Helmut B ester and Wer ner G uth 3y
November 1994
Abst ra ct
We devel op an e vol utionary app roach toexpl ain al trui stic pre fe re nces. Gi ven
thei rpreference s,i ndi vid ualsi nte ractrati onall ywithe achother. Bycompari ngthe
succ essofpl ayerswithdi erentpreferen ces,weinvesti gatewhethe revol utionfavors
altrui sti c or sel sh atti tu des. The ou tc ome d ep e nds on whether the i nd ivi dual s'
i nteractions are strategic comple ments or substitutes. A ltrui sm an d sel f-i nte re st
are conte xtd ep e ndent.
Keywords: Altrui sm, Evoluti onary Stabi li ty, End ogenous Preference s, S trate gi c
Comp leme nts and Substi tu tes; J ELClassi cation No.: A13,C72,D64
3
CentER, Tilbur g Univers ity, and Humb oldt Unive rsity, Ber lin; r es p ec tive ly. The s ec ond author
is grate ful t o the Humboldt Foundation for sup p ortin g his visit at Ce ntER, where this re search was
comple ted.
y
1 Introduct io n
There is a n abunda nce of o bservations show ing tha t individuals do not always pursue
self- interest: Peop le risking their ow n life to rescue others, s old iers volunta rily go ing to
war, the many fo rms of cha rity etc. These o bservations can be made cons istent w ith
sta ndardecono micth eo ryby p o stulatingutilityfunctionsth atin cludethe well-b eing of
othersina dditionto theownon e. Yet,this onlyrep hrasesthequestio nofw hy
individu-alsb ehave in this way. Instead ofexp laining altruis ticbehavior,one nowhas to exp lain
why p eople s ometimes have a ltruistic preferences . It is this question tha t we want to
add ress .
Wea dopta nevolutionarya pproa chtoinvestiga tewheth era ltruismmayhaveevolved
in huma ns thro ugh a process of na tural or cultural selectio n. Fo rma lly, the degree of
altruismisexpres sedbyapreferencepa rameterdes cribinghowmuchanin divid ual cares
for the success of o thers. T he ra nge of pos sible para meters includes pure self-interest
as th e special cas e wh ere an ag ent's objective is identica l to h is private success . In
the interactio n with others, each player ra tio nally selects a strategy to maximize his
preferences . As a result, in equilibrium each p layer's e ective succes s depends on the
altruistic attitudes of all the invo lved players. This allow s usto compare the su ccess of
players with di erent preference pa rameters. In a n evolutio nary environment, players
with a hig her exp ected succes s are less likely to be eliminated. Sin ce success is related
to preferences , weca ns tu dythe questionof whetherevo lutionfavo rsaltru istico rsel sh
attitudes. Altruismissa idtob eevo lutiona rilystableifitsurvivesevo lutiona ryselection .
Instead o f studyin gdirectlythe evolutiono f b ehavior,w hich is th eus ual appro achin
evolutionary bio log y 1
and in evolutio nary ga me th eo ry (see, fo r in stance, Ha mmerstein
and Selten (19 94 )), we consider ra tio nal beh avior for given preferences. These
prefer-ences d etermine the players ' behavior a nd their e ective s uccess via their e ect on the
outco meof stra teg icinteractio ns. By assu ming ra tio nal b ehavior a nd ap plyin gthe co
stra teg ies, we endo genou sly determine preferences. Our appro ach thus o ers a way of
endog enizing individual objective functions, which neocla ssica l theory u sually trea ts as
exo genous . 2
Our ana lysis o f in divid ual interactio ns yields two insig hts: First, a comparison of
the interactio n between a ltruists and th e intera ction b etween egoists revea ls that the
altruists a chieve a higher material payo than the ego is ts. Th is is so b eca use a ltruistic
preferencesinternalizes omeextern alitiesinthe ga meb etweentheplayers . Seco nd,when
an altru istintera cts with an ego is t, th ea ltruist's materia l payo is lower than the ego
-ist's payo . This ndingis in line withthe conventio nal viewtha t altruisticp referen ces
reducethe individua l'ssucces s,whileatthesametimeincrea singtheo pp o nent'ssuccess .
Th e second res ult is o ften used as an a rgument that altruis m canno tpossibly evo lve
by natural selectio n. Yet, th is a rgument does no t directly address evolutio nary co
n-sideratio ns. For th e pro cess of n atural s election, th e relevant questio n is wheth er an
egoistic mutant fa cing a population o f altruis ts is more success ful th an the a ltruists
amon g thems elves. Altruism will b e evo lutiona rily stable if a n ego ist in the interaction
with an a ltruist receives a lower materia l payo than a n altruist. In o ur mo del, this
dep ends o n the strategic dep endence between the players. Altruism tu rns out to b e
evolutionarilys table o nly if the ga me exh ibits stra teg ic complementarities in the sense
ofBulowet. a l. (19 85 ). Thiss ugg eststhat preferencesmaybeco ntextdep endent.
Situ-ationa lfa cto rsmaydecidewhetherin divid ualsare motivatedbyaltruis morself-interes t.
AsFrank(1 98 7,1 988 )andSchelling(1 978 ),o urana lysisemp hasizesthestrategicrole
of p referen ces a nd emo tio ns. A player's preferences a ect n ot on ly his own equilibrium
b ehavior but a lso the b ehavio r of his o pp o nent. Dep ending o n the typ e o f interaction ,
this e ectcan beeither b ene cia lor ha rmfulfor aplayerw ithaltruistic preferences. As
aresult,natura lselectio nfavors altru isminth ecase ofstra teg iccomplementsbut no tin
p-These arguments s how th at evolutio n can sus tain a ltruism between genetically linked
individuals (see, e.g. Bergstro ma nd Sta rk (199 3)).
Th e following section describes the interaction b etween in divid uals and de nes their
succes s resulting from their b ehavior. Section 3 studies the interaction between eg oistic
players an d dis cus ses eciency implications . Altruistic preferences are introduced in
section 4 , wh ere we a lso study the impact of preferences o n the equilib rium outcome.
Section 5investig ates the evolutionary stab ility o f a ltruism. In s ectio n 6we extend our
conclus io ns to a mo re general framewo rk. Fina lly, section 7 con cludes a nd discusses
extensions .
2 Success and Behavior
Co nsid erapopulationwhos emembersinteractwitheacho therinpairs. Allmembersare
identica la nd s otheintera ction b etweenapairofindividua lsisdescrib edby asymmetric
ga me. Inthis ga me,one ofthe playersis lab elledas player1a nd theo th er isla b elledas
player 2 . Player 1's choice of action is denoted by x 0; player 2 choo sess ome action
y0:Ea chplayer'smateria lpayo orevolu tion arysuccess dep endso nthe jointactio ns
(x;y )a ccord ing to U 1 (x;y )x(ky+m0x); U 2 (x;y )y(kx+m0y); (1)
where the para meters k a nd m a reassumedto satisfy the restriction
01<k<1 and m>0: (2)
The functionU
i
(1)does no tnecess arily repres entp layeri'ss ubjective utility o rhis
pref-erences. In the intera ction with his opponent, player i s eeks to maximize the utility
V
i
(x;y): The functio n V
i
(1); w hich may di er from U
i
(1); w ill b e de ned in Sectio n 4 .
The parametric sp eci cation of payo s allow s us to derive a closed fo rm so lution for
the players ' equilib rium success . Assumption (2) to gether with th e s p eci cation of the
utility functio nV
i
The speci catio n of ma terial payo s in (1 ) is suciently general to illustra te the main
arg umentso f our ana lysis; weco nsider more g enera lpayo functio ns insectio n 6.
By (1), each ind ivid ual's success dep ends n oto nly o n hisow n actio nbut also on the
cho ice of the o ther p layer. If k > 0 the game exhibits p o sitive externa lities beca use a
higher a ction by player i in creases the succes s o f player j: Negative externalities occur
if k <0: The simplest example is a productio n g ame with externalities , where x a nd y
denotethe players 'e o rtorinp utdecisio ns. Player1'ssu ccesscanthenb ede nedasthe
di eren ceb etweenhisoutput,x(ky+m);a ndhis(qu adratic)e ortcost,x 2
:E quivalently,
inthe pres enceo f cos texterna lities,his o utputis mxand hisco stisx(ky0x): Po sitive
productio n externalities may not only result from tech nological interdependence; they
also occur whena gentssha re the joint outp utof theirindividua l pro d uction e ortsor if
their e orts contribute to the p ro duction of a public goo d. Neg ative cost externa lities
arise na turally whenth e p layers exploita co mmon res ource.
Several autho rs have used evo lutiona ry a rguments to explain the market behavior
of rms (s ee, e.g. Penro se (195 2) a nd Winter (19 71 )). We can a pply o ur app ro ach to
the s tandard models of oligo p o listic co mpetition by identifyin g a rm's success with its
pro ts: Player 1 a nd 2 are enga ged in a s ymmetric duopoly g ame with hetero geneo us
productsa nd linear d emand functio ns. In aC ournot market, the actio nsx and ywould
repres ent the rms' quantity cho ices. Their products are imperfect subs titutes for all
k 2(01;0) a nd their pricesare m+ky0x an d m+kx0y : In aBertrandma rket,the
rms would compete by choos ing prices x and y; res p ectively. They fa ce the demand
functio nsm+ky0xand m+kx0yand theirpro d uctsa reimp erfect subs titutesforall
k 2(0;1 ):T hus ,thepayo sin(1 )canb einterpretedas theCo urnot or Bertra ndpro ts
in asymmetric duo p olymarketwith zero productio n costs .
As ab enchma rk,wed e neasymmetrico ptimumby actio ns(^x;y )^ that maximizethe
players'joint success, i.e.
(^x;y )^ 2arg ma x[U
1
(x;y)+U
2
Since 01 < k < 1 ; this op timum is well-de ned and determined by the necessa ry and
sucient rst-o rder co ndition s x=(2 ky+m)=2 an d y=(2kx+m)=2 :T herefore,
^ x=y^= m 202k a nd U 1 (^x;y)^ =U 2 (^x;y )^ = m 2 4(10k) : (4)
Typically, the presence o f externa lities prevents the players from rea ching the o utco me
(^x;y )^ thro ugh individua l preference maximizatio n. In the fo llowin g two s ections, we
inves tiga te the relation b etweenaltruis tic preferences an d this ineciency.
3 Equilibrium with Egoistic Preferences
An ego istic player seeks to ma ximize his priva te succes s. He shows no con cern fo r the
succes s o f hispa rtner. Tha t is,player iacts eg oistica lly if his subjective utility satis es
V
i
(x;y) = U
i
(x;y ): Since the players interact non- coopera tively, each of them chooses
his action ta king the a ction o f the other as given. T his resu lts in a ctions (~x;y)~ that
constitute a Nas hequ ilibriumof the g ame. Accordingly,
~ x 2arg ma x x U 1 (x;y);~ y~2argmax y U 1 (~x;y ): (5)
The players'b est- respons e functions are g iven by
~
x=0:5(ky+m); y~=0 :5 (kx+m): (6)
Tochara cterizethe typ eo fs trategicinterdep endence,itwillb eusefultoemployth e
ter-mino lo gyo f Bulow et. al. (19 85): For k >0;the reaction functions a reupwards sloping
and the g ame exhib its s tra tegic complementa rities . If k < 0; the game exhibits
strate-gics ubstitu tes becaus e the rea ction functio ns are dow nwa rds slo ping. Fo r insta nce,the
Co urnot ga me discussed in Section 2 induces strategic s ubstitutes , while the Bertrand
ga me leads to stra teg ic complements .
Th e players'reactions g enera tethe fo llowing equilibriuma ctions and payo s:
~ x=y~= m ; U 1 (~x;y)~ =U 2 (~x;y )~ = m 2 2 : (7)
As a res ult U
i
(~x;y )~ < U
i
(^x;y);^ i = 1;2 ; unless k = 0: The reaso n is, of course, that
with egoisticbeh avioreachplayerign ores the impact ofhis a ction o n the other player's
succes s. Thiskindofexterna lityexpla in swhyx~=y~<x^=y^ifk >0;andx~=y~>x^=y^
if k <0 :
Usua lly, o ne de nes evolutio nary s tability in terms o f stra teg ies rather than
preferences . 3
T hede nitionofa nevo lutiona rilysta bles trategyimpliesimmediatelythat
this stra teg y co nstitutes a symmetric Nash equilibriu m. In fact, if a symmetric Na sh
equ ilibrium is `strict' in the s ens e that the players' b est res p ons es are unique, then the
equ ilibrium stra teg y is also evolutionarily stable. By (6) the equ ilibrium (~x;y )~ is strict
and , sincex~=y ;~ itiss ymmetric. Therefore,o nlythe s trategy x~isevolutio narily stable.
Tha t is, onlythe eg oistic b ehavior x~=y~survivess electiono f the most successful s
trat-egy. Toexplainthe evolutio n o faltruism,on ehas to ad opta n alternativemethod. This
is do ne by our `indirect' evolutionary appro ach, which applies the idea o f evolutionary
selectio nto preferences instea d of s trategies.
4 Altruistic P references
A player is altru istic when his preferences re ect so me concern for th e o ther player's
succes s. We describe suchpreferences by
V 1 (x;y)= U 1 (x;y)+(10 )U 2 (x;y ); V 2 (x;y )= U 2 (x;y )+(10 )U 1 (x;y): (8)
Accordingly, the co ncern tha t players 1 a nd 2 exp ress for the other player's success is
repres ented bythe weig hts10 and 10 ;respectively. If ; <1;theplayersa resaid
to b e altruis tic. This formu lation o f altruism ha sb een emp loyed alrea dyby Edgeworth
(18 81 ,p. 53 ),w ho calledthe va lues(10 )= and(10 )= the `coecientsof e ective
sympathy'. In w hat follows, we restrict these coecients to lie in the unit interval by
considering onlyvalues o f a nd such that
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x = 1 < 1 <1 =1 y x x ( x 3 ;y 3 ) (x;~ y)~ (x;^ y^) P P P P P P P P q X X X X X X X y P P P P P P P P i
Fig ure 1: Altruisma nd EquilibriumBeh avior
Tha tis ,eachplayer istakentoweig hhisownsuccessat least asmuch asth eopp o nent's
succes s. We ma intain the as sumptio n of common knowledge to a nalyse the game b
e-tweenthe 0 an d the 0player. This means, no tonlythe ma terialpayo s b utalsothe
preference pa rameters a nd are co mmonlyknow n bythe p layers. We willd iscussthe
signi cance of this a ssumption later inthis sectio nand in section 7.
Altruismin uences thestrategicintera ctionsb etweentheplayerseventhoug hitdoes
notdirectlya ecttheirs uccessas de nedby(1). Altruismha sa nindirectimpa ctonthe
players' succes s s ince their b ehavio r dep ends on the pa rameters and : Ea ch p layer
seeks to maximize his subjective preferences so that
x 3 2arg ma x x V 1 (x;y 3 ); y 3 2a rgmax y V 2 (x 3 ;y ): (1 0)
Fromth e rst-o rderco nditio nsfo rpreferencemaximiza tion wecanderiveth eplayers '
b est respons e fu nctions :
x= ky+ m 2 ; y= kx+ m 2 : (1 1)
own-resp o nse for given para meter values = 1 and < 1 : S imilarly, player 2's behavior is
repres ented fo rtwodi erentvaluesof :Th eintuitio nfo r thise ectisthat ana ltruistic
playerinternalizes,atlea stpartially,the externalityofhisb ehavio ro nthe otherplayer's
succes s. Thisinducesh imtoselectahigheractionwithp o sitiveexterna litiesan dalower
action w ith n eg ative externalities.
Th e equilibriumo f the ga me between two players with preference para meters and
; resp ectively, isg iven by
x 3 ( ; )= m(2 +k) 4 0k 2 ; y 3 ( ; )= m(2 +k) 4 0k 2 : (1 2)
In Figure1 the equilibriu m is determined as the intersectio n o f the players' best
re-sponse functio n. Fo r = =1;this is the point(~x;y ):~ In aga mebetweentwoa ltruists
(x 3
;y 3
) is realized a s ; < 1 : As the g ure illu strates, this o utco me is clos er to the
optimum (^x;y )^ than the ego is tic equilibrium (~x;y):~
For what fo llows, it is imp o rtant to no tice that ea ch player's preference pa rameter
not only a ects his own equilib rium b ehavio r but a lso the opponent's choice o f action .
Sincethe playersa reenga gedinan on-coopera tivega me,eacho fthembaseshisdecision
on hisknowledg ea b ou tthe other player's attitudes. FollowingSchelling (1 978 ,p. 2 29 ),
who ca lls \ abehavioral propensity [...] s tra tegicif it in uences others by a ecting their
expecta tion s," we refer to the depen dence of x 3
on a nd of y 3
on a s the `strategic'
e ect ofaltruism. Thiss tra teg ice ectisco nsistentwiththe ps ychological evidence that
individuals do no t a ct un iformly ag ainst other in divid uals; rather, they condition their
own b ehavio r o n th e attitudes o f tho se with w hom they intera ct. 4
Th is, of co urse,
pre-sumes that they can a nticipate the attitudes of their opponent. Preferences ca n have
a strategic e ect o nly if, a t leas t to s ome extent, they are co mmunica ted to the other
player. In this sense, our an alys is refersto environments where the players lea rnabout
each other b efore cho o sing their a ctions . In fact, as Frank (1 98 7, 19 88) arg ues , ma ny
obs erva ble phys ical s ymptoms may provide some indica tio n o f a perso n's a ective co
evidence tha t, even o n the basis o f b rief enco unters involving strang ers , s ubjects are
adept a tpredicting the behaviorof their opponent (seeFra nk (19 88),ch. 7).
Using (1 2), we can d etermine the directio n of the stra teg ic e ect. As @x 3
=@ < 0
and @y 3
=@ <0 fo r all k 6=0 ; the opponent's equilibrium actio n will b e the higher the
more altru istica lly inclined a player is. In the ca se o f p os itive externalities (k > 0 );
therefo re,the s trategice ectha sap o sitive impact onthe a ltruisticplayer'ssu ccess.
Ef-fectively, th e op p onent willchoose a mo refavorab leactio n beca useh e interactswith an
altruist. If k <0; however,th e stra teg ic e ect tu rns out to b e disadva nta geous : P layer
i'saltruisminducesplayerj to choo seahig heractio nandthisreducesplayerj'ssuccess .
Ca nap o pulatio no faltruis ticplayersreachahigherlevelofsuccessthaneg oisticp
lay-ers? Weans wer thisqu estionbyco nsidering the outcomeofth eintera ctionb etweentwo
players with id entica l preference parameters . A co mp aris on with the egoistic o utco me
and the symmetric o ptimum shows that, for a ll 1= 2< <1;
~ x =y~<x 3 ( ; )=y 3 ( ; )<x^=y ;^ if k >0; (1 3) ~ x =y~>x 3 ( ; )=y 3 ( ; )>x^=y ;^ if k <0: (1 4)
Altruisms hiftsthe equilibrium o utco meclo ser towa rd s optima l behavior. Infa ct,inthe
extremeca se =1 =2theplayers'equilibriumactio nsb eco meidenticaltothesymmetric
optimum. Th is has the following implication fo r the players ' success.
Proposition 1: Letk 6=0 :The na populationof altruistic playersreaches ahig her le ve l
of su cce ss than a popul at ion of egoists, i.e. U
i (~x;y )~ < U i (x 3 ( ; );y 3 ( ; )); i =1 ;2; if <1:
Pro p o sition 1 sh ows that altruis m produces more ecient ou tco mes. 5
Yet, this does
not mean that an a ltruistica lly inclined a cto r is more s uccessful th an a playerw ho acts
follow s fromL emma 7in the App endix, con rms this intuition.
Proposition 2: Let k 6= 0: Then in the in terac tion be twee n two players, the
more al truist icall y motiv ated pl aye r is l ess successful than his oppone nt. That is
U 1 (x 3 ( ; );y 3 ( ; ))<U 2 (x 3 ( ; );y 3 ( ; ));for all < :
An altruis t is w illing to redu ce his own succes s in order to increas e the succes s of
others. Therefo re, one might conclu de tha t self-interest ha s a higher surviva l va lue
than a ltruism. Yet,Pro p o sition 2 presents only o necons ideration tha t is important for
evolutionary selectio n. As Pro p os ition 1 indicates, a population consisting la rgely of
altruistswill p erformbetterthana p o pula tio nofeg oists. Aneg ois twithinapopulation
of altru ists may h ave a relatively low exp ected s uccess b eca use the altruists a mo ng
thems elves attain ahigher levelof successthan the ego ist ag ainstthe altruists . In fact,
evena na ltruistintera cting witha nego istmayhaveahighers uccessthan aneg oistw ho
faces ano ther ego ist. In the following sectio n we will address th e issue of evolutionary
preference selection by using the concept of evolutio nary sta bility.
5 The Stability of Altruism
Ca n altruism emerg e in an evo lutiona ry pro cess w here only the mo st success fulplayers
survive? By Propositio n 1, a population of altruis ts is more s uccessful th an a p o pula
-tion ofego is ts. But th isdoesno tnecess arilymean thataltruismisevolutio narily stable.
Whena neg ois tinvadesapopulationofaltru istsan dperfo rmsb ettertha nhisopp o nents ,
thenego ismw illspreado utan d eliminatea ltruisticb ehavio rinthe processof evolu tion .
Co nvers ely, an altruis t may s uccessfully invad e a p o pula tio n o f ego is ts if he doesbetter
than the eg oists aga ins t ea ch other.
To study the evo lutiona ry s tability of altruis m, we employ the `ind irect' evolutio
n-ary appro ach , which is schema tically presented in Fig ure 2 . In th e previous s ectio n we
re-Selection Evolution ary
Preferen ces
Subjective Equilibriu m
Behavior Material Success 6 -?
Figure 2: Evo lutiona ry Selection of Preferences
evolutionary selection favors the more succes sful players , players w ith lower materia l
payo s will beco me extinct. In this way, preferences a re selected for their capa city to
generate materia lp ayo s.
Tocompleteouranalysis ,weinvestig atewhetheramon omorphicp opu la tionofplayers
withpara meter 3
isimmun ea ga instinvadingmutantplayerswithad i erentpreference
para meter. In wha tfo llows,R( ; )deno tes aplayer'ssuccess w henhehas thealtruism
para meter whilehisopponentha sthepa rameter :Sincethe intera ctionb etweenth ese
playersresults inthe equilibrium (x 3 ( ; );y 3 ( ; )); we get R ( ; )U 1 (x 3 ( ; );y 3 ( ; )): (1 5)
The muta nt sp ace M = [1=2 ;1] is the set of all possible va lues for the para meters
and : Th e fu nction R(1) to gether with the s et M de nes a s ymmetric evolutionary
ga me. Thisgamea llows usto study theevo lutiona ry sta bilityo f apreferencepa rameter
byusingth eco ncepto fevolutionarilystablestrategies(ESS,s eeMaynardS mith(19 82 )).
De nition: A preference parameter 3
2[1 =2;1 ] is called evolutio narily sta ble if
R( 3 ; 3 ) R ( ; 3 ) fo r all 2[1= 2;1];an d (1 6) R( 3 ; ) >R( ; ) w henever R ( 3 ; 3 )=R ( ; 3 ): (1 7)
Th es e conditio ns ca pture the idea tha t a population with p arameter 3
ment,a nevolutio narilysta blepara meter 3
isabestreplya ga ins titself. Any 0mutant
inva ding asociety of 3
- playerscan not b e mo res uccessful than the memberso f the so
-ciety. If several parameters are equa lly success fu l, th e s econd co ndition ru les o ut that
an alterna tive best reply 6= 3
can spread o ut in the p o pula tio n: Since 3
is better
ag ainst th an itself, w ill b e eliminateda s so o nas itb ecomes morefrequentwithin
the p o pulatio n.
Th e ESS-concept o rig ina tes from biolog y and is bas ed on the idea that hig her
suc-ces s re ects an a dvantag e in reproducing . In an econo mic co ntext, of cours e, s uccess is
mostlyidenti edw ithmonetarypayo s. Onecandirectlyextendtheideaofevolutionary
sta bility to this context when monetary payo is an importa nt d eterminant fo r rep ro
-ductive success. Indeed, so me empirical evidence indica tes tha t, over the more recent
huma n histo ry, individua lwealth h asb eenp o sitively related to the numb erof surviving
o spring. 6
Fo rthe eco nomist,however, the socialmechanismsof learninga nd imitation
arepro bablymo reimp o rta ntthanth eg en eticmecha nis m: Evo lution aryselection o ccurs
b ecaus e s uccessful b ehavio ralattitudes tend to b e imita ted. In divid ual traits that yield
lower payo swill,therefore, be driveno utby more su ccessfultraits . In this way, imita
-tionmayinduceaproces sthatresemblesna turals electionorthe`s urvivalofthe ttest'. 7
We rst a pply the ESS -co ncept to the ca se k > 0; where the players' interactio ns
exh ibit strategic co mplementarities. By Lemma s 4 - 6 in the App endix we g et the
fol-lowing result.
Proposition 3: Let k > 0 : Then 3
= (2 0k)= 2 is t he uniq ue ev olution arily stabl e
prefe ren ce paramete r.
As 3
< 1; evo lutiona rily sta ble p referen ces must exhibit so me deg ree o f a ltruism.
The level of a ltruism is p o sitively related to th e pa rameter k: Altruism b eco mes more
important when thes trategic interdep endenceb etweenthe players is rela tively high. In
Why ca na n eg oistic muta nt with > 3
not inva dea population of 3
-individuals?
Actua lly, by P rop o sition 2,s uch amutant ha sa higher su ccess th an th ememberof the
p o pulatio n w ith whom he interacts. Yet, the low payo of a n 3
- player ag ainst a n
in-vad ingmuta ntislessimp o rtantforevolutio narycons iderations. For th emembersofthe
p o pulatio n the likelihoo d of intera cting with the mutant is s ma ll. Mos tly they interact
with ea ch o th er a nd so, by Pro p o sition 1 , their exp ected level of su ccess is relatively
high. Thepa rameter 3
<1is evolutiona rily stable b ecauseinth egame b etweena pa ir
of 3
- individua ls each of th em g ets a la rger materia l payo th an the eg oist a gainst an
3
-o pp o nent.
Als o, th e uniqu eness o f 3
in Propositio n 3 implies that a population of ego ists is
vulnera ble a ga ins t inva sion by altruis tic agents. T his is so b ecause the interaction b
e-tween the ego is ts results inlow payo s. If an a ltruist enters a p o pula tio no f egoists,his
payo will b e lowertha n the on eof his partner. Nonetheless, heis still more success fu l
than a ll the o ther eg ois ts who h ave an egoist as th eir partner. This hap p ens b ecause
preferences haveas tra teg ice ect: Asitwas s hown in th efo regoing section, the a ltruist
induces his o pp o nent to increa se his actio n level. In the ca se of p o sitive externalities ,
this is bene cia l ands o hew ill s ucceed in invad ing a society of eg oists.
Th e la st a rgument indicates tha t the s ign of k may be imp o rtant for the evolution
of altruis m. In fact,the follow ing result reveals that eg oistic preferences are the unique
evolutionary o utcomein th eca seof stra teg ics ubstitu tes.
Proposition 4: Let k < 0: The n 3
= 1 is the uniq ue ev ol utionarily st ab le pre feren ce
parame ter.
Th eproofof thissta tementfollow simmediately fro mL emmas 4-6intheApp endix.
situationsandego isticallyinothers. Oursimpleexampleo fstrategicinteractio nsdemo
n-stra tes this by the d epend ence o f 3
up on the pa rameter k: When k <0; a population
of egoists will d efeat entry o f a ltruism. On averag e the ego ists will b e more success fu l
than an invading mutant. Infact, an altruisticentra nt willsu erfo r two reaso ns. Firs t,
his choice of action does no t a im at ma ximizing priva te succes s. Second, as k <0; the
stra teg ice ectof hisattitudeturnsout tobeharmful. Hiseg oistico pp o nentw illchoose
a hig her actio n level when fa cing a n a ltruist. In the presence o f negative externa lities
this lowers the altruist'sp ayo .
In terms of the examples discuss ed in section 2 , our ana lysis show s tha t altruism
emerges inth e presence of p o sitive productio n extern alities , in the case of output sh
ar-ing, or in a Bertrand market. Self-interest is s table in an environment with nega tive
productio n externa lities, with commo n reso urce exploita tio n, a nd in a C ournot
mar-ket. The stra teg ic e ect of preferences explains w hy altru ism is evolutio narily sta ble
for k > 0 ; whereas ego ism is evolutio narily stable fo r k < 0: When a ltruism induces a
harmfulreactio nby th eotherp layer,one isb ettero byeg ois tically ma ximizin gp rivate
succes s. Altruism may emerge o nly if itss trategic e ect is bene cial. In this s itua tion ,
the evolutio narily stab le para meter 3
is determined by the following tra deo . On the
one han d, the altruist reduces his succes s by choos ing an actio n that re ectsso me co
n-cern fo r the other player's success; on the o ther hand, his attitude ca uses a favora ble
reactio nby th eo therplayer. Th elattere ectb eco mes mo reimp orta nt forlargerva lues
of k:T herefore, 3
an d k a reneg atively rela ted .
6 A Generaliza tion
In the p revio us sectio nswe haveemployed the parametric speci ca tio n of material
pay-o sinequation(1) tos tudytheevolutio narystab ilityo fa ltruism. Forthis speci ca tion ,
the equilibriu m de ned by (1 0) is u niquely determined s o that the functio n R(1;1) in
(15 )isun ambiguo uslyde ned . Moreover,thereisaunique preference parameter 3
s
this may no long er be the ca se. Even when the evolu tion ary g ame in section 5 is
well-de ned, it may ha pp en that the p arameter 3
is no t u nique o r th at an evolutio narily
sta ble para meterdoes not exist. No netheless,we ca n extendou r ma in conclusions to a
more generalframewo rk.
In this section, we w ill generalize the speci ca tio n o f materia l payo s. As befo re, we
consideramono mo rphicp o pula tio no fplayerswhointeractpairwise. Theg amebetween
any pa ir of players, say player 1 and player 2, determines th eir evo lutiona ry success .
This is rep resented by the functio ns U
1
(x;y) and U
2
(x;y); where x a nd y a re the
ac-tions cho sen by player 1 and 2, resp ectively. Th e game is s ymmetric in the s ens e that
U
1
(x;y)=U
2
(y;x):Bysymmetry,thepayo o f astrategyisindep endentofw hetherthe
player acts in the ro le of player 1 o r p layer 2 . We assu me U
1
(1;1) to be strictly concave
and tw ice di erentiable.
To characterize the intera ction b etween the p layers, we extend th e termin ology in
the previou s sectio ns to the more general case. L et the signs of @U
1 (x;y)=@y and @ 2 U 1
(x;y )=@x@y be consta nt for all (x;y) 0: T he ga me is sa id to exhibit p o sitive
externa lities if @U
1
(x;y)=@y > 0 an d neg ative externalities if @U
1
(x;y )= @y < 0 : The
players face stra teg ic complementa rities if @ 2
U
1
(x;y)=@x@y > 0 and strategic
substi-tutes if @ 2
U
1
(x;y)=@x@y < 0: We fo cus on situations wh ere @U
1 (x;y)=@y 6= 0 and @ 2 U 1 (x;y )=@x@y 6=0 fora ll (x;y )0:
Whenever two individua ls intera ct with each o ther, each player i seeks to maximize
his subjective u tility V
i
(x;y); a s de ned by (8). An equilib rium is a pa ir o f a ctions ,
(x 3
( ; );y 3
( ; ));that s atis es co ndition (1 0). As long as @U
1 (0 ;y
3
)=@xis su ciently
large,the equilibriumactio nss atisfyx 3
>0a ndy 3
>0so th attheyca nbederivedfrom
the rst orderconditio ns
@V 1 (x 3 ( ; );y 3 ( ; )) @x =0; @V 2 (x 3 ( ; );y 3 ( ; )) @y =0: (1 8)
Toens urethatR ( ; )in(15 ) is well- de ned,wea ssumethat(1 8)ha sau niquesolution
Th e evolutio nary succes s o f preferences depends o n their impact o n equilibrium b
e-havio r. By di erentia ting (18 ), we o btain for that 9 sig n " d x 3 ( ; ) d # = sig n " 0 @U 1 (x 3 ;y 3 ) @y # a nd (1 9) sign " dy 3 ( ; ) d # = sig n " 0 @U 1 (x 3 ;y 3 ) @y @ 2 U 1 (x 3 ;y 3 ) @x@y # : (2 0)
The e ect d es crib edby (1 9) has the sa me intuition as in the mo re specia l case s tudied
b efore. The mo realtruisticplayer1is,i.e. the lower is,themore hetendsto
internal-ize the externality of h is action up o nthe otherp layer's utility. Therefore, and x 3
are
nega tively rela ted in g ames with p o sitive externalities a nd pos itively related in ga mes
with nega tive externa lities. E qua tio n (20 ) generalizes the strategic e ect d iscuss ed in
the previou s sectio ns. As befo re, altruis m induces the o pp o nent to select a hig her
ac-tion whenboth the externa lities andthe s trategic interdep endenceb etweenthe players '
actions have the same sig n. But, in the mo re g en era l situation considered h ere,
altru-ismmay also reduce the oth er player's equilibrium actio n. This happens in g ames w ith
stra teg ic complements when the externa lities are nega tive and in ga mes with s tra tegic
subs titutes w hen the externalitiesare positive.
How does the strategic e ect in uence a player's succes s? Cons ider a game w ith
stra teg icco mplements. Ifthe ga me has p os itiveexternalities , then altruis minducesthe
opponenttochooseah igh era ctionlevel. C learly,thise ectisbene cia lfo rthealtruist's
succes s s ince, in the presence of p os itive extern alities, ra ising the o ther player's action
level increases his own success. Simila rly, in a game with s trategic complements and
nega tive externalities altruism red uces the o pp o nent's actio n level. Again, the a ltruist
ga ins from the strategic e ect. In ga mes with stra teg ic su bstitutes th is co nclusion is
reversed. For insta nce, in g ames with strategic substitutes and neg ative externalities ,
altruismincreasesth eo therplayer'sactio n. Thisisha rmfulbecau seitcreatesanega tive
externa lity. In summa ry, the stra teg ic e ect o f a ltruism on the other player's behavior
Our p reviousa nalysissug geststha t altruis ms urvives evolutio naryselectio nonlyif it
is as sociated with a b ene cial strategic e ect. The fo llowin g result, which is proved in
the App endix, extends this conclus io n to the mo re genera l enviro nment.
Proposition 5: The prefere nce parame te r 3
= 1 is ev olution arily stabl e onl y if the
int eract ion s betw een individual s are characte rized b y strategic substit utes. A paramete r
3
<1 is ev olution arily st able on ly if t hese inte ractions inv olve strat eg ic compl emen ts.
Th is result is wea ker than Pro p os itions 3 and 4 b ecause it d o es no t es tablish the
existenceor uniqueness ofa nevolu tion arily s ta blepreferenceparameter. Nonetheless,it
show s tha t pure ego is m ca nnot evolve in a n environment with stra teg ic co
mplementar-ities. In s uch a n enviro nment on ly so me form of a ltruism has th e potential to s urvive
evolutionary selection. C onversely, altruis m will not survivethe invas io nof eg oistic
mu-tantswhen interactio nsexhibit s trategicsubs titutes. Th eevo lution of altruismrequires
an environment of stra teg ic co mplements. Alto gether, on e sho uld no texp ect evolution
to resultinasociety whereindividuals alwayseither pursuepures elf-interes to rca refor
the well-b ein g of o thers. Ins tea d, evo lutiona ry a rguments sugg est that these a ttitudes
will beco ntingent on the strategicinterdependen ce between individua l behaviors .
7 Co nclusions
Unlike otherevo lutiona rystu diesof altruis ticbehaviorins trategicinteractio n,o ur
indi-rectevolutio narya pproa chdoesnot deny ratio naldecis io nmakin g. Inp rincipleita llows
for a ny hyp o thes es s p ecifying how stimuli, e.g. preferences, in uencebeh avior. A p ro
-ces s o f na tural o r culturalselection then determines wh ich stimuliemerge in the course
of evo lution. Our study employs the us ual rationality ass ump tion s of ga me theory to
endog enizepreferences, w hich neo classical theory typically treats as exog eno us. In this
Th e most important nding of our study is tha t evo lutiona rily s table altruism
de-p ends o n the typ e o f strategic intera ction, a s expressed by the sig ns of the derivatives
of materia l payo s U
i
(x;y ): Alth oughin o urco ntext a ltruisma lways produces more
ef- cient outcomes, it is evo lutiona rily stable only if it induces the interaction pa rtner to
resp o nd favorably. As the evolutio n o f preferences dep ends on this stra teg ic e ect,one
may expect altruis m to mitig ate ineciencies o nly w hen interactions can b e chara
cter-izeda s stra teg ic complements .
Another requirement fo r the evo lu tion of altru ism is related to the individuals'
in-formation ab o ut preferences . Our a nalys is employs the usua l co mmon know ledge a
s-sumption of ga me theory, w hich implies that the p reference parameters and are
commo nly known. Toillu strate theposs ibleimpact of incompleteinformatio n,co nsider
amo nomorphicp op ula tio nofa ltruists w ithpa rameter <1 :Ifnowa nego isticmutant
appears, ea ch altruis t will co nsider the pro bability of interactin g with the mutant as
neglig ible. Under incomplete information, the ego ist will be treated a s a n a ltruist and
he will earn a higher ma terial payo than his altruis tic encou nter. As result, altruism
will become vulnerab leag ainst ego is tic muta nts .
Our ana lysis, therefore, sugg es ts that altruism is more likely to emerge in societies
where individuals are no t a nonymo us. For insta nce, altruis m may b e restricted to
rel-atives a nd clo se friends. In contras t with the kin-s election s election a rgument, in our
framewo rk th isha pp ens no tb eca use familymembers a reg en etica lly linked but b ecause
they a rebetter info rmedabout eacho ther. Nonetheless,evenw hen preferences are not
directlykn own,a ltruismmayevo lveif th erea resignalsthatindicateap erso n'sattitude.
Ina ddition to the physicalsymptoms mentio nedby Fra nk(19 87 ,19 88 ),for instancedo
-nations to charities might signal altrustic preferences. An ego ist is less willing th an an
altruist to don ate. If imita tion is too co stly for th e eg oist, d onations can b ecome a
Appendix Lemma 1: Let @R ( 3 ; 3 )=@ =0: Then eit he r 3 =0k= 2 or 3 =(20k)= 2:
Proof: By de nition,
R ( ; )= m 2 (k+2 )[k 2 ( 01)+ k(2 01 )+2 ] (k 2 04 ) 2 : (2 1)
Therefore,@R( ; )=@ =0is equiva lentto
=[4 +k(20k)]= [4 ( +k)]: (2 2)
Setting = = 3
a nd s olving the res ulting quadra ticequation for 3
lea dsto thetwo
so lutionsstated in the L emma. Q.E.D .
Lemma 2: The paramete r =0k= 2 is not ev olution arily st able .
Proof: Sin ce R ( ;0k=2) =m 2
= 4; =0k= 2 sa tis es th e rs t requirement of sta bility.
The second requirement, R ( ; )>R ( ; )is equivalentto the con dition (k+1) <k:
As (k+1 )>0 ; thisimplies k >0: But then <0;a contradiction. Q.E.D .
Lemma 3: The paramete r =1=2 is n ote vol utionarily stab le.
Proof: Straig htfo rward calcu lations show tha t fo r > = 1=2 the requirement
R ( ; ) R ( ; ) is equivalent to [k 2 +k(2 01)01 ]=[k01]0 : (2 3) As k < 1 this is equivalent to k 2
+k(2 01 ) 1: If k >0 ; this cond ition ca nnot hold
for clos eenoug hto 1 =2:If k<0 ; then(2 3) h olds fo r =1 o nly if k 2
+k 1 :Butfor
01<k <0 one canno thave k 2
+k 1: This proves that =1 =2 d o es no ts atisfy the
rst requirement of evo lutiona ry stability. Q.E.D .
Lemma 4: Let 3
be e volu tionaril y stabl e. The n either 3
=1 or 3
=(20k)=2 :
Proof: The statementsimply follows fromthe fa ct tha t bythe rst requirementofevo
-lutio narys tabilityonemust have@R( 3 ; 3 )= @ =0whenever1 =2 < 3 <1:ByL emma
1, this equality has exactly two so lutions ,0k=2 and (2 0k)= 2: Lemmas 2 and 3
elimi-nate the possibility tha t =0k= 2 o r =1=2 are evo lutiona ry s table. T his leaves o nly
thetwovalues 3
=1and 3
=(20k)=2a scandidatesfo revolutio narystability. Q.E.D .
Lemma 5: The paramete r 3
=(20k)=2 is ev olut ion aril y stabl e if and on ly if k >0 :
Proof: No tethat, by as sumptio n (2), 3
2[1= 2;1]if and onlyif k0 :S traig htfo rward
calculationsshowtha tfo r 3 =(2 0k)=2theinequalityR ( 3 ; 3 )R ( ; 3 )isequivalent to [k 2 04 ][k02(10 )] 2 =[k01]0: (2 4)
By a ssumptio n (2) this inequa lity is always satis ed. T he inequ ality a ls o shows that
R ( 3 ; 3 )>R ( ; 3 ) fo r 6= 3
:This proves that also the secondrequirementof
evolu-tionary s tability is s atis ed. Q.E.D .
Lemma 6: The paramete r 3
=1 is e vol utionarily stab le if and onl y if k <0:
Proof: Stra ig htfo rwa rd ca lculatio ns show tha t fo r < 3 = 1 the requirement R ( 3 ; 3 )R( ; 3 )is equivalentto k 3 02k 2 (10 )04 k+4 (10 )0: (2 5)
For k 2 (0;1 ) this condition does not ho ld for close enoug h to unity. But for
k 2 (01;0] it ho lds fo r all 2 [1= 2;1] so tha t the rst requirement of evolutionary
sta bility is satis ed. Indeed, since the strict inequa lity ho lds in (25) fo r <1; on eh as
R ( 3 ; 3 )>R ( ; 3
):Th erefore,als othe seco nd requiremento f evolutio narystability is
sa tis ed. Q.E.D . Lemma 7: U 1 (x 3 ( ; );y 3 ( ; ))<U 2 (x 3 ( ; );y 3 ( ; )); for all < ;k 6=0 :
Proof: Bys ymmetryo fthefunctionsU
1 (1);U
2
(1)a ndbyde nition ofR( ; );th e
state-ment of the Lemma is equiva lent to R ( ; )<R( ; ); < : Us ing the expres sio n for
R (1)fromL emma1,thisisequiva lenttok 2
(k+ + )>0:By(2 )a nd(9 ),thisinequa lity
Proof of P rop osition 5: By (15 ) one ha s dR ( ; ) d = @U 1 (x 3 ;y 3 ) @x dx 3 ( ; ) d + @U 1 (x 3 ;y 3 ) @y d y 3 ( ; ) d : (2 6)
Suppose th at the game exh ibits s trategic co mplements a nd tha t 3
= 1: Then 3
=
1 tog ether with (8) and (18 ) imp lies @U
1 (x
3
;y 3
)=@x = 0: T his in combina tio n w ith
@ 2 U 1 (x;y )=@x@y >0; a nd (2 0) implies dR ( 3 ; 3
)=d < 0: Thus for some < 1in the
neig hborhood of 3 on egets R( 3 ; 3 )<R( ; 3
); a co ntra diction to requirement (16 ).
This provesthat 3
=1 on ly if the ga me exhibits s tra tegic s ubstitutes .
Now supp o se tha t the g ame exhibits stra teg ic s ubstitu tesand that 3 <1:T hen(8) and (18) imply @U 1 (x 3 ;y 3 )=@x=0(10 3 )= 3 1@U 2 (x 3 ;y 3 )=@x: By (19 ) and symmetry ofU i (1);this yields@U 1 (x 3 ;y 3 )=@x1dx 3 = d >0:Similarly,@ 2 U 1 (x;y)=@x@y<0a nd(2 0) imply@U 1 (x 3 ;y 3 )= @y1dy 3 = d >0:Therefo re,dR ( 3 ; 3
)=d >0 :Thusfors ome > 3
intheneighb o rho odof 3 oneg etsR ( 3 ; 3 )<R ( ; 3
);aco ntra dictionto requirement
(16 ). This proves that 3
Footnotes
1. Notethatalsoinevolutio narybiologyoneoftenco nsid erstheass ump tionof
geneti-callydetermin edbehaviora sques tio nable(s eeva nLawick-G o odall(197 4)). Higher
develo p edspecieslikemammalsliveinsuchaco mplexa ndstocha sticenvironment
thatag enetically determined reactio n b ehaviorto allcircumstancesappea rsto b e
impossible.
2. The exceptions include Becker (19 76),Fra nk(19 87 ) a nd, more recently, G uth and
Ya ari (199 2), Guth a nd Kliemt (19 94), Hanso n and Stu art (19 90), Rab in (19 93 ),
Rog ers (199 4),an d Waldman (1 994 ).
3. A strategy x s
is evolutionarilystable if (i) U
1 (x s ;x s )U 1 (y ;x s ) fo r ally ; a nd (ii) U 1 (x s ;y )>U 1 (y ;y) whenever U 1 (x s ;x s )=U 1 (y;x s ):
4. For ab riefpres entationo f someeviden ce,seeRa bin (1 99 3)who incorpora testh ese
factsby derivinga `psycho log icalg ame' from ba sic`materia l g ames'.
5. A setting in which a ltruism induces inecient b ehavio r is studied by Lindb eck
and Weibull (19 88). For a discussion ofthe eciency aspects of a ltruism, see also
Friedman (1 98 8).
6. See, e.g ., Cha gno n an d Irons (1 97 9)o r Boyer (198 9).
7. See, e.g., Ma ilath (1 992 ) and Selten (19 91 ) fo r a discu ssion. Bjornerstedt and
Weibull(199 4) s howtha t p o pula tio n dynamics based o nimitationmay b eclosely
rela ted to biological dynamics.
8. Friedman (1 98 6, p.4 2 )presentsconditio nsg uara nteeing a unique equilibrium.
9. In the d erivation of (1 9) and (20 ) we use the symmetry o f the g ame and the fact
that V
i
References
Becker, Gary S., \ Altruis m, E goism, and Genetic Fitness : Econo mics and
Sociobiol-og y," Journal of Econ omic Literatu re1 4(3), Septemb er 1 97 6, 817 -8 26.
Bergstrom, TheodoreC . and S ta rk, Oded,\ HowAltruism Ca nPreva il inanEvo
-lutio nary E nvironment," Ame rican Economic Rev iew (Papers a nd Proceeding s) 8 3(2 ),
May 19 93,14 9- 155 .
Bjorners tedt, Jona s and Weib ull, Jorgen, \Nash Equilibrium and Evo lution by
Imitation," mimeo, Dept. o f Econo mics , S to ckho lmUniversity,February 1 99 4.
Boyer, George,\ Ma lthusWas Rig htAfter All: Poor Relief a nd Birth Rates inSo
uth-easternEn gla nd," Journ al of Political Economy97 (1), Feb ruary 19 89 , 9 3-1 14 .
Bulow, Jeremy I., Geanakoplos, Joh nD., and Pa ul D. Klemperer,
\Multimar-ket Oligopoly: Strategic Substitutes a nd Complements ," Journ al of Polit ical Econ omy
93 (3), June 19 85 , 4 88 -51 1.
Ch agnon, Napoleon A. and Irons, William,eds. Ev olut ion aryB iolog yandHuman
Social Be hav ior, North Scitua te, MA: Duxbury, 19 79.
Edgeworth, Francis Y.,Mathematical Physic s, L ondon : P.Keg an, 18 81 ,
Fra nk, Rob ert H., \If Homo Econo micus C ould Ch o o se His Own Utility Function ,
Wou ldHe Want One W itha Co nscience?," Ame rican Economic Rev iew 77 (4),Sep
tem-b er 1 98 7, 593 -6 04.
Fra nk, Robert H., Passions Wit hin Reason, New York: W. W. No rton,19 88 .
Friedma n, David D., \ Does Altruism Produce Ecient Ou tco mes? Mars hall versus
Kaldor," Journal of Leg al S tudies 17(1 ), J anuary19 88 , 1 -13 .
Friedma n, James W.,Game Theory wit hApplication s toEconomics, NewYork-
Ox-ford: Oxfo rd Un iversity Pres s, 198 6.
Guth, Werner and Yaari, Menahem, \ An Evo lutiona ry Ap proach to Explain
Re-ciprocal Behavio r in a Simple S tra teg ic Ga me," in Ex plainin g Process and Chang e
-Approac hes toEvolu tionaryEconomics, edited byUlrichWitt,AnnArbor: Th e
Univer-sity o f Michig an Press ,1 99 2, 23 -34 .
Evolu-tionary E co nomics o f Trust," Me troecon omica 4 5(3), October 199 4, 15 5-1 87 .
Hammerstein, Peter and Selten , Reinhard, \Ga me Theory a nd E volutionary
Bi-olog y," Cha pter 2 8 in Han dbook of Game Theory with Economic Appl ications, Vol. 2,
edited by RobertJ. Aumann and Serg iu Ha rt, Ams terda m: Els evier, 19 94 , 9 29 -99 3.
Hanson, Ingemar an d Stuart, C harles, \ Ma lthusian Selection of P references,"
American Econ omic Re view 80 (3), June 1 990 , 529 -54 4.
Lind b eck, Ass ar a nd Weibull, Jorgen,\ Altruisma nd T imeCons istency: T heEco
-nomics of Fa it Accompli," Journ al of Pol itical Econ omy 96(6 ), December 19 88, 1 165
-11 82 .
Mailath,GeorgeJ.,\ Introduction : Symp o siumo nE volutionaryGa meTheory,"
Jour-nal of E con omic Theory5 7(2 ), Augus t 19 92, 2 59- 277 .
Mayn ard Smith, John , Evolu tion an d t he Theory of Games,C ambridge: C ambridge
University Pres s, 19 82.
Penrose,Edith,\Biolog icalAna lo giesintheT heo ryo ftheFirm,"Ame ricanEconomic
Rev iew 42 (5), December 195 2,80 4-8 19 .
Rabin, M atth ew ,\Incorp o rating Fa irness into G ameTheory a nd Eco nomics,"
Amer-ican Econ omicRe vie w 8 3(5), Decemb er 1 993 , 128 1-1 302 .
Rogers, A la nR.,\Evolutio no fT imePreferencebyNa turalSelection,"Ame rican
Eco-nomic Rev iew 84 (3), June 19 94, 4 60- 481 .
Selten, Rein hard, \Evolutio n, L earning, and Econo mic Behavio r," Games an d
Eco-nomic Be hav ior 3(1), February 19 91 ,3 -24 .
Sch elling, Thomas C.,\ Altruis m, Mea nnes s,and Other Potentially Stra teg ic
Behav-iors," Ame rican Economic Revie w (Pa p ers a nd Proceedings) 68(2 ), May 1 987 , 229 -23 0.
va n Lawick-Go odall, Ja ne,In the Shadow of Man , L ondon : Fontana , 1 97 4.
Waldman, Michael,\ Sys tematic Errorsand the Theoryo f Na tural Selectio n,"
Amer-ican Econ omicRe vie w 8 4(3), June 1 99 4, 48 2-4 97.
Winter, Sidney G., \Sa tis cing, Selection, a nd the Innovating Remnant," Quarterly
