Games of Strategy

by Dixit, Avinash K.; Skeath, Susan

• ISBN13: 9780393974218
• ISBN10: 0393974219
• Format: Hardcover
• Copyright: 1999-06-01
• Publisher: W W Norton & Co Inc

Table of Contents

Preface	xix
PART ONE Introduction and General Principles
Basic Ideas and Examples	1	(14)
What is a Game of Strategy?	2	(2)
Some Examples and Stories of Strategic Games	4	(8)
Which Passing Shot?	4	(1)
The GPA Trap	5	(1)
``We Can't Take the Exam Because We Had a Flat Tire''	6	(2)
Why Are Professors So Mean?	8	(1)
Roommates and Families on the Brink	9	(2)
The Dating Game	11	(1)
Our Strategy For Studying Games of Strategy	12	(3)
Summary	14	(1)
How to Think About Strategic Games	15	(28)
Decisions Versus Games	16	(2)
Classifying Games	18	(6)
Are the Moves in the Game Sequential or Simultaneous?	18	(1)
Are the Players' Interests in Total Conflict, or Is There Some Commonality?	19	(1)
Is the Game Played Once or Repeatedly, and with the Same or Changing Opponents?	20	(1)
Do the Players Have Full or Equal Information?	21	(1)
Are the Rules of the Game Fixed or Manipulable?	22	(1)
Are Agreements to Cooperate Enforceable?	23	(1)
Some Terminology and Background Assumptions	24	(10)
Strategies	25	(1)
Payoffs	26	(1)
Rationality	27	(2)
Common Knowledge of Rules	29	(1)
Equilibrium	30	(2)
Dynamics and Evolutionary Games	32	(1)
Observation and Experiment	33	(1)
The Uses of Game Theory	34	(1)
The Structure of The Chapters to Follow	35	(8)
Summary	38	(1)
Key Terms	39	(1)
Exercises	39	(4)
PART TWO Concepts and Techniques
Games with Sequential Moves	43	(36)
A Senate Race as a Sequential-Move Game	44	(2)
Illustrating Sequential-Move Games	46	(1)
Describing Strategies	47	(2)
Rollback Equilibrium	49	(4)
A Sequential-Move Game with Only ``One'' Player	53	(3)
Order Advantages	56	(2)
Adding More Players	58	(5)
Adding More Moves	63	(7)
Tic-Tac-Toe	63	(2)
Chess	65	(5)
Experiments in Strategy	70	(9)
Summary	73	(1)
Key Terms	74	(1)
Exercises	74	(5)
Games with Simultaneous Moves	79	(45)
Illustrating Simultaneous-Move Games	80	(2)
Zero-Sum Versus Non-Zero-Sum Games	80	(1)
Constructing an Actual Game Table	81	(1)
Nash Equilibrium	82	(1)
Dominant Strategies	83	(2)
When Both Players Have Dominant Strategies	85	(2)
When Only One Player Has a Dominant Strategy	87	(2)
Successive Elimination of Dominated Strategies	89	(4)
Symmetric Games	92	(1)
Weak Versus Strict Dominance	93	(1)
Minimax Strategies in Zero-Sum Games	93	(4)
Cell-by-Cell Inspection	97	(2)
Pure Strategies That are Continuous Variables	99	(5)
Three Players	104	(3)
Multiple Equilibria in Pure Strategies	107	(9)
Assurance	107	(3)
Chicken	110	(2)
The Battle of the Two Cultures	112	(2)
Weak Dominance	114	(2)
No Equilibrium in Pure Strategies	116	(8)
Summary	118	(1)
Key Terms	118	(1)
Exercises	119	(5)
Simultaneous-Move Games with Mixed Strategies	124	(39)
What is a Mixed Strategy?	125	(1)
What does a Mixed Strategy Accomplish?	125	(7)
The Row Player's Perspective	127	(4)
The Column Player's Perspective	131	(1)
Equilibrium in Mixed Strategies	132	(4)
Mixing in Non-Zero-Sum Games	136	(7)
Chicken	136	(4)
The Battle of the Two Cultures	140	(3)
Further Discussion of Mixed Strategies	143	(8)
The Odds Method	143	(4)
Counterintuitive Outcomes with Mixed Strategies	147	(2)
Using Mixed Strategies in Practice	149	(2)
Mixing when one Player has Three or More Pure Strategies	151	(12)
A General Case	152	(4)
A Coincidental Case	156	(3)
Summary	159	(1)
Key Terms	160	(1)
Exercises	160	(3)
Appendix: Probability and Expected Utility	163	(122)
The Basic Algebra of Probabilities	163	(7)
The Addition Rule	165	(1)
The Modified Addition Rule	166	(1)
The Multiplication Rule	166	(1)
The Modified Multiplication Rule	167	(1)
The Combination Rule	168	(1)
Expected Values	169	(1)
Inferring Event Probabilities from Observing Consequences	170	(3)
Attitudes Toward Risk and Expected Utility	173	(5)
Summary	176	(1)
Key Terms	177	(1)
Combining Simultaneous And Sequential Moves	178	(31)
Illustrating Games in Both Extensive and Strategic Form	179	(3)
Games with Both Simultaneous and Sequential Moves	182	(3)
Combined Sequential-Play and Mixed-Strategy Equilibria	185	(4)
Rules Change I: Converting From Sequential to Simultaneous Play	189	(3)
Solving the Sequential-Move Game From its Strategic Form	192	(3)
Subgame-Perfect Equilibria	195	(4)
Rules Change II: Converting From Simultaneous to Sequential Play	199	(10)
Summary	205	(1)
Key Terms	206	(1)
Exercises	206	(3)
Consolidation, Extension, and Discussion	209	(46)
Validity of the Nash Equilibrium Concept	210	(13)
Is the Nash Equilibrium Concept Too Imprecise?	211	(2)
Do Players in Actual Games Play Nash Equilibrium Strategies?	213	(3)
Does Rationality by Itself Imply Nash Equilibrium?	216	(2)
Does the Nash Equilibrium Account for Risks Properly?	218	(1)
Is the Expected-Payoff Maximization Assumption Reasonable?	219	(4)
Games of Dynamic Competition	223	(9)
Calculating the Probabilities of Winning at Tennis	225	(4)
Strategy in Tennis	229	(2)
Applying Tennis Analysis to Business	231	(1)
Nash Equilibrium With Continuous Strategies	232	(2)
Mixing Among Many Strategies: Examples	234	(6)
A Zero-Sum, Three-by-Three Games	234	(4)
A Three-by-Three Example with Unused Strategies	238	(2)
Mixing Among Many Strategies: General Theory	240	(15)
Summary	247	(1)
Key Terms	248	(1)
Exercises	248	(7)
PART THREE Some Broad Classes of Games and Strategies
The Prisoners' Dilemma Game	255	(30)
The Basic Game (Review)	256	(1)
Solutions I: Repetition	257	(9)
Finite Repetition	258	(1)
Infinite Repetition	259	(3)
Games of Unknown Length	262	(1)
General Theory	263	(3)
Solutions II: Penalties and Rewards	266	(3)
Solutions III: Leadership	269	(2)
Experimental Evidence	271	(3)
Real-World Dilemmas	274	(11)
Policy Setting	274	(2)
Labor Arbitration	276	(1)
Evolutionary Biology	277	(1)
Price Matching	278	(2)
Summary	280	(1)
Key Terms	281	(1)
Exercises	281	(4)
Appendix: Infinite Sums	285	(298)
Games with Strategic Moves	288	(32)
A Classification of Strategic Moves	289	(3)
Unconditional Strategic Moves	290	(1)
Conditional Strategic Moves	291	(1)
Credibility of Strategic Moves	292	(2)
Commitments	294	(4)
Threats and Promises	298	(8)
Example of a Threat: U.S.---Japanese Trade Relations	298	(5)
Example of a Promise: The Pizza Pricing Game	303	(1)
Example Combining Threat and Promise: Joint U.S.---European Military Operations	304	(2)
Some Additional Issues	306	(2)
When Do Strategic Moves Help?	306	(1)
Deterrence Versus Compellence	307	(1)
Acquiring Credibility	308	(5)
Reducing Your Freedom of Action	308	(2)
Changing Your Payoffs	310	(3)
Countering Your Opponent's Strategic Moves	313	(7)
Irrationality	314	(1)
Cutting Off Communication	314	(1)
Leaving Escape Routes Open	314	(1)
Undermining Your Opponent's Motive to Uphold His Reputation	314	(1)
Salami Tactics	315	(1)
Summary	315	(1)
Key Terms	316	(1)
Exercises	316	(4)
Evolutionary Games	320	(36)
The Framework	321	(3)
The Prisoners' Dilemma	324	(7)
The Twice-Played Prisoners' Dilemma	326	(3)
Multiple Repetitions	329	(1)
Comparing the Evolutionary and Rational-Player Models	330	(1)
Chicken	331	(3)
The Assurance Game	334	(3)
Interactions Across Species	337	(4)
The Hawk-Dove Game	341	(4)
Rational Strategic Choice and Equilibrium	341	(1)
Evolutionary Stability for V>C	342	(1)
Evolutionary Stability for V<C	342	(1)
V<C: Stable Polymorphic Population	343	(1)
V<C: Each Individual Mixes Strategies	344	(1)
Some General Theory	345	(2)
Dynamics With Three Types in The Population	347	(3)
Evolution of Cooperation and Altruism	350	(6)
Summary	352	(1)
Key Terms	353	(1)
Exercises	354	(2)
Collective-Action Games	356	(41)
Collective-Action Games with Two Players	357	(5)
Numerical Examples	358	(3)
Generalization of the Two-Person Case	361	(1)
Collective-Action Problems in Large Groups	362	(6)
A Brief History of Ideas	368	(1)
Solving Collective-Action Problems	369	(8)
Analysis	371	(4)
Applications	375	(2)
Spillovers, or Externalities	377	(11)
The Calculus of the General Case	380	(1)
Negative Spillovers	381	(4)
Positive Spillovers	385	(3)
``Help!''---a Game of Chicken With Mixed Strategies	388	(9)
Summary	392	(1)
Key Terms	393	(1)
Exercises	394	(3)
Uncertainty and Information	397	(38)
Controlling and Manipulating Risk	398	(5)
Strategies to Reduce Risk	398	(3)
Using Risk	401	(1)
Manipulating Risk in Contests	402	(1)
Some Strategies to Manipulate Information	403	(6)
Literal and Strategic Liars	405	(1)
King Solomon's Unwisdom	406	(3)
Incentives to Induce Effort	409	(3)
Screening and Signaling	412	(4)
Separation and Pooling	416	(8)
Separating Equilibrium	419	(1)
Pooling Equilibrium	420	(1)
Semiseparating Equilibrium	421	(3)
Some Evidence for Signaling and Screening	424	(2)
Additional Reading on Information Manipulation	426	(9)
Summary	427	(1)
Key Terms	428	(1)
Exercises	429	(6)
PART FOUR Applications to Specific Strategic Situations
Brinkmanship: The Cuban Missile Crisis	435	(27)
A Brief Narration of Events	436	(7)
A Simple Game-Theoretic Explanation	443	(2)
Accounting For Additional Complexities	445	(6)
A Probabilistic Threat	451	(3)
Practicing Brinkmanship	454	(8)
Summary	459	(1)
Key Terms	459	(1)
Exercises	460	(2)
Strategy and Voting	462	(32)
Voting Rules and Procedures	463	(4)
Binary Methods	463	(1)
Plurative Methods	464	(1)
Mixed Methods	465	(2)
Voting Paradoxes	467	(6)
The Condorcet Paradox	467	(2)
The Reversal Paradox	469	(1)
The Agenda Paradox	470	(1)
Change the Voting Method, Change the Outcome	471	(2)
Evaluating Vote Aggregation Methods	473	(1)
Strategic Voting	474	(7)
Plurality Rule	475	(2)
Pairwise Voting	477	(4)
The Borda Count	481	(1)
The Median Voter Theorem	481	(13)
Discrete Political Spectrum	482	(4)
Continuous Political Spectrum	486	(2)
Summary	488	(1)
Key Terms	489	(1)
Exercises	490	(4)
Bidding Strategy and Auction Design	494	(27)
Types of Auctions	495	(2)
The Winner's Curse	497	(3)
Bidding Strategies	500	(1)
Vickrey's Truth Serum	501	(2)
All-Pay Auctions	503	(2)
How to Sell at Auction	505	(4)
Risk-Neutral Bidders and Independent Estimates	506	(1)
Correlated Estimates	507	(1)
Risk-Averse Bidders	508	(1)
Some Added Twists to Consider	509	(3)
Multiple Objects	509	(2)
Defeating the System	511	(1)
Information Disclosure	511	(1)
The Airwave Spectrum Auctions	512	(9)
Designing the Rules	513	(2)
How the Auctions Have Fared	515	(1)
Two Specific Bidding Issues	516	(2)
Summary	518	(1)
Key Terms	518	(1)
Exercises	519	(2)
Bargaining	521	(29)
Nash's Cooperative Solution	523	(6)
Numerical Example	523	(1)
General Theory	524	(5)
Variable-Threat Bargaining	529	(2)
Alternating-Offers Model I: Total Value Decays	531	(3)
Experimental Evidence	534	(3)
Alternating-Offers Model II: Impatience	537	(5)
Manipulating Information in Bargaining	542	(2)
Bargaining With Many Parties and Issues	544	(6)
Multi-Issue Bargaining	545	(1)
Multiparty Bargaining	546	(1)
Summary	547	(1)
Key Terms	547	(1)
Exercises	548	(2)
Markets and Competition	550	(33)
A Simple Trading Game	552	(8)
The Core	560	(7)
Numerical Example	562	(1)
Some Properties of the Core	563	(2)
Discussion	565	(2)
The Market Mechanism	567	(5)
Properties of the Market Mechanism	569	(2)
Experimental Evidence	571	(1)
The Shapley Value	572	(5)
Power in Legislatures and Committees	574	(1)
Allocation of Joint Costs	575	(2)
Fair Division Mechanisms	577	(6)
Summary	579	(1)
Key Terms	580	(1)
Exercises	580	(3)
Index	583