An Evolutionary Dynamic Approach to Altruism

40 Pages·2010·0.31 MB·English

An Evolutionary Dynamic Approach to Aliruism™

Pier Luigi Sacco
Department of own
University of Florence

and

Stefmo Zamagai
Department of Econem
University of Bologna

June 1993

JEL classification mubers: C72, C73, D74,

Abseract

After revicwing recent add less reocnt Tirerature on altmism and
selfishmess, the paper discusses in detail the issue of une elevunce of altuistic
motivations. us opposed to sell- inter:st. in a well grounkled theory of rations?
choice. ‘The main point is that proper dynamical analysis of the allocative
consequences of altruism mus! facus not only en the actual Jeve) of altruism that
characterizes the economy. hut also on the types, Keeping im mind thal. Ux: time
evolution of the stock of uliriism etuedally depends on the distrihution of the
various types across the populalion. Tr is shown the the model here presonted
can be used to infeapret altruistieslly - driven ptienemena of tansalion between
social conventions

* Hlnanelal support though MURST 40% fandls ix gratefully acknowledged
“A man who is a mathematician and nothing but a math-
ematician may live a stunted life, but he does not do any harm.
An economist who is nothing but an economist is a danger to
his neighbours, Economics is not a thing in itself; it is a study
of one aspect of the life of man in society... Modern economics
is eubject to a real danger of Machiavelliom — the treatment
of social problems as matters of technique, uot as facets of Uhe
general search for the Good Life” (Hicks (1941)}

1. Introduction.

A. social convention is, according to the classical definition of
Lowis (1969), » state of things which is customary, expected and self—
enforcing, Tn game theoretic terms (as pointed out e.g. by Ullman—
Margalit (1977)), these requirements can be translated into the familiar
Nash equilibrium conditions, Very recently, Sugden (1989) has pointed
ont that hisLorieally relevant social conventions need not. only be self
enforcing vis-a-vis themselves but also against the possible ‘invasion’
of ‘rival’ conventions, i.e. ayainyl Lhe possibility that a relatively sinall
nuuiber of players act as ‘deviants’. This additional feature amounts to a
relinement of Nash cquilibrium known as evolutiouary stability (see e.g
van Damme (1987)}. This characterization of social conventions clearly
atreases their stability, i.e, the fact Lhat, once the social convention has
Leen established, its destruction requires the successful coordination of
a relatively large oumber of players. Unfortunately, as il is well known,
it is offen the case Ghat social conventions do ual correspond to socially
desirable outcomes; this ean be due Lo Lhe fack una:

a) there exist aauy possible social couveutioas, bul for some reason
the ‘wrong’ one has become salient. One such exauple is lke so
called coordination [ailure: workers coordinate on an imeffcieutly
low level of activity despite the fact thal a uniformly higher level of
activity would make all them beller off (see e.g, Cooper and John
(1988)}

b) the only feasible social convention is Pareto inferior to some other,
aon implementable outcome. The most famous example in this re-
spect is the prisoner's dilemma game; another well known situation

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is the go called Uragedy of the commons (ser ¢.g. Hardin (1968) bur

also Bromley (1991)).

Even when socially preferable conventions other Uian the ruling
one exist, the (ransition from the laLler to the former is problematic for
the reasous hinted at above. To explain the transition between social
conventions one has therefore to invoke some addilional feature that
forces the economy away from the original silualion. Boyer and Orlean
(1992) provide an example of tranyition belween conventious based on
a certain pallern of localization of strategic interaction belween play-
erg, More examples based ou different factors may be devised; in this
paper, we are particularly interesled in one of them, uamely altruistic
behavionr,

To understand how the emergence of allraistic behaviour may cause
the transitiou between different social couventions or even the emergence
of a desirable convention whea there is none, cousider, as a simple ex-
aruple, the following specilication of the standard prisoner's dilemma,
game:

Cc D
c (9) (eta)
De +Ag— (0,0)

where §,9,4 > 0,4 > ¢,

As it. can be easily checked, {),D) is the only Nash equilibrium
here, and hence the only enforceable social convention. Hf on the other
hand al leasl one player (say, the row player) is altruistic in the senge
that her target payoff function is a weighted average of her own and the
opponent's payoff, it turns oul thal conperation is a dominant slralegy
for her provided that w, ie. the weight agsigued lo the opponent's
payofl, is large enough. More precisely, if ¢-+ A > 1, it is required
that w > A/{A+ 8), whereas if ¢ +2 < a, it is required Ubal w >
~s/A+¥).

Tf on the other band hoth players are altruistic, mutual cooperation
may hecame the only enforceable social convention, It migl be objected
thal the emergence of mutual cooperation as 4 yocial convention requires
a relatively high degree of altruism. IL can indeed be showa thal, when

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S+A< d, even for lower degrees of (row player's) altruism (namely, for
MOAB) < w< (b—9)/(\+ 9) the original prisoner's dilemma can
be transformed into a so-called aseurance game in which free riding is
not the inosl attractive option for the allraistio player (who oow ranks
‘outcomes as follows: (CC) » (D.C) > (D,D) = (C, Dh; see eg, Sen
(1967}). The payoff matrix then becomes (with the tow player au the
altruist)

a D
C (sc) (-8+A+4¥)w.c4 A)
Di (6+A-(A4 Bhw,s— 8) (0.0)

In this case, the allcuistic player has ao longer a dominant strat-
is often suggested (sce c.g, Elster (1984)) that defection is the
rational strategy for her to play. Huwever, as argued by Collard (1978),
the row's player assurance ahout the opponent's choice of (cooperative)
strategy need not be complete in order for her to choose to behave co-
operatively, The altruistic player will indeed cooperate ax long as her
subjective estimate p of the probability that the opponent will covper-
ate is large enough’; it is easily checked that, the larger the player's
altruism, the less aseurouce she requires to justify her own coopera-
tion®, If on the other Land both players are sufliciently altruistic (i.¢.,
w > M/(X4 #)}, the cooperative outcome is again self-enforcing, i.
mintual cooperation is a (stable) social convention. In conclusion, seme
(portibly relatively small) degree of aliruism may upset. the noncouper-
ative social convention; if moreover a large euuugh number of players
behave (possibly just moderately) altruistically, an efficient, cooperative
social couvention conld be eventually brought about.

Analogong arguments might be constructed for other games in
which players’ self-inlerest causes the emergence of inetficient social

‘Specifically, the altruistic player will cooperate if p >
sh)w}/(ai—¢—A); recall that the restrictions yb > A1 ¢ and w aay
are nceded here.

* Al w = (—c]/(A +) she will comperate even if she believes thar the
opponent will certainly defect.
conventions, as in the well known centipede game. These results sug:
gest Lhal allroism is not easily dismissable as au instance of irrational
decision making aud that, consequently, it might be au important mo-
ivating factor for players at least in certain silualions. This possibilily
is somewhat backed by the available experimental evideuce thal shows
that cooperative behaviour tends to be observed more often than it
should he ou the basis of the standard model of self-interested play-
ers and that coaperation is typically Uhe ‘default? initial choice (see .g.
Roth (1991)), as well av by the evidence that shows Uhat equity consid-
erations play a substantial role in individual bargaining decisions (see
‘Ochs and Roth (1989). Tn fact, recent experiunental results by Frank,
Gilovich and Regan (1993) suggest Lhal subjects which have been ex-
posed to microeconomics courses based on the notion of rational choice
as self interested maximizing behaviour tend to cooperate significantly
eas frequently than subjects who have not. ‘Ihis seems Lo indicate that
dhe slandard paradign of self-interest: may have a self-fulfilling nature:
the exposed subjects are bronght. to perceive vel-inuerest. as a norma
‘tive characterization of rational behaviour and 10 act accordingly. Thuy,
rather paradoxically, one could conclude that the takeover of Ute self
interes! paradigm outside the narrow community of economists might
induce an inefficient social convention at. which cooperalive deals be-
come harder to enforce than it. might otherwise be®

Once made clear that allraism may play au imporlant role in the
solution of some well known social dilemmas and that. self-interest may
work in the apposite direction, ane has to explain why self-interest Las
traditioually become the domitant behavioural assumption on which
the theory of ratioual decision making has been built. It is indeed true
Unat a vast literature on altroismn has developed nowadays (aa a mere but
representative example see Beruliei and Stark (1988), Stark (1989)}
But what about the main message

Some trails that are common Lo the various authors may be iden

conveyed by such literature?

*LaLlimare (1992) examines the results of a standard ultimatum bar-
gaining game involving economists who behave according to Lhe famitiar
self-interest paradigm aud non-economists who value atliuudes such
as fairness and altruisin. The (relatively) aurpriving finding is that
economists make smaller expected monelary gains than non-evowutisis.

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titled:
1) altruism is represented as a preeaisting, lixed ‘stock’,
il) the analysis focuses on the allacative elfects of the Axed stock;
iL turns out thal if the {evel of altruism falls below a certain Lhresh-
old, negative welfare effects emerge, in that, iu order to prevent sys
tematic exploitation, the allruist must undertake inefficient courses
of action (the so called altruist’s moral hazard);
iv) if Ube level of altruisin falls above the threshold, welfare effects are
instead positive;
on the uther hand, given that high levels of altruism are uot prac-
tically reachable, self-interested behaviour seems preferable: the
welfare losses the economy must bear Lefure a large enongh stack
of altrnism is buill are likely to be too large.
In conclusion, the main message of this literature seems Lo be that,
all things considered, altruism is irrelevant and/or wasteful! Tt is our
opinion thal this conclusion heavily depends on an incorrect concep-
tualization of altrnism aud more specifically of its role in he complex
motivational system that Hes behind individual decisions. A first, pe-
ripheral remark is that allrniam cannot be understood as a stock that
is worn out by use, as it is the case wilh any scarce resource. Aluru-
ism is not a resource, it is a virtue. As a consequence, as Arisiolle put
. is stock is likely to be increased by feequenl use, rather than worn
out. More importanlly, the standard approach to altruisia is Lawed
by a basic methodological error. If is assumed that the preference or-
derings of
it be pli

layers do not change as the proces of choice unfolds, i.e.,
ly postulated that behavioue and experience do not feed
back on players’ preference jndgements, Now, while thie aseummplion is
certainly reasouable in comparative stalic analyses, it is auch too re-
strictive when it comes to dynamics, A player’s degree of aliruism at
a certain time is likely to be affected by his past history of choices and
experiences; this ia turn implics that his original preference judgements
may be reskaped several times and in several different. ways. A second,

related point ig thal ‘alirnisn”’ is a far too vague notion that calls for
further qualification; in fact, one can consistently deline several different
types of allraism, all of which having peculiar allocative conseqnences.
‘Therefore, once admitted that there are important feedbacks from the
dynamic choice process to individual judgements, it aust be recognized

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thay such judgements tay evolve towards, or away from, different sorts
of allruisin, and that the actual law of motion may in principle heav-
ily depend on the type of altrnism that is curreully actualized in the
player's preference judgements,

Tn cone

jon, & proper dynamical analysis of the allocative conse-
quences of allruisin must focus not only on the actual level of altrnisn
that characterizes the economy, but also on the fype(s), keeping in mind
thak the time evolution of the stock(s) of altrnism crucially cepeuds on
the distribution of the various types across the population. The dys
namical mechanism just outlined lends itself quite naturally to an eve~
lationary dynamic treatment; in this perspective, the diflusion and the
eventual takeover of a certain type of altruistic norm of behaviour (or of,
a cerbain distribution of types of altruisin across Uhe population) may be
seen as the emergence of a social convention in the sense of Lewis and
Sugdent, Lo Unis framework one can also easily model ‘altruistically

driven’ phenomena of transilion between conventions, hy studying if and
how the appearance of some ‘new’ sort of altruism upsets the existing
social conventiou laying the foundatious of a new, different one, with

the corresponding bearings in terms of social welfare

‘The remainder of the paper is organized as follows. In section 2
we review suiue recent and some loss recent literature on altruism and
selfishness to elucidate the current stale of the debate. In sections 3
and 4 we disenss in graler detail the issne of the relevauce of altruishic
, in a well grounded theory of
rational choice, Section 5 discusses the basic characlerislies of our evo-
Intionary approach. Sections 6 and 7 describe the reference model we
use for onr formal analysis. Section 8 discusses the dynamical slructure
of the model, Section 9 describes our resulls. Section (0 provides a
short sututuary of our main findings.

motivations, as opposed lo self-interes

A brief review of new and old lilerature.

‘The aged to model social conventions as the outcomes of density de-
pendent dynamical evolutionary processes has already been pointed out
by Bicehieri (1990)
‘The approach to ralional choice Uhat identifies self-interest as the
id individual decisions is stili the dominant
‘ne in the current lileralure, Several justifications have been given
for this choise. As Tullock (1976) pnts it, “As a result of empirical
research...the average huinan being is about 95 per cent selfish in the
narrow sense of Lhe term”. On the other hand, Downs (1956), p. 29, ob-
serves that “In reality, men are not always selfish, even in politics. da ev-
ery field, no account of human behaviour is complete without meation of
such allraism... Nevertheless, general theories of social action always rely
heavily on the self interest axiom". Stigler (1981) explaina econoinic be-
haviour ae almost entirely sell interested, He contenda that deviations
from narrow self-interest are genetally confined to one’s “family, plus a
close circle of associates”. Mueller (1986). p. 14, argues Uhat. “the only
assumption essential to a deseviptive and predictive science of huinan
behaviour is egoism”.

Sen’s 1977 celebrated paper (on “Rational fools") is the first mo-
Jor theoretical attack against the self-interest assumplion. Sen argued
‘that eympathy for other people aud cornmitment Lo a principle produce
two key deparlures from velf-intorest and that commitment whieh in-
volves courerpreferential choice “drives a wedge hetween personal choice
and personal welfare” while “much of Waditional economic theory re-
lies on the identity of the two” {p. 388). In 1978, Collard’s "“Alimn-
ism and economy" supported the thesis thal “human heings are not
entirely selfish, even in theit economic dealings? {p. 3). Hirshman’s
“Against parsimony” in 1984 criticized the parsimonious poslulate of
a “self-interested, isolated individual” and argued for a now focus on
changes in values (rather than ‘wanton’ tastes) and on uoninstramen-
Lal action. Very recently, Kirmer (1990) has made the fine point thal
“Self inlerest is indeed a central element, but this sell-interest mast. .be
understood with a certain subtlety. Properly understoud, self-interest
does not exclude altrnistic motivation; it depends on purposefnlness,
bul not on any selfishness of purpose. The paint to be ulressed ie thal
it is voe’s own purposes which inspice onc’s actions and excite one's
aleriness, Que’y purposes inay be altruiatle or otherwise” (p. 39). Li
other words, it i the agent who makes the agent's choicen,
but the interests pursed need not he those of the agent. Thus, the
familiar suggestion that every action is necessarily self-interested (“T

8
am pursuing my coucern that other should be able lo...) misses the
point since it coufuses the concept of choice as purposeful action with
the concept of choice as self-interested action — a purpose is not the
al point, rank (1988) ar-
gues that there is no eed for economics to assume exclusive rationality,
understood as complete freedom from emotion and pausioa. The va-
lidity of economics ig therefure not threatened by pervasive real world
examples of passionate behaviour. Building ou earlier work of Schelling
and others, Frank shows how the practice of moral behaviour may nol
only be goud for saciely, but it may also be materially beneficial to the
practicing individnals themselves

Tn a recent work, Seu (1987) marks the current state of the debate
with the following, sweeping judgement: “Univeral selfishness as ac-

same thing as personal interest. Ax a ge

tuatity may well he false, but nniversal sclfishuesy as a requirement. of
rationality is pateatly absurd” (p. 16).

Neither one should think Urat the tension between self interest and
altruium as motivating forces behind ratioual choice was not felt: by the
founding tathers of the modera orthodoxy. Sleedman (1989) has a mou
illuminating discussion of Wicksteed’s thought centered on the relations
between rational choice theory, as commonly understood in cvouomies,
and a broader conception of (he individnal in socfety, who might have
allruislie purposes, social and ethical ideals. Sceedinan's paper provokes
important reflection om Uhe relations hetsveen raciouality and allraism:
alernistic conduct, when it occurs, is fully consislent with rational eco-
nomic conduct, Already toward the end of past century, Wicksteed
{1933} pointed out that “The economic relation ducs nol exclude from
my mind every one bal me, it potentially includes every one but: you"
(p. 174), Ty stress this point Wickeleed introduced the term ‘non
tuiem’ lo mean that, in an economic relation, A’s lack of concern for
the purposes of 8 (and vice versa} by no means entails that A acts for
selfish motives. “The specific characteristic of an economic relation is
not its ‘egeiem' but its nou- Luis (p. 180}. Tt follows from the above
characterization of the nature of the economic relation that: “The pro-
posal to exclide ‘benevolent? or ‘altruistic’ motives from considerati
in the study of Economics is...vholly irrelevant and beside the marl
(p. 179).

In fact, by further widening our historical perspective, we discover

9
Ghat even apart froin the classical references to Mandeville aud Smith,
the issue of the rule of altruism vg. seliishness in the working of complex
economies and societies is far from being a recent: discovery. Through-
ont history, economic philosophers were fascinated by the phenomenon
that general welfare develops from egoism of merchants. Té seems that.
the earliest writer who uoticed this point was Auonymous Jamblichi, a
Sophist and apparently au expert in economic ethics, wha wrote around
450 B.C. Tle compared the wealth of the Greek city-states — the poleés
+ which did uot Lave mnch gold, with the general Persian poverty
that existed despite the immensurable Lreasmre in gold possessed by the
Great King. Anonymous Jamblichi solved this paradox by slating that
it is the merchants’ activity that caused Greek wealth. In tura, this
activily of the Greek merchants wae made possible by the manifold r
ations of trust and credit that existed ag a legal framework both with
and hetween the numerous city states in the Greck koing, Thay, result-
ing from the egoism of the many, a general system of welfare developed
(see Fikentscher (1988)}.

‘The Javin philosopher Seneca, in his De Beneficifa, says that a mer-
chant selling coru does no henefit even if, in reality, he saves an indi-
vidual or a whole city, Nobody of those who profit by his action iz
obliged to him, because he did not mean to help Whem, but had in mind
his own interest (Seneca, VI, 14, 4). The sentence with which Seneca
explains that whatever is done to make a profit is no beuefil, has a.
Smithian favour: he brings advantage to other people in order to have
hie own (ad alienum commodura pro suo weniunt, IV, 13, 3}. Therefore,
merchants produce a ‘goad? result withont having this purpose.

Much before the celebrated Mandeville’s “Fable of the bees”, in
1564 the German scholar Leonhard Fronsherger from Ulm published an
esvay, Vora Tob de Byer Nutsen (The praive of nelf-interest), where
he explained that Lhe farmers, merchants and artisans are busy only
in pursuit of their self-interest and in doing sa creale public order and
wall- being in the general interest (sve Schultze (1987)

Although very brief and of course qnite incomplete, our survey
demoustrates that the issue of the relevance of aliruism in the motiva-
tional syutem of ratiowal decision makers is far [rom being a marginal or
ephemeral one; indeed, it may be regarded as one of the few issues that
permeate tbe whole western intellectual history. Its somewhat marginal

ww