Introduction to Game Theory / Edition 1

Introduction to Game Theory / Edition 1

by Peter Morris
     
 

ISBN-10: 038794284X

ISBN-13: 9780387942841

Pub. Date: 07/28/1994

Publisher: Springer New York

This advanced textbook covers the central topics in game theory and provides a strong basis from which readers can go on to more advanced topics. The subject matter is approached in a mathematically rigorous, yet lively and interesting way. New definitions and topics are motivated as thoroughly as possible. Coverage includes the idea of iterated Prisoner's Dilemma

Overview

This advanced textbook covers the central topics in game theory and provides a strong basis from which readers can go on to more advanced topics. The subject matter is approached in a mathematically rigorous, yet lively and interesting way. New definitions and topics are motivated as thoroughly as possible. Coverage includes the idea of iterated Prisoner's Dilemma (super games) and challenging game-playing computer programs.

Product Details

ISBN-13:
9780387942841
Publisher:
Springer New York
Publication date:
07/28/1994
Series:
Universitext Series
Edition description:
1994
Pages:
252
Product dimensions:
9.21(w) x 6.14(h) x 0.53(d)

Table of Contents

1. Games in Extensive Form.- 1.1. Trees.- 1.2. Game Trees.- 1.2.1. Information Sets.- 1.3. Choice Functions and Strategies.- 1.3.1. Choice Subtrees.- 1.4. Games with Chance Moves.- 1.4.1. A Theorem on Payoffs.- 1.5. Equilibrium N-tuples of Strategies.- 1.6. Normal Forms.- 2. Two-Person Zero-Sum Games.- 2.1. Saddle Points.- 2.2. Mixed Strategies.- 2.2.1. Row Values and Column Values.- 2.2.2. Dominated Rows and Columns.- 2.3. Small Games.- 2.3.1. 2 × n and m × 2 Games.- 2.4. Symmetric Games.- 2.4.1. Solving Symmetric Games.- 3. Linear Programming.- 3.1. Primal and Dual Problems.- 3.1.1. Primal Problems and Their Duals.- 3.2. Basic Forms and Pivots.- 3.2.1. Pivots.- 3.2.2. Dual Basic Forms.- 3.3. The Simplex Algorithm.- 3.3.1. Tableaus.- 3.3.2. The Simplex Algorithm.- 3.4. Avoiding Cycles and Achieving Feasibility.- 3.4.1. Degeneracy and Cycles.- 3.4.2. The Initial Feasible Tableau.- 3.5. Duality.- 3.5.1. The Dual Simplex Algorithm.- 3.5.2. The Duality Theorem.- 4. Solving Matrix Games.- 4.1. The Minimax Theorem.- 4.2. Some Examples.- 4.2.1. Scissors-Paper-Stone.- 4.2.2. Three-Finger Morra.- 4.2.3. Colonel Blotto’s Game.- 4.2.4. Simple Poker.- 5. Non-Zero-Sum Games.- 5.1. Noncooperative Games.- 5.1.1. Mixed Strategies.- 5.1.2. Maximin Values.- 5.1.3. Equilibrium N-tuples of Mixed Strategies.- 5.1.4. A Graphical Method for Computing Equilibrium Pairs.- 5.2. Solution Concepts for Noncooperative Games.- 5.2.1. Battle of the Buddies.- 5.2.2. Prisoner’s Dilemma.- 5.2.3. Another Game.- 5.2.4. Supergames.- 5.3. Cooperative Games.- 5.3.1. Nash Bargaining Axioms.- 5.3.2. Convex Sets.- 5.3.3. Nash’s Theorem.- 5.3.4. Computing Arbitration Pairs.- 5.3.5. Remarks.- 6. N-Person Cooperative Games.- 6.1. Coalitions.- 6.1.1. The Characteristic Function.- 6.1.2. Essential and Inessential Games.- 6.2. Imputations.- 6.2.1. Dominance of Imputations.- 6.2.2. The Core.- 6.2.3. Constant-Sum Games.- 6.2.4. A Voting Game.- 6.3. Strategic Equivalence.- 6.3.1. Equivalence and Imputations.- 6.3.2. (0,1)-Reduced Form.- 6.3.3. Classification of Small Games.- 6.4. Two Solution Concepts.- 6.4.1. Stable Sets of Imputations.- 6.4.2. Shapley Values.- 7. Game-Playing Programs.- 7.1. Three Algorithms.- 7.1.1. The Naive Algorithm.- 7.1.2. The Branch and Bound Algorithm.- 7.1.3. The Alpha-Beta Pruning Algorithm.- 7.2. Evaluation Functions.- 7.2.1. Depth-Limited Subgames.- 7.2.2. Mancala.- 7.2.3. Nine-Men’s Morris.- Appendix. Solutions.

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