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