Game Theory and Evolutionary Biology

1、Game Theory and Evolutionary BiologyChapter 28 GAME THEORY AND EVOLUTIONARY BIOLOGY PETER HAMMERSTEIN Max-Planck-Institfutr Verhaltensphysiologie REINHARD SELTEN Universityo f Bonn Contents 1. Introduction 931 2. Conceptuabl ackground 932 2.1. Evolutionarsyt ability 932 2.2. The Darwinianv iew of na

2、turasl election 933 2.3. Payoffs 934 2.4. Gamet heorya ndp opulationge netics 935 2.5. Players 936 2.6. Symmetry 936 3. Symmetritcw o-persogna mes 937 3.1. Definitionsa ndn otation 937 3.2. The Hawk-Doveg arne 937 3.3. Evolutionarsyt ability 938 3.4. Propertieos fevolutionarilsyt ables trategies 940

3、 4. Playing thfeie ld 942 5. Dynamicf oundations 948 5.1. Replicatodr ynamics 948 5.2. Disequilibriumre sults 951 5.3. A look at populationge netics 952 6. Asymmetrico nflicts 962 * We areg ratefutlo Olof Leimar,S ido Mylius,R olf WeinzierlF, ranjoW eissinga, nda n anonymous refereew hoa ll helpedu

4、s witht heirc riticacl ommentsW. e alsot hankt heI nstitutefo r AdvancedS tudy Berlinf or supportintgh ef inalr evisiono f thisp aper. Handbooko f Garne Theory, Volu2m, eE ditedb y R.J. Aumanna nd S. Hart ? Elsevier Science B.V., 1A9ll9 r4ig. hts reserved 930 P. Hammersteainn d R. Selten 7. Extensiv

5、et wo-persong ames 965 7.1. Extensiveg arnes 965 7.2. Symmetriec xtensivgea rnes 966 7.3. Evolutionarsyt ability 968 7.4. Imagec onfrontatioan dd etachment 969 7.5. Decomposition 970 8. Biologicala pplications 971 8.1. Basicq nestionasb outa nimacl ontesbt ehavior 972 8.2. Asymmetriacn imacl ontests

6、 974 8.3. War of attritiona,s sessmenatn, ds ignalling 978 8.4. The evolutiono f cooperation 980 8.5. The greatv arietyo f biologicagl arnes 983 References 987 Ch. 28: GameT heorya ndE volutionarByi ology 931 1. Introduction The subjectm attero f evolutionargya met heoryis the analysiso f conflicta

7、nd cooperatioin animalsa ndp lants.O riginallyg arnet heoryw as developeads a theoryo f humans trategicb ehaviorb asedo n an idealizedp ictureo f rational decisionm akingE. volutionargya rneth eoryd oesn otr elyo n rationalitays sumptions buto n thei deat hatt heD arwinianp rocesso f naturasl electi

8、ondr iveso rganisms towardsth eo ptimizatioonf reproductivseu ccess. A seminapl aperb y MaynardS mitha nd Price (1973)is the startingp ointo f evolutionargya rnet heoryb ut therea re somef orerunnersF.i sher( 19301, 958) alreadyu seda game-theoreatircg umenint his sexr atiot heoryH. amilton(1 967) i

9、n a relatedsp eciacl ontexcto nceivetdh en otiono f an unbeatabsletr ategyA.n un- beatables trategyc an be describeda s a symmetriec quilibriums trategyo f a symmetrigca meT. rivers( 1971r)e ferredto supergamteh eoryw henh e introduced thec oncepot fr eciprocaall truismH. owevert,h ee ffortso f thef

10、 orerunneres mained isolatedw hereatsh ec onceptuainl novatiobny MaynardS mitha ndP ricei mmediately generatead f lowo fs uccessfuell aborationasn da pplicationTsh. eb ooko f Maynard Smith( 1982as) ummarizeths er esultso f thei nitiald evelopmeonft t hef ield.I n the beginningth erew asl ittlei nter

11、actiobne tweenb iologistsa ndg amet heoristbs ut nowadaytsh ec oncepot f an evolutionarilsyt ables trategayn di ts mathematical exploratiohna sb eeni ntegrateidn to the broaderfi eld of non-cooperatigvaer ne theory.A n excellenot verviewc oncerninmg athematicraels ultsis givenb y van Damme( 1987)i n

12、 Chapte9r of his book on stabilitya nd perfectiono f Nash equilibriaA. nothero verviewp aperw ith a similaro rientatioins due to Bomze (1986).H owever,it mustb e emphasizetdh at the readerw ho is interesteidn substantiadle velopmenbti,o logicaal pplicationa,n dc onceptuadli scussionm ust turnt o the

13、b iologicalli teraturwe hichw ill be reviewedin Section8 . Thei nterpretationf g arnem odelsin biologyo n theo neh anda ndi n economics andt hes ocials cienceos n theo therh andi s fundamentadlliyff erentT. hereforeit, is necessartyo clarifyt he conceptuabla ckgrounodf evolutionargya met heory. This

14、w ill bed onein then exts ectionW. e thenp roceedto introducteh em athematical definitiono f evolutionarsyt abilityf or bimatrixg arnesi n Section3 ; important propertieosf evolutionarislyta bles trategiewsi ll be discussetdh ereI.n Section4 wes hallc onsidesri tuationisn whicht hem emberosf a popul

15、atioanr en oti nvolved in pairwisec onflictsb ut in a global competitioanm onga ll memberso f the populationS.u ch situationasr eo ftend escribebdy thew ords; playingth ef ield;. The mathematicdael finitiono evolutionarsyt abilityfo r modelso f this kind will bei ntroduceadn di ts propertiewsi ll be

16、d iscussedS.e ction5 dealsw itht hed ynamic foundationosf evolutionarsyta bilitym; osto f ther esultsc overedco ncerna simple systemo f asexuarle productiocna lledr eplicatodr ynamics;o mer emarksw ill be madea boutd ynamicp opulatiogne neticms odelso f sexuarl eproductionS.e ction 932 P. Hammerstei

17、ann d R. Selten 6 presenttsw o-sideda symmetrcico nflictsI.t is firsts hownh owa symmetrcico nflicts can be imbeddedin symmetrigc ames.A classo f gamem odelsw ith incomplete informationw ill be examinedin which animalsc an find themselveisn different roless ucha s ownera ndi ntruderin a territoriacl

18、 onflict.I f ther oleso n boths ides are alwaysd ifferentt,h ena n evolutionarilsyt ables trategym ustb e pure.S ection 7 is devotedto evolutionarsyt abilityin extensivgea mesp, roblemsa risew ith the usualn ormalf ormd efinitiono f an evolutionarilsyt ables trategyA. concepwt hich is bettera dapted

19、to the extensivfeo rm will be defineda nd its propertiews ill be discussedI.n thel asts ections omer emarksw ill be madeo n applicationasn dt heir impacto n currentb iologic?tl hrought. 2. Conceptuabla ckground In biologys trategieasr e consideretdo be inheritedp rogramsw hich controlt he individual

20、bs ehaviorT. ypicallyo nel ooksa t a populationof memberosf thes ame speciesw ho interactg eneratioanf terg eneratioinn games ituationso f the same type.A gaina nda gaint hej ointa ctiono f mutationa nds electionre placest rategies by othersw ith a higherr eproductivseu ccessT. his dynamicp rocessm

21、ayo r may notr eacha stablee quilibriumM. ost of evolutionargya rnet heoryfo cusesa ttention on thosec asesw heres tablee quilibriumis reachedH. owever,t he dynamicso f evolutionarpyr ocesseisn disequilibriumis also an activea reao f research(s ee Section5 ). 2.1. Evolutionarsyt ability In theirs em

22、inapl aperJo hn MaynardS mitha ndG eorgeR . Price( 1973i)n troduced the notion of an evolutionarilyst ables trategyw hich has becomet he central equilibriumco ncepot f evolutionargya rnet heoryC. onsidera populationin which all membersp lay the sames trategyA. ssumet hat in this populationa mutant a

23、risesw ho plays a differents trategyS. upposet hat initially only a very small fractiono f the populationp layst he mutants trategyT. he strategyp layedb y the vast majorityo f the populationis stablea gainstt he mutants trategyif in this situationt he mutants trategyh as the lower reproductivseu cc

24、essT. his has the consequencteh att he mutants trategyis selecteda gainsta nd eventuallvya nishes fromt hep opulationA. strategyis callede volutionarislyta bleif it is stable,in the senseju st explaineda, gainsta ny mutantw hichm aya rise. A populationst ateis monomorphifi ce verym embeur sest hes a

25、mes trategya nd polymorphiifc m oret hano nes trategiys presentA. mixeds trateghya sa monomor- phic and a polymorphicin terpretationO.n the one hand we may think of a monomorphpico pulationst atein whiche veryin dividuapl layst hism ixeds trategy. Ch. 28: GarneT heorya ndE volutionarByi ology 933 On

26、 theo therh anda mixeds trategcya na lso be interpreteads a descriptioonf a polymorphipco pulationst atei n whicho nlyp ures trategieosc cur;i n this picture thep robabilitieosf them ixeds trategdye scribeth er elativefr equencieosf thep ure strategies. The explanatioonf evolutionarsyt abilityg iven

27、a bovei s monomorphicn the senset hati t referst o the dynamics tabilityo f a monomorphipco pulations tate against he invasiono f mutantsA. similari deac anb e appliedt o a polymorphic populationst ated escribebdy a mixeds trategyIn. thisp olymorphiicn terpretation a potentiaml utants trategyis a pu

28、res trategyn ot representeind the population stateS. tabilityo fa polymorphisct atere quirens oto nlys tabilitya gainstth ei nvasion of mutantbs uta lsoa gainsst mallp erturbationosf ther elativefr equencieasl ready presenitn the population. Biologistsa re reluctant o relinquisht he intuitivec oncep

29、to f evolutionary stabilityto a generaml athematicdael finitions incet heyf eelt hatt heg reatv ariety of naturallyo ccurrings electionr egimesr equirea n opennessw ith respectt o formalizationT.h ereforet heyd o not alwaysu se the terme volutionarilsyt able strategyin the exacts enseo f the definit

30、ionp revailingin the formall iterature MaynarSdm itha ndP rice( 1973)M, aynardS mith( 1982)T.h is definitiona ndi ts connectiontso thei ntuitiven otiono f evolutionarsyt abilityw ill be introduceidn Sections3 and4 . 2.2. The Darwinianv iewo f naturals election Darwinst heoryo f naturasl electionis t

31、he basiso f evolutionargya met heory.A commonm isunderstandionfg th eD arwinianv iewi s thatn aturasl electioonp timizes thew elfareo f thes peciesI.n thep aste vene minenbt iologistes xplainepdh enomena of animailn teractiobny vaguelyd efinedb enefittso thes peciesI.t is notc learw hat the welfareo

32、 f the speciess houldb e. Is it the numbero f individualst,h e total biomasso,r thee xpectesdu rvivaol f thes pecieisn thel ongr un?E veni f a reasonable measureo f this typec ouldb e definedit is not clearh ow the interactioanm ong species houldr esulti n its optimization. The dynamicos f selection

33、a mongin dividualsw ithint he sames peciesis much quickert hant hep rocessw hichc reatesn ews peciesa nde liminateost hersT. his is duet o thef actt hatt hel ife spano f an individuails negligiblys horti n comparison to thato f the speciesA. n adiabatica pproximatiosne emst o bej ustifiedF. or the p

34、urposeo f thei nvestigatioonf speciesin teractioenq uilibriumw ithint he species can be assumedto prevail.T his showst hat the processo f individuals election withint he speciesis the moreb asico ne whichm ustb e fully understoobde fore thee ffectso f speciesin teractiocna nb e exploredT. odaym ostb

35、 iologistsa greet hat explanationosn the basis of individuals electiona mongm emberso f the same specieas rem uchm oref ruitfutl hana rgumentrse lyingo n speciebs enefits Maynard Smith( 1976). 934 P. Hammersteiann d R. Selten In the1 960sa theoryo f groups electiown asp roposed (Wynne-Edwar(d1s9 62)

36、 whichm aintainsth ate volutionm ayf avort hed evelopmenotf traitsl ike restraint in reproductionw hich are favorablef or a local group within a structured populationev eni f theyd iminisht her eproductivseu ccesos f thei ndividualI.t must be emphasizetdh att heoreticaelx planationosf groups electio

37、nca nb e constructed on the basiso f individuals electionI.n asfara s suche xplanationasr e offeredt he idea of group selectionis not in contradictionto the usual Darwinianv iew. However,t he debateo n group selectionh as shown that extremep arameter constellationasre n eededin theoreticaml odelsin

38、ordert o produceth ep henomenon Levin(s1 970),B oormana nd Levitt( 1972,1 973),M aynardS mith( 1976),s eea lso Grafen( 1984)f or recentd iscussionos n the termg roups election. Onlyv eryf ewe mpiricacl aseso f groups electioanr ed ocumenteind thel iterature, e.g.t hec aseo f myxomatos(isa diseaseo f

39、 rabbitsin Australia)A. quickerg rowth ratew ithint hei nfectedra bbiti s advantageoufosr thei ndividuapl arasiteb ut bad for theg roupo f parasiteisn thes amea nimals incea shorterli fe spano f ther abbit decreaseths eo pportunitiefosr i nfectiono fo ther abbits MaynarSdm ith( 1989). The speciesa n

40、d the groupa re too high levelso f aggregatiofno r the studyo f eonflicti n animalsa nd plants.I t is moref ruitfult o look at the individuala s the unit of naturals electionO. ftena n evenm orer eductionisvti ewi s proposedin the literaturet;h eg ener athert hant hei ndividuails lookedu pona s the

41、basicu nit of naturasl election e.gW. illiams( 1966),D awkins( 19761, 982)It. mustb e admitted thats omep henomenrae quirea n explanatioin termso f genesw hichp ursuet heir own interesto thed isadvantagoef thei ndividualF. or examplea, genem ayf ind a wayt o influenceth ep rocesso f meiosisin its fa

42、vor;t hisp rocessd eterminewsh ich of two geneso f a pair of chromosomeins a patenti s contributetdo an egg or sperm.H oweveri,n the absenceo f strongh intsi n this directiono neu suallyd oes not look for suche ffectsin thee xplanatioonf morphologicaln db ehavioratlr aits in animalso r plants.T he r

43、eseareehx periencseh owst hatt hei ndividuaal s thel evel of aggregatioins a reasonablsei mplificationT.h e significanceo f morphological andb ehavioratlr aitsf or thes urvivaol f thei ndividuael xerts trongp ressuraeg ainst disfunctionarle sultso f genec ompetitiown ithint he individual. 2.3. Payof

44、fs Payoffsi n biologicalg arnesa re in termso f fitness,a measureo f reproductive successI.n manyc asest hef itnesso f an individuacl anb e describda s thee xpected numbero f offspring.H owever,it is sometimense cessartyo use a morer efined definitiono f fitnessF. or examplei,n modelsf or thed eterm

45、inatioonf thes exr atio amongo ffspringit is necessartyo look moret hano ne generatioanh eada nd to countg randchildrein steado f children Fishe(r1 958),M aynardS mith( 1982a). In modelsin volvingd ecisionso n whetheor ffsprings houldb e borne arliero r later Ch.2 8: GarneT heorya ndE volutionaBryio

46、 logy 935 in thel ifetimeo f them otheirt mayb e necessartyo weighe arliero ffspringm ore heavilyth anl atero nes.U nderc onditionosf externev ariationosf thee nvironment whicha ffecta ll individualws ith thes ames trategiyn thes amew ?yt hee xpected logarithmof then umbeor f offspringm ayb e a bett

47、edr efinitiono f fitnesst hant he usualo ne Gillespi(e1 977). The significanceo f the fitnessc onceplti es in its abilityt o connecst hortr un reproductivseu ccessw ith long run equilibriump ropertiesD. arwiniant heoryis nott autologicaIlt. doesn ots ayt hatt hoses urvivew hos urviveI.n steado f thi

48、si t derivest he structureo f long-rune quilibriumfr om the way in whichs hort-term reproductivseu ccessm easurebdy fitnessd ependso n the environmenatn d the populations tate.H owever,a s it has beene xplaineda bove,d ifferent ypeso f processeos f naturasl electionm ayr equired ifferenwt ayso f mak

49、ingt hei ntuitive concepot f reproductivseu ccesms orep recise. 2.4. Garnet heorya nd population9 enetics Biologistss peako f frequency-dependsenletc tionif thef itnesso f a typed epends ont hef requencdyi stributioonv ert ypesin thep opulationT.h isd oesn otn ecessarily meant hats everalt ypesm ust

50、b e presenat t equilibriumF. requency-dependent selectionh as beend iscussedin the biologicali teraturelo ng beforet he rise of evolutionargya rnet heory.G ame-theoretpicro blemsin biologyc an be looked upona s topicso f frequency-dependsenletc tiona ndt hereforseo meb iologistfse el thatg arnet heo

51、ryd oesn ota dda nythingne wt o populatiogne neticsH. oweveri,t mustb e emphasizetdh att het ypicapl opulatiogne neticstr eatmenotf frequency- dependenste lectionfo cuseso n theg eneticm echanismof inheritancaen da voids thed escriptioonf complexs trategiicn teractionC.o ntraryt o this the modelso f

52、 evolutionargya rnet heoryig noret hei ntricacieosf geneticm echanismasn df ocus on thes tructuroef strategiicn teraction. The empiricailn vestigatowrh ow antst o models trategipch enomenina nature usuallyh as littlei nformatioonn the exactw ay in whicht he relevantr aitsa re inheritedT. hereforeg a

53、mem odelsa re bettera daptedto the needso f empirical researcihn sociobiologayn db ehavioraelc ologyth and ynamimc odelsin population geneticst heory.O f courset he treatmenotf problemsin the foundationo f evolutionargya rnet heorym ayr equirea basisi n populationge neticsH. owever, in applicationit

54、s is ortenp referableto ignoref oundationpalr oblemes veni f they aren ot yetc ompletelsyo lved. In biologyt he word genotypere ferst o a descriptiono f the exactg enetic structuroef an individuawl hereatsh et ermp henotypies usedf or thes ystemo f morphologicanl db ehavioratrl aitso fa ni ndividuaM

55、l. anyg enotypemsa yr esulitn thes amep henotypTeh. em odelos fe volutionagrya meth eorya rec alledp henotypical sincet heyf ocuso n phenotypersa thert hang enotypes. 936 P. Hammersteiann d R. Selten 2.5. Players The biologicailn terpretatioonf games ituationes mphasizesst rategiersa thert han playe

56、rsI.f onel ooksa t strategiicn teractionws ithina populationit is important to know the relativef requencieosf actions,it is less interestintgo know which membepr laysw hichs trategyT.h ereforet,h eq uestionw ho aret hep layersis rarely discussedin the biologicali terature. It seemst o be adequatteo

57、 think of a ;player;a s a randomlys electeda nimal. Therea re two wayso f elaboratintgh is idea.S upposeth att herea reN animalsin thep opulationW. e imagineth att heg ameis playedb y N playersw hoa rer andomly assignedto theN animalsE. ach playerh ase qualc hancesto become acho neo f the N animalsW

58、. e call this the; many-playeinr terpretation;. Anotheri nterpretatioisn b asedo n thei deat hatt herea re only a smalln umber of players,f or example2 , which are assignedt o the two roles (e.g. ownera nd intruderi)n a conflicta t randomB. othh avet hes amec hancet o be in eacho f both roles.M oreo

59、vert, herem ayb e a universeo f possiblec onflictsf rom which one is chosenw ith thea ppropriatper obabilityT. herem ayb e incompletien formatioinn the senset hatt he playersd o not know exactlyw hich conflicth as beens elected whent heyh avet o maket heird ecisionW. e call this the ;few-playeirn terpreta- tion;. The few-playeirn terpretatiocna nb e ext