information concealing games

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