Table Of Content(cid:3)
Maladaptive Reciprocal Altruism
Ernesto Reuben
Columbia University and IZA, e-mail: [email protected]
Sigrid Suetens
Tilburg University, CentER, TILEC, and TIBER, e-mail: [email protected]
Abstract
Evidence from economic experiments reveals that unrelated individuals cooperate with each
other in settings where they interact anonymously and there are no future gains to reap
from cooperation. This evidence is in line with strong reciprocity—the willingness to reward
anonymous others for cooperative behavior and punish them for uncooperative behavior
even if there is no future interaction. However, it is also consistent with the mistaken use
of repeated-interaction strategies. In this paper, we report the results from an experiment
designed to determine whether the mistaken use a reciprocal altruism strategy, which we
call maladaptive reciprocal altruism, is an important explanation, separate from strong reci-
procity, for cooperation in such settings. The experiment shows that maladaptive reciprocal
altruism exists and explains a substantial part of the observed cooperation.
This version: July 2011
JEL Codes: C91, D01, D74
Keywords: cooperation, reputation building, strong reciprocity, reciprocal altruism, bounded
rationality
(cid:3)We acknowledge financial support from the Netherlands Organization for Scientific Research (NWO).
Introduction
It is commonly observed in economic experiments that people cooperate with anonymous others
in settings where cooperation is not predicted to occur if one assumes all individuals are ratio-
nal and solely maximize their own material payoff (e.g., Marwell and Ames, 1981; Fehr et al.,
1993; Berg et al., 1995; Fehr and G¨achter, 2002). The interpretation of this evidence is an on-
going debate in the social sciences as well as evolutionary biology (see, Fehr and Henrich, 2003;
West et al., 2011). Broadly speaking, there are two explanations for the observed cooperative
behavior.1 Ontheonehand,theevidencecanbetakenassupportfortheexistenceofstrong reci-
procity—a willingness to reward/punish anonymous others for cooperative/uncooperative acts
evenintheabsenceoffutureinteraction—that, asproposedbyGintis(2000), mighthaveevolved
through a process of cultural group selection (see also, Boyd et al., 2003).2 On the other hand,
cooperative behavior can be seen simply as a mistake (Haley and Fessler, 2005; Ku¨mmerli et al.,
2010)3 that, as argued by Hagen and Hammerstein (2006) and others,4 might be due to the use
of strategies that are optimal in commonly-encountered environments with repeated interaction
in arguably rarer situations in which they are suboptimal.
Atthecenterofthedebateisthefactthat,forthemostpart,bothexplanationsmakeidentical
behavioral predictions in the studied experiments, and this makes it practically impossible to
determine the reason behind the observed cooperative behavior. For example, in a one-shot
prisoner’s dilemma game, strong reciprocators and individuals who misapply a repeated-game
strategy like reciprocal altruism (Trivers, 1971; Axelrod, 1981), to whom we refer as maladaptive
reciprocal altruists, exhibit the same behavior: they would cooperate if they believe others will
also cooperate and otherwise defect.5 In the former case, cooperation is due to the (expected)
cooperation of others, while in the latter, to the mistaken belief that present cooperation will
1Cooperation in settings where individuals are identifiable in some way and/or interact repeatedly for a suf-
ficiently long time can be readily explained by theories such as kin selection, direct reciprocity, and indirect
reciprocity (Hamilton, 1964; Trivers, 1971; Nowak and Sigmund, 1998).
2Besides cultural group selection, strong reciprocity can be shown to emerge in models with limited dispersal
that increase relatedness between interacting individuals (see, Lehmann and Keller, 2006; Lehmann et al., 2007).
3See also Palfrey and Prisbrey (1996), Goeree and Holt (1999), and Houser and Kurzban (2002).
4For example, see the discussions in Burnham and Johnson (2005), Binmore (2006), Levitt and List (2007),
West et al. (2007), and West et al. (2011).
5Infact,theywouldalsoexhibitthesamerelationshipbetweenexpectationsandbehavior,andtherefore,data
on expectations do not help to disentangle both explanations.
1
lead to cooperation by others in some future interaction. Therefore, in one-shot settings such as
the one described above, the effect of either explanation cannot be determined.
The main argument for strong reciprocity (made by e.g., Fehr and Henrich, 2003) is that
individuals do understand the one-shot nature of the interaction because they behave differently
in repeated games with random rematching compared to repeated games with no rematching
(for evidence see, Fehr and Schneider, 2010). However, the importance of framing effects and
social cues for levels of altruistic behavior (for evidence see e.g., Houser and Kurzban, 2002;
Haley and Fessler, 2005; Bateson et al., 2006; Kurzban et al., 2007; Ernest-Jones et al., 2011) is
often taken as evidence that one-shot games are not devoid of reputational concerns.6 Hence,
it can be said that both strong reciprocity and maladaptive reciprocal altruism are plausible
explanations for the observed behavior. On the one hand, while cooperation rates tend to be
lower under random rematching than under no rematching, this does not imply that all cooper-
ation under random rematching must be due to strong reciprocity. A model where individuals
optimize by using pre-established heuristics (Todd and Gigerenzer, 1999), in this case a heuristic
to reciprocate, but have heterogeneous mental costs concerning heuristic search, would make a
similar prediction (see the discussion in, Hagen and Hammerstein, 2006; West et al., 2011). On
the other hand, it is difficult to know whether framing or social cues have an effect because they
affectexpectationsconcerningthecooperativebehaviorofothers(andthereforethewillingnessto
strongly reciprocate) or expectations of future interaction. In this paper, we present results from
an experiment designed to directly observe cooperation due to maladaptive reciprocal altruism
as an explanation separate from strong reciprocity.7
6Reputationalconcernstowardsthirdpartiesinsettingwhereindirectreciprocityisviablehavealsobeenshown
toincreasecooperation(see,Milinski et al.,2002). Inthispaperwefocusonasettingwhereonlydirectreciprocity
applies.
7Papers that have looked at maladaptive behavior have focused on games where cooperation is the payoff-
maximizing action (e.g., Ku¨mmerli et al., 2010). Since not all individuals cooperate in these games, one can
make a strong case that individuals do behave maladaptively (although they also might be uncooperative due
to antisocial preferences). Our paper differs from this approach in that we demonstrate the mistaken use of a
cooperative strategy, which is more applicable to the games used to support the existence of strong reciprocity.
2
LOW HIGH
Column player Column player
C D C D
Row C 30, 30 9, 50 Row C 37, 37 9, 50
player D 50, 9 25, 25 player D 50, 9 25, 25
Figure 1: Prisoner’s dilemma games
Methods
Measurement of strategies
In the experiment, pairs of participants play one of the two prisoner’s dilemma games seen in
Figure 1. Participants play the game with the same person at least once (period 1), and with a
known probability equal to 1, they play a second time (period 2). We use the procedure below
2
to determine how much cooperation can be attributed to strong reciprocity and how much to
maladaptive reciprocal altruism.
When playing the game, column players make their decisions using the direct-response
method: at the beginning of period 1 and period 2 (if played), they choose to cooperate (C)
or to defect (D). By contrast, row players make their decisions using the contingent-response
method, which they can use to condition their choice on the decision of the column player and
on the period being played.8 Namely, they choose to cooperate or to defect in four cases: (i) in
period 1 when the column player cooperates, (ii) in period 1 when the column player defects,
(iii) in period 2 when the column player cooperates, and (iv) in period 2 when the column player
defects. Since row players can condition their choices and column players cannot, the (stage)
game is strategically equivalent to a sequential prisoner’s dilemma.
The game develops as follows. After making their initial decisions, players learn the outcome
of the game in period 1. Subsequently, we use a coin toss to determine whether period 2 is
played. If period 2 is played, column players submit their second choice, which is then matched
with the strategy that had already been entered by the row player. Thereafter, both players
8Previous experimental evidence suggests that decisions made with the contingent-response method are
not different than those made with the direct-response method in sequential prisoner’s dilemma games (see,
Brandts and Charness, 2011). In particular, Reuben and Suetens (2011) thoroughly compare decisions under the
contingent-response and direct-response methods with a similar type of contingent responses used in this paper
and find no differences between the two.
3
Table 1: Selected strategies of row players
Column player’s action in
Period 1 Period 2
Row player’s strategies C D C D
Always defect D D D D
Maladaptive reciprocal altruism C D D D
Strong reciprocity C D C D
Unconditional altruism C C C C
learn the outcome of the game in period 2.
Thecrucialfeatureofourdesignisthatitelicitsthestrategiesusedbyrowplayers,9 whichal-
lowsustodistinguishbetweenstrongreciprocatorsandmaladaptivereciprocalaltruists. Thekey
difference between the two is how behavior is conditioned in period 2. As is commonly assumed
in the literature (e.g., Sethi and Somanathan, 2001; Boyd et al., 2003; Bowles and Gintis, 2004),
we define a strong reciprocator as a row player who always reciprocates the column player’s
choice irrespective of whether they are playing period 1 or period 2. In other words, strong re-
ciprocators cooperate in period t if the column player cooperates in period t and defect in period
t if the column player defects in period t. By contrast, a maladaptive reciprocal altruist is a row
player who reciprocates the column player’s choice in period 1 (when there is still potential for
future interaction) but not in period 2. Table 1 gives an overview of four strategies of interest
for row players (the complete set of strategies is available in the supplementary materials).
When is reciprocal altruism maladaptive?
Giventhatwearelookingformaladaptive reciprocalaltruists, weneedtoensurethatrowplayers
who choose this strategy are not maximizing their own payoff. Intuitively, reciprocal altruism
is a payoff-maximizing strategy only if the likelihood that period 2 is played is high enough
9To be precise, we observe Markov strategies since row players can condition their choice in period 2 on
the column player’s decision in period 2 but not on their decision in period 1. Hence, we assume that the
row player’s choice depends only on the payoff-relevant history (see, Maskin and Tirole, 2001). This fits well
with common implementations of reciprocity such as tit-for-tat strategies (e.g. see, Axelrod and Hamilton, 1981;
Nowak et al., 2004). Moreover, as demonstrated by Bruttel and Kamecke (2011), Markov strategies describe the
vast majority of strategies chosen by participants in experiments. For additional support see Selten et al. (1997)
and Dal B´o and Fr´echette (2011).
4
and the probability that the column player cooperates in period 2 given they both cooperate
in period 1 is sufficiently high compared to the probability he cooperates in period 2 given any
of the other outcomes in period 1 (see, Kreps et al., 1982). To exclude this possibility, we use
parameter values such that, irrespective of how column players condition their behavior, the
expected payoff of reciprocal altruism is never larger than the expected payoff of the strategy
to always defect. Therefore, if we observe the reciprocal altruism strategy in the experiment,
we know it is indeed maladaptive. In fact, with our parameter values, always defect weakly
dominates not only reciprocal altruism but also all the other strategies of row players (as shown
in the supplementary materials).
The two games in Figure 1 are designed to systematically vary the (maximum) magnitude by
whichtheexpectedpayoffofreciprocalaltruismandthatofalwaysdefectdiffer. Toseethis,note
that if the column playerdefects in period 1 then both reciprocal altruism and alwaysdefect lead
to the same outcome, and therefore, differences between the two occur only if the column player
initially cooperates. If this is the case and we define pC (pD) as the probability that the column
player cooperates in period 2 given that the row player cooperates (defects) in period 1, then the
expected payoff of reciprocal altruism in LOW equals 30+1(pC50+(1(cid:0)pC)25), which is strictly
2
smaller than the payoff of always defect, 50+ 1(pD50+(1(cid:0)pD)25), for any pC;pD 2 [0;1]. In
2
the best case for reciprocal altruism (i.e., when pC = 1 and pD = 0), the former payoff equals
55 points and the latter equals 621 points. In HIGH, these payoffs equal 62 and 621 points
2 2
respectively. Based on past empirical evidence, we expect people to make less “mistakes” the
more costly they are (see, McKelvey and Palfrey, 1995; Goeree and Holt, 1999). Therefore, if we
are indeed measuring what we intend to measure—the mistaken use of reciprocal altruism—then
we should see more maladaptive reciprocal altruism in HIGH than in LOW.
Experimental procedure
The one-hour long experiment was conducted using z-Tree (Fischbacher, 2007) in the laboratory
of Northwestern University. Participants were contacted through an online recruitment system.
Intotal, 70studentsparticipatedintheLOWtreatmentand72intheHIGHtreatment. Overall,
62% of the participants were female. Each student participated only once in a session of 10 to
12 people. After their arrival, participants drew a card to be randomly assigned to a seat in the
laboratory and consequently to a treatment and role.
Once everyone was seated, participants were given the instructions of the experiment. The
instructions were written with neutral language (see the supplementary materials for a sam-
5
ple). Participants were informed that the experiment consists of multiple parts and that the
instructions for the subsequent parts would be provided after the first part had finished. After
reading the instructions, they answered control questions to corroborate their understanding of
the game. Thereafter, participants learned whether their role would be that of the row or the
column player. They kept the same role throughout the experiment. At the end of the session,
participants were paid in private. Mean earnings were $16.10 and ranged from $11.70 to $24.40.
Lastly, giventhatthereisevidencethatparticipantsneedsometimetolearninenvironments
where strategic cooperation is an equilibrium (Dal B´o and Fr´echette, 2011), the experiment was
divided into parts. In a first part, and without knowledge of what would be the second part, par-
ticipantsplayone repetitionofourpotentiallytwo-periodgame. Inthesecondpart, participants
play 15 repetitions of the game with different randomly-matched opponents. This design allows
us to observe the frequency of maladaptive reciprocal altruism with inexperienced participants
and then to study whether experience with the game reduces this type of mistake.
Results
Table 2 provides an overview of cooperation rates in each period by treatment. In order to
observe the behavior of participants when they are inexperienced, we provide statistics for the
first part of the experiment. Moreover, as a measure of the participants’ behavior once they have
had time to learn (labeled as experienced), we provide statistics for the last five repetitions of
the second part.
The cooperation rate of column players ranges from 33% to 11% when participants are
inexperienced and drops to between 12% and 3% once they have gained some experience. The
cooperation rate of row players ranges from 11% to 9% for inexperienced participants and drops
to between 7% and 4% for experienced participants.
The clearest source of variation in cooperation rates is due to participants reciprocating their
partner’s choice. Row players are significantly more likely to cooperate when the column player
cooperates than when he defects, with the only exception occurring for period 2 in HIGH (in
HIGH: p (cid:20) 0:025 for period 1 and p > 0:125 for period 2; in LOW: p (cid:20) 0:077 for both periods).10
Similarly, in both HIGH and LOW, column players are significantly more likely to cooperate in
10Throughout the paper, we test for statistical differences in cooperation rates using logit regressions with
individual random effects and standard errors robust to interdependencies within sessions. However, we obtain
the same results with standard nonparametric tests.
6
Table 2: Cooperation rates for inexperienced and experienced participants
Inexperienced Experienced
LOW HIGH LOW HIGH
Period 1 2 1 2 1 2 1 2
Column player 11% 17% 33% 11% 6% 2% 12% 4%
Row player 9% 13% 19% 11% 4% 4% 7% 5%
If column player cooperates 23% 23% 31% 19% 21% 19% 35% 19%
If column player defects 6% 9% 11% 11% 2% 1% 3% 3%
period 2 if the row player cooperated in period 1 (p (cid:20) 0:016). The other clear pattern occurs
in HIGH where the row players’ cooperation rate conditional on the column player cooperating
dropsfromperiod1to2(p (cid:20) 0:069). Takentogether,thecooperationratessuggestanimportant
roleforconditionalstrategiessuchasstrongreciprocityandmaladaptivereciprocalaltruism. We
now turn to the paper’s main results.
The observed distribution of strategies of row players by treatment is depicted in Figure 2.
The distribution of strategies conditional on them containing some cooperation is also shown.
The figure reveals that the majority of choices of row players correspond to always defect, which
is the payoff-maximizing strategy: it is chosen over 70% of the time in LOW and just under 60%
of the time in HIGH. It also shows that maladaptive reciprocal altruism and strong reciprocity
account for a significant fraction of the row players’ choices. Maladaptive reciprocal altruism is
chosenbetween6%and19%ofthetimeandstrongreciprocityischosenbetween11%and14%of
the time.11 If we concentrate on explaining cooperation, we can see that maladaptive reciprocal
altruism and strong reciprocity account for over 60% of the strategy choices of inexperienced
row players that include some cooperation. Moreover, this percentage goes up to 78% once row
players have gained experience. On its own, maladaptive reciprocal altruism accounts for around
20%ofthestrategychoicesthatincludesomecooperationinLOWandupto47%inHIGH,which
makes it the most common reason for cooperation in the latter treatment. These results clearly
indicate that maladaptive reciprocal altruism is an important explanation—distinct from strong
reciprocity—for cooperation in settings where cooperation by rational own-payoff maximizing
players is not an equilibrium.12
11The next most common strategy accounts for 5% of all choices in both HIGH and LOW. The complete
distribution of strategies is available in the supplementary materials.
12Weshouldnotethatchoosingmaladaptivereciprocalaltruismoveralwaysdefectwasindeedamistakeforown-
7
LOW HIGH
Inexperienced Experienced Inexperienced Experienced
20% 20% 18%
6%3% 5%1% 2% 14% 33% 7%1% 1%
10%
14% 14% 3% 14%
7% 34%
6% 11%
6%
50% 56% 14% 27% 19%
47%
33%
71% 20% 74% 22%
58% 59%
Always defect Maladaptive reciprocal altruism
Strong reciprocity Unconditional altruism Other
Figure 2: Observed strategies of row players
WhilewedonotfindsignificantdifferencesbetweenHIGHandLOWinthefrequencyofeach
strategy when row players are inexperienced, we do find that maladaptive reciprocal altruism is
significantlymorefrequentinHIGHcomparedtoLOWwhenplayersareexperienced(p = 0:017).
That maladaptive reciprocal altruism is more common in the treatment where the expected
payoff difference between this strategy and always defect is relatively low is consistent with
the prediction that individuals mistakenly choose the strategy of reciprocal altruism as long
as doing so is not too costly. However, it is interesting to note that, on its own, the cost of
deviating from the payoff-maximizing strategy (always defect) does not explain the observed
strategy choices (particularly in HIGH). For instance, if we take the behavior of column players
asgiven, wefindthatthestrategytounconditionallydefectinperiod1andcooperateinperiod2
only if the column player cooperates has a higher expected payoff than maladaptive reciprocal
altruism, but it is chosen considerably less often (3% vs. 19% of the time in HIGH and 3% vs.
6% of the time in LOW). This finding is consistent with the idea that individuals are prone to
mistakenly use the reciprocal altruism strategy (as opposed to other strategies) because they
payoff maximizers. Among experienced row players, the realized earnings of the former strategy are significantly
lowerthanthoseofthelatter(p=0:049inLOWandp=0:001inHIGH;OLSregressionswithindividualrandom
effects and standard errors robust to interdependencies within sessions). We do not have enough observations to
run the same test with inexperienced row players.
8
are accustomed to environments with repeated interaction where such a strategy is optimal
(Hagen and Hammerstein, 2006; West et al., 2011).
Lastly, if we look at the effect of experience, we find that the distribution of the strategies
within each treatment and the difference between HIGH and LOW remain largely the same.
In both HIGH and LOW, the frequencies of the most important strategies are not significantly
different between inexperienced and experienced row players (p > 0:626 for always defect, p >
0:488 for maladaptive reciprocal altruism, and p > 0:641 for strong reciprocity). The only effect
of experience seems to occur in HIGH where the frequency of unconditional altruism and that
of strategies in the “other” category fall significantly (p (cid:20) 0:065; in LOW p > 0:299). Hence, it
looks like maladaptive reciprocal altruism is a “mistake” that individuals find hard to overcome.
Conclusions
It is well-known that in many experiments with anonymous interaction people cooperate more
than is predicted if all individuals are rational own-payoff maximizers. This evidence has been
interpreted by some as support for theories of strong reciprocity while others see it as proof that
people wrongly apply familiar repeated-game strategies from their daily life to an unfamiliar
environmentsuchasanexperiment(i.e.,maladaptivereciprocalaltruism). Inordertodisentangle
the two explanations, we designed an experiment in which we can observe if an individual is
cooperating because of potential future interaction. However, we use parameter values such
that doing so does not maximize the individual’s own payoff (irrespective of the choices of other
players). In other words, we can see whether individuals mistakenly use a reciprocal altruism
strategy in an environment where doing so is maladaptive.
Our experiment shows that maladaptive reciprocal altruism is an important behavioral force:
it accounts for almost half of the observed cooperation. The fact that maladaptive reciprocal
altruism is used less when it is costlier is consistent with it being a mistake. However, given that
it is a mistake that was made consistently used by some players, its frequency did not decrease
with experience, and it was made more often than other equally-costly mistakes is consistent
with reciprocal altruism being a commonly used strategy that is optimal in many settings but is
sometimes misapplied.
All in all, our results suggest that one should not assume that individuals do not use recip-
rocal strategies that work well in repeated settings simply because doing so is not optimal in
9
Description:Maladaptive Reciprocal Altruism Ernesto Reuben Columbia University and IZA, e-mail:
[email protected] Sigrid Suetens Tilburg University, CentER, TILEC, and TIBER
