information concealing games
TRANSCRIPT
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Informa(on-concealinggamesIPAMWorkshop:The CarlT.Bergstromdecep(onofselfandothers. DepartmentofBiologyMay27th2016,UCLAUniversityofWashington
www.insectdesigns.com
ccflickr:AndreVandal
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CoauthorsKevinZollmanSimonHuReggerDepartmentofPhilosophy LogicandPhilosophyofScienceCarnegieMellonUniversity UniversityofCaliforniaIrvine
Funding:NSFEF-1038456
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Decep(oncanbeabouttellinglies.
ccflickr:BrianGratwicke
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Butitisalsoaboutconcealingthetruth.
www.insectdesigns.com
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ccflickr:SallyCrosswaithe ccflickr:MaRhewTosh
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BLUFFING:
Doing something to avoid letting on as to the actual situation.
ccflickr:San(agoMuñozPérez
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Informa(ve
Inten(onal Misleading
Decep(on
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Informa(ve
Inten(onal Misleading
Decep(on
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H.PaulGrice
naturalvs.
non-naturalmeaning
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ccflickr:telomi “AllIneedaretastywaves…”
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Cue:anyfeatureoftheworld,animateorinanimate,thatcanbeusedbyananimalasaguidetofutureac(on.Signal:anyactorstructure• whichaltersbehaviorof
otherorganisms,• whichevolvedbecauseof
thateffect,and• whichiseffec(vebecause
receiver’sresponsealsoevolved.
JohnMaynardSmith
FromJMSandHarper(2003)
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Informa(ve
Inten(onal Misleading
Decep(on
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Inten(onality?
(cc)Im
agesfrom
NIH,N
IAAD
C.T.Bergstrom
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Teleoseman(capproach
Themeaningofasignalarisesnotfromsignaler’sinten(ons,butfromthefunc(onofthesignalthatleadittohaveevolved.
Millikan,Skyrms,Harms,Shea,GodfreySmith,etc.
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Informa(ve
Inten(onal Misleading
Decep(on
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BergstromandLachmann(2004)
Howcantherebedecep(onatNashequilibrium?
Can’tbebasedonsurprise.Everyplayerknowsexactly
whatshe’sgejng.
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BergstromandLachmann(2004)
Howcantherebedecep(onatNashequilibrium?
Can’tbebasedonsurprise.Everyplayerknowsexactly
whatshe’sgejng.
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Theproblemwithdefiningdecep(onintermsofpayoffs
High Medium LowFigh(ngability
Signal Don’tsignal
ARackAvoidReceiver’sidealbehavior
Signalingwheninmediumcondi(onhelpssignalerandharmsreceiver–butcanwereallysayitisdecep(ve?
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“Whatthesenderisdoingisrefusingtotellthewholetruth,butwhatissaidissimplytrue.Thesenderissayingsomethinglogicallyweakerthanwhattheyknow…Tosaysomethinglogicallyweakerthanwhatyoumightsayisnottodeceive.Totellhalfthetruthisnottotellahalftruth.” –PeterGodfreySmith(Mind,2012)
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Figh(ng
abilityGood Medium Mol(ng
Don’tthreaten
Threaten
Thisdisjunc(vepoolingseemssomehowdishonest
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Good MediumMol(ngWillingnessto
riskafight
Threaten
Don’tthreatenButhowwedon’ttheyaren’tsayingthisinstead?
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Ac(on-responsegames
AliceMessage
Bob
Private information
Actions
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Discreteac(on-responsegame
State BState A
Down
Up
Up
Down
RightLeft
RightLeft
RightLeft RightLeft
SENDER
RECEIVER
RECEIVER
NATURE
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Discreteac(on-responsegame
State BState A
Down
Up
Up
Down
RightLeft
RightLeft
RightLeft RightLeft
SENDER
RECEIVER
RECEIVER
NATURE
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Howdowespotthesignalsinasignalinggame?Howdoesinforma(onconcealingbehaviorfitin?
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ccflickr:wilsonseverino
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High qualityLow quality
big tail
small tail
mate don’t
mate don’t
mate don’t mate don’t
PEACOCK
PEAHEN
PEAHEN
NATURE
1-d,0 -d,1 -c,0 1-c,1
0,1 1,0 0,0 1,1
big tail
small tail
Peacocksignalinggamed>1>c
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High qualityLow quality
big tail
small tail
mate don’t
mate don’t
mate don’t mate don’t
PEACOCK
PEAHEN
PEAHEN
NATURE
1-d,0 -d,1 -c,0 1-c,1
0,1 1,0 0,0 1,1
big tail
small tail
Separa(ngequilibriumd>1>c
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• Asetofnplayersp1,p2,…pn• Arootedtreerepresen(ngtheplayers’possiblemoves
• Payoffs:ann-vectorw(t)foreachterminalnodet.
• Informa(onsets:apar((ononthedecisionnodesforeachplayer.
Extensiveformgamesofimperfectinforma(on,aredefinedby:
Thiscompletelydescribesthegame.
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Buthowdoweknowwhichmovesofthegamearesignals?
Fromtheformalgamealone,wedon’t!
Whichmovesaresignalingmovesisonly
spelledoutinthestorythatgetsoverlaidonthegame.
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Myaimistofixthis.
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Intui(vely,amoveisinforma(onalif:Aplayerwouldnotbothertodoitiftheotherplayeralreadykneweverythingshedid.
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Defini(on:Amovemispurelyinforma(onalif• Itisperformedwhenplayer1knowsthingsthatareunknowntoplayer2• Butitisnotperformedwhenplayer2hasalloftheinforma(onavailabletoplayer1whenshechosem.
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High qualityLow quality
big tail
small tail
mate don’t
mate don’t
mate don’t mate don’t
PEACOCK
PEAHEN
PEAHEN
NATURE
1-d,0 -d,1 -c,0 1-c,1
0,1 1,0 0,0 1,1
big tail
small tail
Separa(ngequilibrium
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Equilibriumofcomparatorgame
High qualityLow quality
big tail
small tail
mate don’t
mate don’t
mate don’t mate don’t
PEACOCK
PEAHEN
PEAHEN
NATURE
1-d,0 -d,1 -c,0 1-c,1
0,1 1,0 0,0 1,1
big tail
small tail
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Informa(onalHigh qualityLow quality
big tail
small tail
mate don’t
mate don’t
mate don’t mate don’t
PEACOCK
PEAHEN
PEAHEN
NATURE
1-d,0 -d,1 -c,0 1-c,1
0,1 1,0 0,0 1,1
big tail
small tail
Originalgame
Comparatorgame
High qualityLow quality
big tail
small tail
mate don’t
mate don’t
mate don’t mate don’t
PEACOCK
PEAHEN
PEAHEN
NATURE
1-d,0 -d,1 -c,0 1-c,1
0,1 1,0 0,0 1,1
big tail
small tail
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Defini(on:LetGbeagenericac(onresponsegameinextensiveformandletC(G)bethecomparatorgameinwhichPlayer2’sinforma(onsetsarereducedtosingletons.Amovembyplayer1issaidtobeaninforma(onalmoveifmisperformedwithposi(veprobabilityinsomeNashequilibriumofGbutisnotperformedwithposi(veprobabilityinanysubgameperfectNashequilibriumofthecomparatorgameC(G).
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ThebeerandquichegameChoandKreps(1982)
Imag
es fr
om p
ngim
g.com
, wiki
pedi
a
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Culturalcontextforthoseunder35
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ccflickr:PeteZarria
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SurlyWimp
beer
quiche
don’tfight
don’tfight
don’tfight don’tfight
VISITOR
LOCAL
LOCAL
NATURE
2,0 0,1 1,0 3,1
1,1 3,0 0,0 2,1
beer
quiche
(p=0.1) (p=0.9)
ThebeerandquichegameChoandKreps(1982)
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Nashequilibriumforbeerandquiche
SurlyWimp
beer
quiche
don’tfight
don’tfight
don’tfight don’tfight
VISITOR
LOCAL
LOCAL
NATURE
2,0 0,1 1,0 3,1
1,1 3,0 0,0 2,1
beer
quiche
(p=0.1) (p=0.9)
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Equilibriumforcomparatorgame
SurlyWimp
beer
quiche
don’tfight
don’tfight
don’tfight don’tfight
VISITOR
LOCAL
LOCAL
NATURE
2,0 0,1 1,0 3,1
1,1 3,0 0,0 2,1
beer
quiche
(p=0.1) (p=0.9)
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Originalgame
Comparatorgame
Informa(onalSurlyWimp
beer
quiche
don’tfight
don’tfight
don’tfight don’tfight
VISITOR
LOCAL
LOCAL
NATURE
2,0 0,1 1,0 3,1
1,1 3,0 0,0 2,1
beer
quiche
(p=0.1) (p=0.9)
SurlyWimp
beer
quiche
don’tfight
don’tfight
don’tfight don’tfight
VISITOR
LOCAL
LOCAL
NATURE
2,0 0,1 1,0 3,1
1,1 3,0 0,0 2,1
beer
quiche
(p=0.1) (p=0.9)
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Asignalconveysnon-naturalmeaning
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Aninforma(on-concealingmoveavoidsconveyingnaturalmeaning
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Amplifiersfacilitate
naturalmeaning
(Hasson1990)
ccflickr:Maggie.Smith ccflickr:BowenChin
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Amplifiersfacilitate
naturalmeaning
(Hasson1990)
ccflickr:Maggie.Smith
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Cryptographyconcealsnon-naturalmeaningfromunintendedreceivers.
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Amoveisinforma(onrevealingifyouseparateintherealgamebutpoolinthecomparator.Amoveisinforma(onconcealingifyoupoolintherealgamebutseparateinthecomparator.
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Tosummarizethusfar1.Wecannowiden(fyinforma(onalmovesfromthegameitself;noneedforastoryoverlay.2.We’venowhighlightedaclassofinforma(on-concealinggames,paralleltosignalinggames.
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Lewissignalinggame
State BState A
Signal B
Signal A
Signal A
Signal B
BA
BA
BA BA
SENDER
RECEIVER
RECEIVER
NATURE
0,0 1,1 0,0 1,1
0,0 1,1 1,1 0,0
Thisgameisnolongergeneric.Whathappenstonaturalmeaning?
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Defini(on:LetGbeanon-genericac(on-responsegameinextensiveform.AmoveminGissaidtobeaninforma(onalmoveifthereexistsasequenceofgenericgamesGnsuchthatGnàGandmisaninforma(onalmoveineverygameGiinthesequence.
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Capturethespy
? ? ?
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USmovesfirst:whotobug?
? ?
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Remarkably,theUSmustbugtheirownspy1/3ofthe(meatNashequilibrium.
? ?
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Intui(on:supposeUSneverbugstheirownspy.ThentheycatchtheUSSR’sspyhalfofthe(me.Theotherhalfofthe(metheUSSRthenknows
ThisrevealstheUSspy.
?
1)Whotheirownspyis.2)WhotheUSthoughttheirspycouldbe.
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SupposeinsteadtheUSbugstheirownspy1/3ofthe(me.Theywinonthefirstmove1/3ofthe(me,butwhentheymisstheUSSRlearnsnothingnew.NowtheyUSSRcanwinatmost1/2*2/3=1/3ofthe(meonthenextmove.Iftheydothatthough,theUScanalwayswinwheymiss.
TheUSwinsmorethan1/2ofthe(me
? ?
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ItturnsoutthatiftheUSdoesn’tcatchtheUSSR’sspyonthefirstround,theUSSR
mustbugtheirspy1/3ofthe(meinturn.
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Hereprivateinforma(onissovaluable
? ? ?
thattheplayerscannotuseitatall!
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Thepoolhallgame
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