Games of Strategy

675 Pages·2010·12.73 MB·English

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A u i n a s h D i x i t
Princeton University
Su sa n S / ce a t h
WellesleyC ollege
W. W. Norton & Company
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I
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PRINTEtDN tHs UNlrEoS rargso pA NarnIc'{'
Editor: JackRePcheck
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Cop y Ed ito r: Pa tty Zimmerman
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Book Design: Gina Webster
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Compositionb y UG / GGSI nformation SeruicesI'n c'
Manufacturing by Courier, Westford
Library of CongressC atalog ing-in-Publication Data
Dixit, Avinash K'
Gameso f strategy / Avinash Dixit' SusanS keath
p.cm'
Includes bibliographical referencesa nd index'
ISBN 0-393-92499-8
l.Gametheory.2.Policysciences.3.Decisionmaking.I'Skeath,Susan.II.Title.
HBr44.D592 004
2003066236
5r93_d.c22
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I
Contents
Prefacet o the SecondE dition xtx
PABTl| lIE
Introduction and GeneralP rinciples
I
BasicI deas and Examples 3
1 wuer rs A GAMEo p srnerrcv? 4
2 soug EXAMPLESA ND STORIESO F STRATEGICG AMES
A. \A/hichP assingS hot? 6
B. TheGPARatRace 7
C. "We Can'tTaketheExam,BecauseWeHadaFlatTire"9
D. \t\ihyAre ProfessorsS o Mean? l0
E. Roommates and Families on the Brink ll
F. The Dating Game 13
3 oun STRATEGYF oR STUDYING GAMESO F STRATEGY I4
vtl
Viii CONTENTS
2 Howto ThinkAbout StrategicG ames t7
1 nnctstor{s vERSUSG AMES 18
2 classrpvtNc GAMES 20
A. Are the Moves in the Game Sequential or Simultaneous? 20
B. Are the Players'I nterests in Total conflict or Is There Some commonality? 21
C. Is the Game Played Once or Repeatedly,a nd with the Sameo r Changing
Opponents? 22
D. Do the PlayersH ave Full or Equal Information? 23
E. Are the Ruleso f the Game Fixed or Manipulable? 24
F. AreAgreementstoCooperateEnforceable?2 5
3 sorrn TERMINoLocY AND BACKGRoUNDA SSUMPTIoNS 27
A. Strategies 27
B. Payoffs 28
C. Rationality 29
D. Common Knowledgeo f Rules 31
E. Equilibrium 33
F. DlnamicsandEvolutionaryGames 34
G. Obsewation and ExPeriment 35
4 rnn usES oF GAME THEoRY 36
5 run srRUcruRE oF THE cHAPTERST o FoLLow 38
SUMMARY 41
KEY TERMS 4I
EXERCISES 42
PABII Wl|
Conceptsa nd Techniques
Gamesw ith SequentialM oves 45
1 cair,rnrn sss 46
A. Nodes,B ranches,a ndPathsofPlay 46
B. Uncertainty and "Nature's Moves" 46
C. OutcomesandPaYoffs 48
D. Strategies 48
E. Tree Construction 49
Viii CONTENTS
2 Howto ThinkAbout StrategicG ames T7
I oe crstoNs vERSUSG AMES 18
2 cl,lssrpvrNc GAMES 20
A. Are the Moves in the Game Sequentialo r Simultaneous? 20
B. Are the Players'Interestsin Total conflict oI Is Theres ome commonality? 2l
C. Is the Game Played Once or Repeatedly,a nd with the Sameo r Changing
Opponents? 22
D. Do the PlayersH ave Full or Equal Information? 23
E. AretheRulesoftheGameFixedorManipulable?2 4
F. AreAgreementstoCooperateFnforceable?2 5
3 soun TERMINor,ocY AND BACKGRouND ASSUMPTIoNS 27
A. Strategies 27
B. Payoffs 28
C. Rationality 29
D. Common Knowledgeo f Rules 31
E. Equilibrium 33
F. DlnamicsandEvolutionaryGames 34
G. ObservationandExPeriment .35
4 rue usES oF GAME THEoRY 36
5 THE STRUCTUREO F THE CHAPTERST O FOLLOW 38
SUMMARY 41
KEY TERMS 4T
EXERCISES 42
PABII Wl|
Conceptsa nd Techniques
Gamesw ith SequentialM oves 45
1 crrtp rner ,s 46
A. Nodes,Branchesa, ndPathsofPlay 46
B. Uncertainty and "Nature's Moves" 46
C. OutcomesandPaYoffs 48
D. Strategies 48
E. Tree Construction 49
COi{TENTS ix
2 sorvtNc GAMESB YU sINGT REES 50
3 eoorNc MoRE PLAYERS 55
4 onopn ADVANTAGES 60
5 aoorNc MoREM ovES 61
A. Tic-Tac-Toe6 1
B. Chess 63
6 nvrnnNcn coNCERNINGR oLLBACK 69
7 srnarscrns rN THE suRVIVoRoc AME 72
SUMMARY 77
KEYT ERMS 78
EXERCISES7 8
4 Simultaneous-MovGe amesw ith PureS trategieIs:
Discrete Strategies 83
I DEPICTING SIMULTANEOUS-MOVEG AMESW ITH DISCRETE
STRATEGIES 84
2 Nnss EeUTLTBRIUM 86
A. SomeF urther Explanation of the Concept of Nash Equilibrium 87
B. Nash EquilibriumAs a Systemo f Beliefs and Choices 89
3 oorrrxeNcs 90
A. Both PlayersH aveD ominant Strategies 92
B. One Player Has a Dominant Strategy 93
C. SuccessiveE limination of Dominated Strategies 95
4 snsr-RespoNSE ANALYSIS 98
5 rnE MINIMAX METHoD FoR zERo-suM GAMES 99
6 runre PLAYERS 101
7 Naurtlpts EeuILIBRIA IN PURE sTRATEGIES 105
B No eeuruBRIUM IN PURE sTRATEGIES 111
SUMMARY f f3
KEY TERMS II4
EXERCTSES ll4
AppENDrSx:o me General Definitions 120
X CONTENTS
Simultaneous-MoveG amesw ith Pure StrategiesI I:
Continuous Strategiesa nd III: Discussiona nd
Evidence L23
I puRg STRATEGIES THAT ARE CONTINUOUS VARIABLES r24
A. Price Competition 124
B. PoliticalCampaignAdvertising I29
2 eN4ptnrcRr-E VIDENCEc oNCERNING NASH EQUILIBRIUM 131
A. Laboratory and ClassroomE xperiments 132
B. Real-WorldE vidence 135
3 cRtrrcel DISCUSSIONo F THE NASH EQUILIBRIUM
coNCEPr 139
A. TheTreatmentofRiskinNashEquilibrium 140
B. MultiplicityofNashEquilibria 142
C. Requirements of Rationality for Nash Equilibrium L44
4nerroNarrzABrLITY I45
A. ApplyingtheConceptofRationalizabiliry L46
B. Rationalizability Leading to Nash Equilibrium 147
SUMMARY 151
KEY TERMS 157
EXERCISES 151
Combining Sequentiala nd SimultaneousM oves 155
1 CRUSS WITH BOTH SIMULTANEOUSA ND SEQUENTIAL
MovES 156
A. Two-StageG amesa nd Subgames 156
B. Configurations of Multistage Games 160
2 cHaNcINc rHE oRDER oF MovES IN A GAME 162
A. Changing Simu-ltaneous-MoveG amesi nto Sequential-Move Games 163
B. Other Changesin the Order of Moves 170
3 cuRruce IN THE METHoD oF ANALYSIS l7I
A. Illustrating Simultaneous-Move Gamesb y Using Trees I7L
B. Showing andAnalyzing Simultaneous-Move Gamesi n StrategicF orm 172
4 ruRnn,-pr,AYERG AMES 176
SUMMARY 179
CONTENTS xi
KEY TERMS lBO
EXERCISES lBO
I Simultaneous-MoveG amesw ith Mixed StrategiesI :
Zero-SumG ames t8s
I wuat IS A MIXED stn,qrEcY? 186
2 uNcsRrRIN ACTIONS: MIXING MovES To KEEPT HE oPPoNENT
cuEssING LB7
A. Best-ResponseAnalYsis lBB
B. TheMinimaxMethod 194
3 xasg EQUILIBRIUM AS A SYSTEMO F BELIEFSA ND RESPONSES 198
4 MIXING WHEN ONE PLAYERH AS THREE OR MORE PURE
sTRATEGIES 199
A. AGeneralCase 200
B. Exceptional Cases 203
C. Caseo f Domination by a Mixed Strategy 204
5 MIXING WHEN BOTH PLAYERSH AVE THREE STRATEGIES 207
A. Full Mixture of All Strategies 208
B. Equilibrium Mixtures with Some StrategiesU nused 210
6 nvronxcn oN MIXING IN zERo-suM GAMES 212
7 uow ro usE MIXED STRATEGIESIN PRACTICE 214
SUMMARY 216
KEY TERMS 2I7
EXERCISES 2I7
AppENDDPcr obability and Expected Utility 22I
1 rur BASICA LGEBRAo F PROBABILITIES 222
A. TheAdditionRtie 224
B. The ModifledAddition Rule 225
C. The Multiplication Rule 225
D. The Modified Multiplication Rule 226
E. The Combination Rule 227
F. ExpectedValues 228
2 aTTTTUOEST OWARDR ISKA ND EXPECTEDU TILITY 228
SUMMARY 231
KEY TERMS 232
Xii CONTENTS
I Simultaneous-MovGe amesw ith MixedS trategieIsI :
Non-Zero-Sum Gamesa nd III: GeneralD iscussion 233
1 tr,ttxtrvcs usrAINED BY UNCERTAINB ELIEFS 234
A. Will HarryMeet Sally? 234
B. DicedChicken? 239
2 Now-znRo-suM MIXING wITH THREE STRATEGIES 24I
3 cENEner DIScussIoN oF MIXED-sTRATEGYE QUILIBRIA 243
A. WeakSenseofEquilibrium 244
B. Opponent's Indifference and GuardingAgainst Exploitation 244
C. Counterintuitive Outcomes with Mixed Strategiesi n Zero-Sum Games 245
D. Another Counterintuitive Result for Non-Zero-Sum Games 249
4 svronNcn oN MTxING IN NoN-zERo-suM GAMES 250
5 UTxTNGA MONG THREE OR MORE STRATEGIESG: ENERAL
THEoRY 250
SUMMARY 257
KEY TERMS 258
EXERCISES 258
PARII HREE
SomeB road Classeso f Gamesa nd Strategies
I Uncertaintya nd Information 263
1 Rsvnaunrnrc TNFoRMATIoN: BASIC IDEAS 264
2 olnrcr COMMUNICATION, oR "CHEAP TALK" 266
3 sIcNatINc AND scREENING 272
4 INcnurrvE PAYMENTS 277
5 EgurrrnnrA rN sIGNALING GAMES 280
A. SeparatingE qullibrium 284
B. Pooling Equilibrium 285
C. SemiseparatingE quilibrium 287
D. GeneralTheory 289
COilTENTS xli'i
6 nvlInNcn ABOUT SIGNALINGA ND SCREENING 292
sUMMARY 294
KEY TERMS 295
EXERCISES 295
APPENDIxn: formation and Risk 300
1 INTBRnTNc PROBABILITIESF ROM OBSERVINGC ONSEQUENCES 3OI
2 coNrnottlNc AND MANIPULATING RISK 304
A. Strategiest o ReduceR isk 304
B. Using Risk 307
C. Manipulating Risk in Contests 307
SUMMARY 309
KEY TERMS 310
| 0 strategicM oves 311
1 a crassIpIcATIoN oF srRArEGIc MovES 312
A. UnconditionaSl trategicM oves 313
B. ConditionaSl trategicM oves 314
2 cnsnrsltlTy oF sTRATEGIMC ovEs 315
3 cotr4rvrrrlnsNrs 317
4 rHnsers AND PRoMISES 321
A. Exampleo f a Threat:U .S.-IapanT radeR elations 322
B. Exampleo f a PromiseT: heR estauranPt ricingG ame 326
C. ExampleC ombiningT hreata ndP romisef:o int U.S.-ChinaP olitical
Action 328
5 soMs ADDITIoNALr oPlcs 329
A. WhenD o StrategicM ovesH elP? 329
B. DeterrencVee rsusC ompellence3 30
6 eceutnIwc cREDIBILITY 331
A. ReducingYourFreedomofActio3n3 1
B. ChangingYourPayoffs3 33
7 couNr.BnrNc youR oPPONENT'ss TRATEGICM ovES 337
A. Irrationality 337
B. CuttingO ff Communication 337
C. LeavingEscapeRoutesOP3e3n8
lF.