Economics and computation : an introduction to algorithmic game theory, computational social choice, and fair division /
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| Imprint: | Heidelberg : Springer, [2015] ©2016 |
|---|---|
| Description: | 1 online resource (xiii, 612 pages) : illustrations (some color) |
| Language: | English |
| Series: | Springer texts in business and economics, 2192-4333 Springer texts in business and economics, |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11247679 |
Table of Contents:
- Intro; Foreword by Matthew O. Jackson and Yoav Shoham; Preface by the Editor; Contents; Contributors; Chapter 1 Playing, Voting, and Dividing; 1.1 Playing; 1.1.1 Noncooperative Game Theory; 1.1.2 Cooperative Game Theory; 1.2 Voting; 1.2.1 Preference Aggregation by Voting; 1.2.2 Manipulative Actions in Single-Peaked Societies; 1.2.3 Judgment Aggregation; 1.3 Dividing; 1.3.1 Cake-cutting: Fair Division of Divisible Goods; 1.3.2 Fair Division of Indivisible Goods; 1.3.3 A Brief Digression to Single-Item Auctions; 1.3.3.1 Classification; 1.3.3.2 English Auction; 1.3.3.3 Dutch Auction
- 1.3.3.4 Vickrey Auction1.3.3.5 American Auction; 1.3.3.6 Expected Revenue; 1.4 Some Literature Pointers; 1.5 A Brief Digression to Computational Complexity; 1.5.1 Some Foundations of Complexity Theory; 1.5.1.1 Turing Machines and Complexity Measures; 1.5.1.2 The Complexity Classes P and NP; 1.5.1.3 Upper and Lower Bounds; 1.5.2 The Satisfiability Problem of Propositional Logic; 1.5.2.1 Definitions; 1.5.2.2 Upper Bounds for SAT; 1.5.2.3 How to Prove Lower Bounds: Reducibility and Hardness; 1.5.2.4 Some Background on Approximation Theory; 1.5.3 A Brief Compendium of Complexity Classes
- 1.5.3.1 Polynomial Space1.5.3.2 The Polynomial Hierarchy; 1.5.3.3 DP: the Second Level of the Boolean Hierarchy over NP; 1.5.3.4 Probabilistic Polynomial Time; Overview; 1.5.3.5 And Now, Finally, . . .; Part I Playing Successfully; Chapter 2 Noncooperative Game Theory; 2.1 Foundations; 2.1.1 Normal Form, Dominant Strategies, and Equilibria; 2.1.1.1 The Prisoners' Dilemma; 2.1.1.2 Noncooperative Games in Normal Form; 2.1.1.3 Dominant Strategies; 2.1.1.4 Nash Equilibria in Pure Strategies; 2.1.1.5 Relations between Solution Concepts; 2.1.2 Further Two-Player Games
- 2.1.2.1 The Battle of the Sexes2.1.2.2 The Chicken Game; 2.1.2.3 The Penalty Game; 2.1.2.4 The Paper-Rock-Scissors Game; 2.1.2.5 The Guessing Numbers Game; 2.2 Nash Equilibria in Mixed Strategies; 2.2.1 Definition and Application to Two-Player Games; 2.2.1.1 Definition of Nash Equilibria in Mixed Strategies; 2.2.1.2 The Penalty Game; 2.2.1.3 The Paper-Rock-Scissors Game; 2.2.1.4 The Battle of the Sexes; 2.2.1.5 The Chicken Game; 2.2.1.6 The Prisoners' Dilemma; 2.2.1.7 Overview of Some Properties of Some Two-Player Games; 2.2.2 Existence of Nash Equilibria in Mixed Strategies
- 2.2.2.1 Definition of Some Notions from Mathematical Topology2.2.2.2 Sperner's Lemma and Brouwer's Fixed Point Theorem; 2.2.2.3 Nash's Theorem; 2.3 Checkmate: Trees for Games with Perfect Information; 2.3.1 Sequential Two-Player Games; 2.3.1.1 Game Trees; 2.3.1.2 Tic-Tac-Toe; 2.3.1.3 Nim; 2.3.1.4 Geography and the Hardness of Finding Winning Strategies; 2.3.2 Equilibria in Game Trees; 2.3.2.1 Edgar's Sequential Campaign Game; 2.3.2.2 Nash Equilibria in Edgar's Sequential Campaign Game; 2.3.2.3 Subgame-Perfect Equilibria; 2.4 Full House: Games with Incomplete Information