria -- More than one Restaurant (optional) -- Exercises -- Using Excel -- Spreadsheet Programs like Excel -- Two-Person Simultaneous Games -- Three-Person Simultaneous Games -- Exercises -- Project 8: Simultaneous Quatro-Uno -- Project 9: Restaurant Location Games -- Project 10: 5 Knights -- Project 11: 5 Cardinals -- Example: Election I -- First Example -- Second Example -- The General Model -- Third Example -- The Eight Cases -- Voting Power Indices (optional) -- Exercises -- Theory 3: Sequential Games I: Perfect Information and no Randomness -- Extensive Form: Game Tree and Game Digraph -- Analyzing the Game: Backward Induction -- Finite Games -- The Procedure.

Zermelo's Theorem -- Additional Topics -- Reality Check -- Playing it Safe---Guaranteed Payoffs -- Two-person Zero-sum Games -- Breaking Ties -- Existing Games -- Greedy Strategies -- Exercises -- Project 12: TAKE SOME -- Project 13: WHO's NEXT(n) -- Project 14: LISA's GAME -- Project 15: 2-AUCTION -- Project 16: 3-AUCTION -- Example: Dividing A Few Items I -- Greedy Strategy -- Backward Induction -- Game Tree -- Game Digraph -- Example: Game Digraph for ABBAB -- An Abbreviated Analysis -- Why it Matters: Complexity (optional) -- Bottom-Up Analysis -- Interdependencies between the Items (optional) -- Exercises -- Example: Shubik Auction I -- Exercises -- Project 17: SHUBIK AUCTION -- Example: Sequential Doctor and Restaurant Location -- General Observations for Symmetric Games -- Doctor Location -- Constant-Sum Games -- Restaurant Location -- Nash Equilibria and First Mover Advantage for Symmetric Games -- Exercises -- Project 18 -- Project 19: Hostile versus Friendly Play -- Theory 4: Probability -- Terminology -- Computing Probabilities -- Equally Likely Simple Events -- Simple Events not Equally Likely -- Expected Value -- Multistep Experiments -- Probability Trees -- Conditional Probabilities -- Probability Digraphs -- Randomness in Simultaneous Games -- Counting without Counting -- Exercises -- Project 20: Tennis -- Project 21: Final Exam -- France 1654 -- Exercises -- Example: DMA Soccer I -- 1-Round 2-Step Experiment for Given Player Distributions -- Expected Goal Difference for the One-Round Game -- 3-Rounds Experiment for Given Player Distributions -- Static Three-round Game -- Static Nine-round DMA Soccer -- Exercises -- Project 22: DMA6* Soccer -- Project 23: DMA7* Soccer -- Example: Dividing A Few Items II -- Goals of Fairness and Efficiency -- Fairness -- Efficiency -- Three Additional Features -- Mechanism Design -- Some Games.

Selecting one by one Games -- Cut and Choose -- Random and Exchange -- Examples -- Comparison of the Games for Seven Items and Complete Information -- Opposing or Similar Preferences -- Incomplete Information -- Exercises -- Project 24: Dividing five items A -- Project 25: Dividing five items B -- Theory 5: Sequential Games with Randomness -- Extensive Form Extended -- Analyzing the Game: Backward Induction again -- Decision Theory: Alone against Nature -- Exercises -- Project 26: Job Interviews -- Project 27: 5 Envelopes -- Project 28: Oh-No or Oh-No6 -- Project 29: 3 4 version of Polyomino REC THE SQUARE with randomness -- Example: Sequential Quiz Show I -- Candidates with Little Knowledge -- More May be Less -- One Candidate Knows More -- Cindy Knows one Answer to be False -- Exercises -- Project 30: SEQUENTIAL QUIZ SHOW, clever Ann -- Project 31: SEQUENTIAL QUIZ SHOW, clever Beth -- Las Vegas 1962 -- Exercises -- Example: Mini Blackjack and Card Counting -- The Basic Game -- Playing against the House -- How Likely are the Distributions? -- Betting High and Low -- Reshuffling -- Exercises -- Project 32: 8 ROUNDS BLACK OR WHITE -- Project 33: x ROUNDS RED, GREEN, OR BLUE -- Project 34: MINI BLACKJACK -- Example: Duel -- One Bullet -- Analysis of One-bullet Variants with Increasing Probabilities without Computer Help -- Analysis of DUEL(1,1|m, 2m, 3m, …) -- Two or more Bullets -- A few Cases of DUEL(2,2|m, 2m, 3m,…) -- Exercises -- Project 35: Drunk Adam -- Project 36: How more dangerous weapons affect the state budget and the health of citizens -- Project 37: Selecting m between 0.04 and 0.13 -- Project 38: What duels are best for society? -- Santa Monica in the 50s -- Theory 6: Extensive Form of General Games -- Extensive Form and Information Sets -- No Backward Induction for Imperfect Information -- Subgames -- Multi-round Games.

Why Trees for Imperfect Information? -- Exercises -- Example: Shubik Auction II -- Possible Sudden End -- Imperfect and Incomplete Information -- The Auctioneer Enters the Game (optional) -- Exercises -- Project 39 -- Project 40 -- Project 41: SHUBIK AUCTION(45, 35, 6, p) -- Project 42: SHUBIK AUCTION(A, B, C, n, p) -- Theory 7: Normal Form and Strategies -- Pure Strategies -- Reduced Pure Strategies -- Normal Form -- Using Tools from Simultaneous Games for the Normal Form -- Subgame Perfectness -- Special Case of Sequential Games with Perfect Information -- Exercises -- Example: VNM POKER and KUHN POKER -- Description -- VNM POKER -- KUHN POKER -- Exercises -- Example: Waiting for Mr. Perfect -- The Last Round -- The Eight Pure Strategies -- Computing the Payoffs -- Domination -- The Reduced Normal Forms in the Three Cases -- The Case p2+2p3 1 -- The Case p2+2p3 = 1 -- Project 43 -- Project 44 -- Project 45 -- Project 46 -- Project 47 -- Project 48 -- Theory 8: Mixed Strategies -- Mixed Strategies -- Best Response -- Brown's Fictitious Play -- Mixed Maximin Strategy, Mixed Security Level, and Linear Programs -- Mixed Nash Equilibria -- Two-player Zero-sum Games -- Non-Zero-sum Games -- Computing Mixed Nash Equilibria -- Small Two-player Zero-sum Games (optional) -- Solving Small non Zero-sum Two-player Games by Solving Equations (optional) -- Exercises -- Project 49: Balanced 3-spinner duel with five options -- Project 50: Balanced 3-spinner duel -- Project 51: COLONEL BLOTTO(4, 9, 9) -- Project 52: Iterated COLONEL BLOTTO -- Project 53: Simultaneous Quatro-Uno -- Project 54 -- Project 55: 4-round Waiting for Mr. Perfect -- Princeton in 1950 -- Example: Airport Shuttle -- The Simple Model -- To the Airport -- From the Airport -- Combining Both -- Impatient Customers -- Exercises -- Example: Election II.

Left Over from Election I -- More Effort into Large Districts -- Defend Where Ahead or Attack Where Weak? -- Is Larger Better? -- ELECTION(7,8,13|-1,-1,2|x,x) -- Exercises -- Example: VNM POKER(2, r, m, n) -- The Case n m 2 - 1 r -- Best Responses -- Reading the Opponent (optional) -- Mixed Nash Equilibrium for n m 2-1 r -- Small Changes in the Parameters -- Exercises -- Theory 9: Behavioral Strategies -- Behavioral versus Mixed Strategies -- Calculating Mixed Strategies from Behavioral Strategies -- Calculating Behavioral Strategies from Mixed Strategies for a Game Tree with Perfect Recall -- Kuhn's Theorem -- Exercises -- Example: Multiple-Round Chicken -- Ordinary Chicken -- Two-round Chicken -- Generalized Backward Induction, using the Extensive Form -- Working with the Normal Form -- Connections between the two Approaches -- Three-round Chicken -- Exercises -- Project 56 -- Project 57 -- Project 58 -- Example: DMA Soccer II -- Multi-round Simultaneous Games -- Information Sets and Moves -- The Optimal Third Move in Selected Cases -- A Detailed Example: (2, 2) versus (3, 1) -- A Second Example: (1, 3) versus (2, 2) -- The Optimal Second Move for Seven Positions -- Couldn't We Analyze the Whole Game? -- How Good a Model is it? -- Example: Sequential Quiz Show II -- Fixed Coalitions -- Ann and Cindy Form a Coalition -- Ann and Beth Form a Coalition -- Beth and Cindy Form a Coalition -- Which Coalition Will Form? -- Fixed 50:50 Split -- Another Variant: Split can be Negotiated -- The Grand Coalition -- The Core -- The Shapley Value -- Exercises -- Project 59 -- Example: VNM POKER(4, 4, 3, 5) -- Mixed Nash Equilibria -- Performance of Pure Strategies against the Mixed Nash Equilibria -- Example: KUHN POKER(3, 4, 2, 3) -- From Behavioral Strategies to Mixed Strategies to Expectations -- From Mixed Strategies to Behavioral Strategies -- Exercises.

Example: End-of-Semester Poker Tournament.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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