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Why cooperation is not running away

  • CNRS - Ecole Normale Supérieure de Paris


A growing number of experimental and theoretical studies show the importance of partner choice as a mechanism to promote the evolution of cooperation, especially in humans. In this paper, we focus on the question of the precise quantitative level of cooperation that should evolve under this mechanism. When individuals compete to be chosen by others, their level of investment in cooperation evolves towards higher values, a process called competitive altruism, or runaway cooperation. Using a classic adaptive dynamics model, we first show that, when the cost of changing partner is low, this runaway process can lead to a profitless escalation of cooperation. In the extreme, when partner choice is entirely frictionless, cooperation even increases up to a level where its cost entirely cancels out its benefit. That is, at evolutionary equilibrium, individuals gain the same payoff than if they had not cooperated at all. Second, importing models from matching theory in economics we, however, show that, when individuals can plastically modulate their choosiness in function of their own cooperation level, partner choice stops being a runaway competition to outbid others, and becomes a competition to form the most optimal partnerships. In this case, when the cost of changing partner tends toward zero, partner choice leads to the evolution of the socially optimum level of cooperation. This last result could explain the observation that human cooperation seems to be often constrained by considerations of social efficiency. This article is protected by copyright. All rights reserved.
J Evol Biol. 2019;00:1–13.    
Cooperation among nonkin constitutes a puzzle for evolutionary
biologists, and a large body of theoretical models, inspired by
game theory, have been developed to solve it. The most commonly
accepted explanation is that cooperation can be enforced if it trig
gers a conditional response on the part of others (West, Griffin,
& Gardner, 2007). Several enforcement mechanisms have been
proposed: direct reciprocity (Axelrod & Hamilton, 1981; Lehmann
& Keller, 2006; Trivers, 1971), indirect reciprocity (Leimar &
Hammerstein, 2001; Nowak & Sigmund, 1998, 2005), punishment
(Bowles & Gintis, 2004; Boyd, Gintis, Bowles, & Richerson, 2003;
Boyd & Richerson, 1992) and partner choice (Bull & Rice, 1991;
Noë & Hammerstein, 1994, 1995; Sachs, Mueller, Wilcox, & Bull,
2004). A growing number of experimental studies support the
idea that among this set of mechanisms, partner choice is likely
to be particularly influential in nature, both in inter‐specific and
in intra‐specific interactions (Bshary & Schäffer, 2002; Fruteau,
Voelkl, Damme, & Noë, 2009; Hammerstein & Noë, 2016; Kiers
et al., 2011; Kiers, Rousseau, West, & Denison, 2003; Schino &
Aureli, 2009; Simms & Taylor, 2002). Besides, partner choice is
DOI: 10.1111/je b.13508
Why cooperation is not running away
Félix Geoffroy1| Nicolas Baumard2| Jean‐Baptiste André2
©2019Europea nSociet yForEvolut ionar yBiolog y.JournalofEvolutionaryBiology©2019EuropeanS ociet yForEvoluti onaryBiolog y
FélixGe offroy,Ni colasBa umardan dJean‐B aptist eAndréco ntrib utedequ allytoth is
1Institut des Sciences de l’Évolution, UMR
5554 ‐ CNRS – Université Montpellier,
Montpellier, France
2Instit utJean‐Nicod(CNR S‐EHESS‐
ENS), Département d’Etudes Cognitives,
Ecole Normale Supérieure, PSL Research
University, Paris, France
Félix Geoffroy, Faculté des Sciences de
Montpellier, Place Eugène Bataillon, 34095
Montpellier, France.
Funding information
Agence Nationale de la Recherche, Grant/
Award Number: ANR‐10‐IDEX‐00 01‐02 PSL
and ANR‐10‐LABX‐0087 IEC
A growing number of experimental and theoretical studies show the importance of
partner choice as a mechanism to promote the evolution of cooperation, especially
cooperation that should evolve under this mechanism. When individuals compete to
be chosen by others, their level of investment in cooperation evolves towards higher
values, a process called competitive altruism, or runaway cooperation. Using a clas‐
sic adaptive dynamics model, we first show that when the cost of changing partner
is low, this runaway process can lead to a profitless escalation of cooperation. In
the extreme, when partner choice is entirely frictionless, cooperation even increases
up to a level where its cost entirely cancels out its benefit. That is, at evolutionary
equilibrium,individuals gainthesamepayoffthaniftheyhad notcooperatedatall.
Second, importing models from matching theory in economics we, however, show
that when individuals can plastically modulate their choosiness in function of their
own cooperation level, partner choice stops being a runaway competition to outbid
others and becomes a competition to form the most optimal partnerships. In this
case, when the cost of changing partner tends towards zero, partner choice leads
to the evolution of the socially optimum level of cooperation. This last result could
explain the observation that human cooperation seems to be often constrained by
considerations of social efficiency.
biological markets, competitive altruism, human cooperation, matching, models, partner
   GEOFFROY Et al.
also believed to play a major role in human cooperation, where
friendships and coalitions are common (Barclay, 2013, 2016;
Baumard, André, & Sperber, 2013) (see also Discussion).
The key idea of partner choice models is that when one happens
to be paired with a defecting partner, one has the option to seek for
another, more cooperative, partner present in the 'biological mar
ket' and interact with her instead of the defector. This possibility
allows cooperators to preferentially interact with each other and,
Sforza, 1982; Bull & Rice, 1991; Noë & Hammerstein, 1994, 1995;
Ferriere et al., 2002; Bergstrom, 2003; Aktipis, 20 04, 2011; Sachs et
al., 2004; Fu, Hauert, Nowak, & Wang, 20 08; Barclay, 2011).
So far, the primary objective of most partner choice models has
been to explain how some cooperation can exist at all in an evolu
swer: partner choice can trigger the evolution of cooperation. In this
paper, however, we are interested in another issue that models gen‐
erally considerwith lessscrutiny:that ofunderstandingthequanti
tative level of cooperation that should evolve under partner choice.
Thisanalysis iscrucialbecausethe quantitative levelofcooper
ation determines the 'social efficiency', also called the Pareto effi‐
ciency, of interactions. Cooperating too little is inefficient because
individuals miss some opportunities to generate social benefits.
But cooperation, as any investment, is likely to have diminishing re‐
turns (Altmann, 1979; Killingback & Doebeli, 2002; Weigel, 1981).
As a result, there is a 'socially optimal' amount of cooperation, an
intermediate level where the sum of the helper and helpee's pay
off is maximized. Cooperating more than this amount is hence also
inefficient, because it increases more the cost of cooperation than
it raises its benefit. In the extreme, there is even a 'wasteful' thresh‐
old beyond which the overall cost of cooperation becomes larger
than its benefit. If two partners cooperate more than this threshold,
the net benefit of their interaction is negative; that is, they are both
worst off than if they had not cooperated at all.
Prima facie, partner choice appears to be a unidirectional pres‐
sure acting on the evolution of cooperation, unlikely to generate
an interme diate equilibr ium. Compet ition to be chose n by others,
called 'competitive altruism' (Hardy & Van Vugt, 2006; Nesse, 2009;
Roberts, 1998), should lead to a runaway of cooperation, as it does
in sexual selection (West‐Eberhard, 1983). In principle, this runaway
should proceed up to the point where the cost of investing into co‐
operation cancels out the benefit of finding a partner (Fisher, 1930;
West‐Eberhard, 1979) that is up to the 'wasteful' threshold where
cooperation becomes fruitless. Is competitive altruism, however,
balanced by opposite forces, leading to an evolutionary stabilization
of cooperation below this threshold? Is this level socially optimal,
or does partner choice lead to the investment into counterproduc‐
tive forms of cooperation to outcompete others as it does in sexual
In the theoretical literature on partner choice, relatively little
portion of models consider cooperation as an all‐or‐nothing decision
andthuscannotstudy its quantitative level (Eshel&Cavalli‐Sforza,
1982; Bergstrom, 2003; Aktipis, 2004, 2011; Fu et al., 2008; Chen,
Fu, & Wang, 2009; Suzuki & Kimura, 2011; Sibly & Curnow, 2012;
2014; Chen, Wu, Li, & Wan g, 2016; Wubs, Bshary, & Lehma nn, 2016).
Second , some models con sider cooper ation as a quanti tative trait
but do not entail diminishing returns, and are thus ill‐suited to study
the social efficiency of cooperative interactions (Foster & Kokko,
2006; Nesse, 2009; Sherratt & Roberts, 1998; Song & Feldman,
2013).Third,still other modelsconsider cooperation as aquantita
tive trait with diminishing returns, but they only focus on one side
of the problem ‐the evolution of cooperation‐ considering the other
side ‐the strategy employed by individuals to choose their partner‐
as an exogenous parameter (Wilson & Dugatkin, 1997; Ferriere et al.,
2002; Barclay, 2011; Wild & Cojocaru, 2016).
To our knowledge, only one existing model studies the joint evo‐
lution of co operation an d partner cho ice in a quantitat ive setting
with diminishing returns (McNamara, Barta, Fromhage, & Houston,
2008). However, McNamara et al. (2008) make two key assumptions
thatturnoutto haveimport antconsequences:(i)theyassumethat
variability in the amount of cooperation is maintained owing to a
very large genetic mutation rate on this trait, which prevents natural
selection to act efficiently, and (ii) they restrict the set of possible
strategies to choose one's partner in such a way that individuals can
never do so in an optimal manner.
In this paper, we build a model inspired by McNamara et al.
(2008),inwhichaquantitativelevel ofcooperationexpressedby
individualsjointly evolveswitha quantitative levelof choosiness
regarding others' cooperation, while relaxing these two assump
tions. First, we observe that competition to be chosen as a partner
leads to a joint rise of both cooperation and choosiness up to a
level that depends on the efficiency of partner choice that is, in
particular, on the cost of changing partner. The more efficient is
partner choice, the higher cooperation is at evolutionary stability.
Moreover, when the cost of changing partner is low, cooperation
can rise beyond its socially optimal level. In fact, in the limit where
partner choice is entirely frictionless (i.e. the cost of changing
partner is zero), cooperation and choosiness rise up to the 'waste
ful threshold' where the cost of cooperation entirely cancels out
its benefit. Individuals gain the same payoff than if they had not
cooperated at all. Hence, at first sight, our analyses show that
partner choice generates no systematic trend towards the socially
optimal level of cooperation.
However, we then import tools from the economics literature
and assume that individuals can plastically modulate their choosi
ness in function of their own cooperation level. This plasticity allows
every individual to behave optimally on the biological market, which
did not occur in the first model. In this second approach, we show
that assortative matching emerges. That is, more cooperative indi‐
viduals are also choosier and thus interact with more cooperative
partn ers. As a co nsequence of t his assor tment, and p rovided tha t
partner choice is efficient enough, cooperation evolves to the so‐
cially optimal level, where the mutual efficiency of cooperation is
2.1 | Partner choice framework
We model par tner choice in an infinite size population using Debove,
André, and Baumard (2015a)'s framework. Solitary individuals ran
domly encounter each other in pairs at a fixed rate
. In each en‐
counter, the two players decide whether they accept one another
as a partner (see below how this decision is made). If one of the two
individuals (or both) refuses the interaction, the two individuals im
mediately split and move back to the solitary pool. If both individuals
accept each other, on the other hand, the interaction takes place and
lasts for an exponentially distributed duration with stopping rate
after which the two individuals move back to the solitary pool again.
The ratio
thus characterizes the 'fluidity' of the biological mar‐
ket. If
is high and
is low,individualsmeeteachotherfrequently
and interact for a long time. In such an almost frictionless market,
partner choice is almost cost‐free so they should be choosy about
their partner's investment in cooperation. Conversely, if
is low,
individuals rarely meet potential partners and interact for a short
time. In such a market, on the contrary, individuals should accept
any partner.
Regarding the encounter rate, here we assume that
is a fixed
constant independent of the density of available partners, an as‐
sumption called 'linear search' that captures a situation in which
already paired individuals do not hinder the encounters of soli
tary individuals (Diamond & Maskin, 1979). In the Supplementary
Information, however, using simulations we also analyse the model
under the assumption that
increases linearly with the propor
tion of solitary individuals in the population, an assumption called
'quadratic search'that corresponds to a situation in which already
matched individuals interfere with the encounters of solitary indi
used in mathematical epidemiology). In the paper, we only describe
the results obtained under linear search. The results obtained under
quadratic search are qualitatively similar (see the Supplementary
Regarding the nature of the social interaction, we consider a
quantitativeversion of theprisoner'sdilemmain continuous time.
Each individual
is genetically characterized by two traits: her coop‐
eration level
and her choosiness
. Cooperation level
thequantitativeamountofef fortthatanindividual
is willing to in‐
vest into cooperation. Choosiness
represents the minimal cooper
ation level that an individual
is willing to accept from a partner; that
is, every potential partner
with cooperation
will be accepted,
whereas every potential partner with
will be rejected. Once
an interaction is accepted by both players, at every instant of the
interaction, each player invests her effort
(see below for the pay‐
off function), and the interaction lasts in expectation for
units of
time, where
is the stopping rate of the interaction.
When they are solitary, individuals gain a payoff normalized to
zero per unit of time. When involved into an interaction, they gain a
social payoff that depends on both partners' cooperation level. The
cooperative interaction is a continuous prisoner's dilemma: making
an investment brings benefits to the partner but comes at a cost to
the provider. As stated in the introduction, we make the additional
assumption that cooperation has diminishing returns (Altmann,
1979; Killingback & Doebeli, 2002; Weigel, 1981). This induces the
existence of an intermediate level of cooperation at which the sum
of the partners' gains is maximized, the so‐called 'social optimum'.
An individual
paired with
gains the following social payoff
per unit of time:
Hence, the expected payoff of an individual
paired with
is the stopping rate of the interaction. The socially optimal
level of cooperation is
. Beyond this level, the net benefit of
cooperation decreases. Eventually, the interaction becomes entirely
profitless, or even costly, if individuals invest more than the 'waste‐
ful threshold'
. We allow both cooperation and choosiness to
take any positive real value.
Previous studies demonstrated that the existence of some vari
ability among individuals is necessary to stabilize conditional co
operation (Ferriere et al., 2002; Foster & Kokko, 2006; McNamara
et al., 2008; McNamara & Leimar, 2010; Song & Feldman, 2013).
Ifevery possible partner is equallycooperative, thenthere is no
choosiness cannot be evolutionarily stable. In order to capture
the effect of variability in the simplest possible way, we assume
that individuals do not perfectly control their investment into
cooperation (as in Song & Feldman, 2013 and André, 2015, for
instance). An individual's actual cooperation level
is a random
variable which follows a truncated‐to‐zero normal distribution
around the individual's gene value x
, with standard deviation
In what follows, we call cooperation level the genetically encoded
cooperation level that individuals aim for, and 'phenotypic cooper
ation' the actual level of cooperation that they express after phe
notypic noise. For the sake of simplicity, here, we assume that an
individual's cooperation level is randomized at every encounter.
In the Supplementary Information, however, we also consider the
alternative assumption where phenotypic noise occurs only once
at birth (see also Section 3.1).
We are interested in the joint evolution of cooperation, and
choosiness by natural selection. We undertake and compare the
consequences of two distinc t assumptions. In a first approach,
we assume that both cooperation and choosiness are hard‐wired
traits; that is, each individual is characterized by a single level of
and a single choosiness
, both expressed uncondi
tionally. In a second approach, we still assume that cooperation
is a hard‐wired trait, but we consider that choosiness is a reac
tion norm by which individuals respond to their own phenotypic
   GEOFFROY Et al.
2.2 | Hard‐wired choosiness
Here, we assume that each individual is genetically characterized
by two traits: his level of cooperation
and his choosiness
; and
we are interested in the evolution of these two traits by natural se
lection. For this, we need to derive the fecundity of a rare mutant
playing strategy
in a resident population
playing strat
. The mutant fecundity is proportional to her cumulative
lifetime payoff
. Without loss of generality, we normalize an in
dividual's lifetime to unity, such as the cumulative lifetime payoff
can be written as (see Supporting information for a detailed
analysis of the model):
is the mean probability for an encounter between the mu‐
tant and a resident to be mutually accepted and
is the mutant
mean social payoff (see Table 1 for a list of the parameters of the
ter model of optimal diet (Schoener, 1971).
The evolutionary trajectory of both the level of cooperation
and the choosiness
can be studied from the analysis of their re
spective selection gradient:
We could not derive an analytical expression of the evolution‐
arily stable strategy. However, we numerically computed the se‐
lection gradient on each trait, in order to study the evolutionary
2.3 | Plastic choosiness
Because cooperation is subject to phenotypic noise (i.e. one does
not perfectly control one's own level of cooperation), it could make
sense, at least in principle, for individuals to adapt plastically their
degree of choosiness to the actual phenot ypic cooperation that they
happen to express. For instance, it could make sense for those indi‐
viduals who happen to be phenotypically more generous to be also
choosier, and vice versa. In our second model, we aim to explore the
consequences of this possibility.Todoso, weassume thatchoosi
ness is not a hard‐wired trait, but a plastic decision that individuals
take in function of their own phenotypic cooperation. An individual's
'choosiness strategy' is thus defined as a reaction norm rather than
a single value.
Our aim in this second model is to study the joint evolution of
on the one hand, and of the 'choosiness strategy'
, defined as the shape of a reaction norm, on the other hand.
One facet of this problem, therefore, consists in seeking for the
equilib rium choosiness s trategy in a situa tion where both one's
own quality (one's phenotypic cooperation level) and the quality
of one's prospective partners vary. Matching theory, a branch of
micro‐economics, provides tools to resolve this problem. Here,
we briefly explain this approach and show how it applies to our
In a first category of approaches, called matching models, chang‐
ing partner is assumed to be entirely cost‐free (Becker, 1973; Gale &
Shapley, 1962). That is to say, agents have an infinite amount of time
available to find each other. In this setting, theory shows that there
notypic cooperation
should only accept to interact with individuals
with at least the same phenotypic cooperation level
; that is, the
equilibriumreactionnorm isthe identityfunction. This equilibrium
strategy leads to a strictly positive assortative matching in which in
dividuals are paired with likes.
Parameter Definition
Cooperation level of individual
(mean value
before applying noise)
Choosiness of individual
Standard deviation of the phenotypic cooperation
βEncounter rate
Split rate
Social payoff of an individual
matched with a
Cost of cooperation
Mean probability for an individual
to interact
when she encounters a resident
Mean social payoff for an individual
with a resident
Cumulative lifetime payoff of an individual
TABLE 1 Parameters of the model
The secon d category of appr oaches, calle d search and matchin g
models, accounts for frictions in the matching process, that is in
corporates an explicit cost for changing partner (Chade, Eeckhout,
& Smith, 2017). These models actually correspond exactly to our
own partner choice framework. Individuals randomly encounter
each other at a given rate, and when an individual refuses an inter
action, she has to wait for some time before encountering a new
cannot be analytically derived in these models. However,
Smith (2006) has shown that a mathematical property of the social
payoff function
allows predicting the shape of this reac
tion norm. If the social payoff function
is strictly log‐super
modular, then
is strictly increasing with
. If this is the case,
the more an individual invests into cooperation, the choosier she
should be.Thisequilibriumiscalled aweaklypositiveassortative
matching. Log‐supermodularity is defined as the following:
is strictly log‐supermodular only if
any investments
. Intuitively, in our setting, log‐su
permodularity captures the idea that individuals who invest more
into cooperation also benefit relatively more from better partners
(Costinot, 2009). Indeed, by definition, log‐supermodularity im
plies that the relative returns to accessing more generous partners
increase in one's level of investment into cooperation:
. For an exhaustive review on modularity and
matching, see Chade et al. (2017) and Smith (2006).
Matching and search and matching models are, however, only in‐
dividuals, assuming a given, fixed distribution of cooperation levels.
As a result, matching models can offer an insight into the evolution
of choosiness, but not into the joint evolution of choosiness and co‐
operation. To study this joint evolution in the case where choosiness
is a reaction norm, and not a single value, we developed individual‐
based simulations.
2.4 | Individual‐based simulations
In addition to our analytical models, we run individual‐based
simulations coded into Python. We simulate the joint evolution
of cooperation and choosiness in a Wright‐Fisher population of
individuals, with the same lifespan
and nonoverlapping gen
erations. Mutations occur at rate
, and mutant genes are drawn
from a normal distribution around the parent's gene value, with
standard deviation
. Large‐effect mutations are implemented
with probability
. In this case, mutant genes are drawn from a
uniform distribution on the interval
. Large‐effect mutations
donot alter theequilibrium result, and theyallow to speed up
the joint evolution process. We run long enough simulations for
both choosiness and cooperation to stabilize. In contrast to pre
vious papers (Foster & Kokko, 2006; McNamara & Leimar, 2010;
Sherratt & Roberts, 1998), here we consider a continuous rather
than discrete trait space, because Sherratt and Roberts (1998)
have shown that too much discretization can produce undesir
able consequenceswhen studying a joint evolution process. In
the Supplementary Information, we also present additional simu
lations based on a Moran process with overlapping generations,
where the lifespan of individuals is determined by a constant
mortality rate (see also Section 3.1 and McNamara et al., 2008).
We run simulations both under the assumption that choosiness
is hard‐wired and under the assumption that it is a reaction norm.
In the second case, we test two types of reaction norms. First, we
consider polynomial functions, the coefficients of which evolve by
natural selection. Second, we consider step functions with evolving
coefficients coding for the value of choosiness for each interval of
cooperation. In the initial generation, all reaction norms are set to
a constant zero function, so that individuals are never choosy at
FIGURE 1 Analytical and numerical results with hard‐wired choosiness. (a) The grey arrows show the vector field of the selection
gradient on both cooperation and choosiness. The red arrows show an evolutionary trajectory from an initial selfish population
for a resident
individual. Parameters are
; and
. The socially optimal solution is
and the interaction becomes profitless if
both individuals invest
(a) (b)
   GEOFFROY Et al.
3.1 | Hard‐wired choosiness
Without variability in cooperation
, there is no selective pres‐
sure to be choosier and, therefore, to be more cooperative. The only
Nash equilibrium is
(see Supporting information for a
When phenotypic cooperation is variable, however, the evolu‐
tionarily stable strategy cannot be formally derived. We therefore
study the joint evolutionary dynamics of cooperation and choosi‐
ness by plotting numerically the selection gradients acting on both
traits. In Figure 1, we show the evolutionary dynamics of coopera‐
tion, choosiness and average payoff, in a case where partner choice
is very effective (high
). When starting from an initially selfish
population, cooperation and choosiness jointly rise above zero
(Figure 1). At first, this leads to an increase in the net social payoff
(Figure 1) because cooperation is efficient (i.e. the marginal benefit
of increasing cooperation for the helpee is larger than its marginal
cost for the helper). At some point, however, cooperation reaches
the socially optimal level where the net payoff of individuals is maxi‐
mized. Beyond this level, the marginal cost of increasing cooperation
is larger than the marginal benefit, but the evolutionary runaway
of cooperation and choosiness does not stop. Cooperation keeps
on rising towards higher values, thereby decreasing the net payoff
(Figure 1). Eventually, cooperation and choosiness stabilize when
cooperation is so high, and therefore so inefficient, that its cost
entirely cancels out its benefit (the so‐called 'wasteful threshold').
That is, at ESS, individuals gain the same payoff than if they had not
cooperated at all.
This runaway process, however, only occurs if partner choice
is very efficient. If partner choice has more frictions (low
), the
rise of cooperation and choosiness halts at an intermediate level
between 0 and the wasteful threshold. In Figure 2, we plot the
level of cooperation (Figure 2), the level of choosiness (Figure 2)
and the average payoff (Figure 2) reached at evolutionary stability,
in function of the efficiency of partner choice (i.e. in function of
the parameter
controlling the fluidity of the social market and
the parameter
controlling the extent of phenotypic variability).
As partner choice becomes more efficient, the evolutionarily sta
ble cooperation and choosiness monotonously rise from zero up to
the wasteful threshold (Figure 2 and Figure S2). Accordingly, the
net payoff obtained by individuals at evolutionary stability varies
with the efficiency of partner choice in a nonmonotonous way.
Increasing the efficiency of partner choice has first a positive and
then a negative effect on payoff (Figure 2). In the extreme, when
partner choice is frictionless, cooperation and choosiness increase
up to the 'wasteful threshold'
at which cooperation is
entirely profitless (as shown in Figure 1). Note that in this case,
choosiness is even slightly larger than the 'wasteful threshold' at
equilibriumbecause,due tophenotypicvariability,someindivid
uals cooperate beyond
higher values of cooperation. In fact, when phenotypic variabil
ity is too high (large
), individuals are so choosy at evolutionary
equilib rium that the equ ilibrium level of co operation is re duced
(Figure 2). These results have been confirmed in individual‐based
simulations (see Supporting information).
The runaway process can be understood intuitively. In any
population, some individuals cooperate more than average, in
FIGURE 2 Analytical results for a range of parameters
for (a) cooperation, (b) choosiness and (c) cumulative lifetime
payoff as a function of the encounter rate
to manipulate the
market fluidity, and for three values of the standard deviation,
𝜎=0.0001; 0.01; and 0.02
respectively for low, medium and high
phenotypic variability. Other parameters are the same as in Figure 1
particular owing to phenotypic variability. As a result, if part
ner choice is sufficiently fluid, it is adaptive to accept only these
hyper‐generous partners. Hence, choosiness increases by natural
selection beyond the average cooperation level. In turn, this fa
vours individuals who cooperate more than average; that is, the
mean level of cooperation increases by natural selection, etc. The
extent to which this process goes on depends, however, on the
efficiency of partner choice owing to the existence of a trade‐off
between the cost and benefit of choosiness. The runaway process
stops at the point where the expected benefit of finding a better
partner is not worth the risk of remaining alone.
In our model so far, the cost and benefit of switching partner are
only determined by two parameters (the market fluidity,
, and the
amount of phenotypic variability,
). Under more realistic biological
assumptions, however, the cost of rejecting a partner should also de
pend on other parameters. For instance, one could model mortality
as a stochastic process. The risk of dying while searching for a new
partner would then constitute a supplementary cost of choosiness
(McNamara et al., 2008). In the Supplementary Information, we de
velop a model based on a Moran process where individuals are subject
to a constant mortality rate. As expected, ceteris paribus, the run
away process results in lower levels of cooperation and choosiness at
evolut io nar yequi li briumwh en themo rta lit yr atei sh ig h.C oo per at io n,
however, still rises beyond the socially optimal level, even up to the
wasteful threshold, if
is large and if the mortality rate is not too high.
Also, in our model, so far, we assume that an individual's pheno
typic level of cooperation is randomized in every encounter. The
distribution of cooperative types in the solitary population is thus a
fixed and exogenous property. To test the robustness of our results, in
the Supplementary Information, we analyse an alternative case where
the phenotypic level of cooperation of an individual is randomized only
once, at birth. In this case, the distribution of cooperative types in the
solitary population is not an exogenous, fixed, property. More coop
erative individuals are less likely to be solitary than average because
they are rapidly accepted as partners (McNamara et al., 2008). Hence,
the population of solitary individuals tends to be biased towards self
ish phenotypes. As a result, the cost of being choosy is larger. Yet, in
Supporting information we show that the runaway process still occurs
in this case, including up to the 'wasteful threshold', as long as partner
choice is efficient enough.
Note that Ferriere et al. (2002) and Wild and Cojocaru (2016),
inspired by Barclay (2011), also showed that partner choice could,
under some circumstances, drive the evolution of cooperation up
to a 'wasteful threshold'. However, in both models, the choosiness
strategy was fixed, and not necessarily optimal; it did not evolve
jointly with cooperation. The present results are thus more robust
and general.
3.2 | Plastic choosiness
Here, an individual's choosiness is a reaction norm to her own phe
notypic cooperation, and we used search and matching models (see
Section 2.3) to derive the two following predictions regarding the
evolutionarily stable reaction norm:
FIGURE 3 Plastic choosiness at the
norms over 30 simulations are shown
in blue, and the corresponding 99%
confident intervals are shown in red with
(a–b) high market fluidity
, (c–d) low
market fluidity
, (a–c) a polynomial
reaction norm and (b–d) a discrete
reaction norm. The orange dashed
line is the optimal reaction norm for a
frictionless matching market (strong form
of positive assortative matching). The
distribution of phenotypic cooperation at
𝜎mut =0.05
; and
(a) (b)
(c) (d)
   GEOFFROY Et al.
1. If the social payoff function is strictly log‐supermodular, an
individual's optimal choosiness is a strictly increasing function
of her own cooperation (weakly positive assortative matching).
2. If the market fluidit y
is high, the reaction norm sho uld be close
(strictly positive assortative matching).
We first show that our production function
is strictly log‐super
modular. Indeed,
which is true for all
. Accordingly, search and
matching models show that the optimal choosiness strategy is an
increasing reaction norm; that is, more phenotypically cooperative
individuals should also be choosier, leading to a positive assortative
matching at equilibrium (phenotypically generous individuals are
matched with other generous individuals, and vice versa).
Individual‐based simulations confirm this result. Figure 3 shows
thereactionnorm atevolutionary equilibrium in these simulations:
choosiness is strictly increasing, at least around the levels of pheno
typic cooperationthat are actually present at equilibrium.Outside
this range, selection is very weak on the reaction norm, and we ob‐
serve larger confidence intervals. As expected, when the market
tends to be frictionless, the reaction norm becomes very close to
the identity function, that is to a strict positive assortative matching
(Figure 3 and Figure S3 orange dashed line).
Importantly, the evolution of a plastic rather than hard‐wired
choosiness strategy has a key consequence regarding the effi
ciency of cooperation at evolutionary equilibrium. In contrast to
the hard‐wired case, when choosiness is plastic, cooperation never
rises above the socially optimal level. As the efficiency of partner
choice (i.e. market fluidity) increases, the level of cooperation at
evolutionary stability increases but, at most, it reaches the socially
optimal level and never more (Figure 4). In particular, when partner
choice is very efficient, cooperation evolves precisely towards the
socially optimal level, that is the level that maximizes the net total
payoff of individuals
This result can also be understood intuitively. In the first model
where choosiness was hard‐wired, it was adaptive to increase one's
cooperation level beyond the population mean because, by doing so,
an individual could s witch from 'being rejected by everyone' to 'being
accepted by everyone'. The runaway process, therefore, proceeded
until cooperation had no benefit at all. In contrast, in the present
model where choosiness is plastic, increasing one's cooperation level
is beneficial because it allows one to access better partners. Hence,
partner is larger than the cost of being more cooperative. As a result,
cooperation only rises up to the social optimum, where its net ben‐
efit is maximized.
Most theoretical works on the evolution of cooperation by partner
choice aim at explaining how some cooperation can be evolutionarily
stabl e. They do not ai m at unders tanding wh ich specif ic quantit a
tive level of cooperation should evolve. In this paper, we have raised
thissecondquestion.Wehave consideredamodelwherecoopera
tion has diminishing returns, such that the most efficient level of
cooperation (the level that maximizes social welfare) is intermedi‐
ate. We have investigated whether partner choice can account for
the evolution of an efficient level of cooperation in this case. In this
aim, we have modelled, both numerically and with individual‐based
simulations, the joint evolution of two traits: cooperation, the ef‐
fort invested into helping others, and choosiness, the minimal level
of cooperation that an individual is willing to accept from a partner.
In a first model, we have found that the mechanism of part‐
ner choice entails no systematic force favouring an efficient level
of cooperation. On the contrary, when partner choice is effective
enough, the level of cooperation increases evolutionarily towards
very large values, beyond the socially optimal level. In the extreme,
when partner choice is very effective, cooperation even increases
up to a level where its cost entirely cancels out its benefit. That is,
they had not cooperated at all.
To understand intuitively, consider a population with a given
distribution of cooperation levels, with some particularly generous
individuals, some particularly stingy individuals and a given mean
cooperation level. In such a population, provided that the variabil
ity of cooperation is sufficiently large and the market sufficiently
fluid, it is always adaptive to accept only partners that are slightly
better than average (McNamara et al., 2008). Hence, natural se
lection favours individuals with a choosiness always slightly larger
than the average cooperation level. In turn, this choosiness selects
for mutants whose cooperation level is la rger than the mean, which
FIGURE 4 Evolution of cooperation for a polynomial reaction
norm. The average cooperation over 30 simulations is shown
for three values for the encounter rate,
𝛽=0.001; 0.01; and 0.1
respectively for low, medium and high market fluidity. Other
parameters are the same as in Figure 3. The socially optimal
solution is
and the interaction becomes profitless if both
individuals invest
leads to a gradual increase in cooperation. Importantly, this run
away process has no particular reason to stop when cooperation
is maximally efficient. Rather, it stops when the cost of searching
for more generous individuals exceeds the benefit of interacting
with them (Figure 2). As long as partner choice is effective (i.e.
the cost of searching is low), it is always worth trying to find a
better‐than‐average partner, irrespective of whether the current
mean level of cooperation is below or beyond the socially optimal
level. Hence, partner choice can prompt individuals to invest into
counterproductive forms of cooperation to outbid others, leading
to an eventually fruitless arms race.
In a second approach, in line with matching models from the eco‐
nomic literature, we have designed a model in which choosiness is
implemented as a reaction norm to the individual's own coopera‐
tion level (see Section 2.3), the shape of which evolves by natural
selection. In this case, both our analytical predictions derived from
search and matching models and our complementary individual‐
based simulations show that the evolutionarily stable reaction norm
is a monotonously increasing function of cooperation (Figure 3). This
implies that more generous individuals are also choosier, leading to a
positive assortative matching: generous individuals tend to interact
with other generous individuals, and vice versa. Furthermore, if the
biological market is fluid enough (i.e. if the cost of changing partner
is low), this positive assortative matching becomes very close to a
perfect matching in which individuals with a given level of coopera‐
tion always interact with other individuals with the exact same level
(Figure 3 and Figure S3).
In this case, and in sharp contrast to the model in which choos‐
iness is a hard‐wired trait, cooperation does not reach the counter‐
productive level where its cost cancels out its benefit when partner
choice is very cheap (Figure 4). More precisely, when the market is
very fluid, the evolutionarily stable cooperation becomes very close
to the social optimum, that is the amount of cooperation that maxi‐
mizes the sum of the partners' payoffs. This can also be understood
intuitively. Because of the strict assortment between cooperative
types, individuals with a given cooperation level interact with other
individuals with the exact same level. Hence, pairs of individuals be‐
come the effective units of selection, like if interactions occurred
among genetic clones (Akçay & Cleve, 2012; Aktipis, 2004; Eshel &
Cavalli‐Sforza, 1982;Wilson & Dugatkin,1997).Consequently,the
socially optimal level of cooperation is favoured.
Hence, the fruitless runaway of cooperation that occurs in a
tion that individuals cannot optimally adapt their degree of choos‐
iness to local circumstances. If individuals are allowed to behave
optimally, which entails in the present case to adapt plastically their
choosiness to their own generosity, then partner choice looks less
like a competition to outbid others, and more like a competition to
form efficient partnerships with others, which leads to a very differ‐
ent outcome regarding the net benefits of cooperation.
Previous work has shown that assortative matching favours the
evolution of cooperation (Bergstrom, 2003; Eshel & Cavalli‐Sforza,
1982; Hamilton, 1971). For instance, in kin selection, assortment
between relatives drives the evolution of cooperation (Hamilton,
1964; Rousset, 2004). To our knowledge, Wilson and Dugatkin
the evolution of socially efficient levels of cooperation. Alger and
Weibull (2013, 2016) have studied the evolution of social prefer‐
ences, rather than strategies, under assortative matching. However,
both analyses did not explicitly model a partner choice strategy, let
alone the evolution of this strategy, but merely assumed that assort‐
ment occurs in one way or another. In contrast, here, we have stud‐
ied the joint evolution of choosiness and cooperation, showing how
a positive assortative matching can emerge from a simple partner
choice mechanism.
In another related work, using individual‐based simulations,
McNamara et al. (2008) also observed a form of assortative match‐
ing in the joint evolution of cooperation and choosiness. One of the
main differences with the present approach, however, is that they
assumed that the variability of cooperation is maintained at the ge‐
netic level, via a high mutation rate, rather than at the phenotypic
level. Under this assumption, negative selection on inefficient mu
librium between cooperation and choosiness, resulting in a positive
assortative matching. For this reason, their work is more similar to
our second model where choosiness is plastic than to our first model
where choosiness is hard‐wired. In McNamara et al. (2008)'s simula‐
tions, however, in contrast to our results, cooperation never reaches
the socially optimal level (in the model where they consider a pay
off function with diminishing returns). In a complementary analysis
(see Supporting information), we showed that this could be a con‐
high, which prevents natural selection from fully optimizing social
Some scholars have already imported principles from matching
theory into evolutionary biology, especially in the field of sexual
and Real (2000) have used matching models, respectively with and
without search frictions, to shed light on mutual mate choice. Both
works focused on the evolution of choosiness with a given, fixed
intensity of assortment may have a dramatic impact on the evolution
of the chosen trait (cooperation, in our case). For instance, further
models could investigate the precise limits of the runaway processes
that occur on weaponry, or on ornamental traits, in sexual selection.
More generally, matching models could be helpful to analyse a large
variety of biological markets (Hammerstein & Noë, 2016; Noë &
Hammerstein, 1994, 1995), including inter‐specific mutualisms, such
as mycorrhizal symbiosis or plant‐rhizobia relationships (Kiers et al.,
2011, 2003; Simms & Taylor, 2002).
As for the human case in particular, several lines of evidence
suggest that partner choice is a likely candidate as a key driving
force in the evolution of cooperation. Numerous experimental stud
ies have shown that human beings indeed do choose their social
partners in function of their cooperative reputation (Barclay, 2013,
2016; Barclay & Raihani, 2016; Barclay & Willer, 2007; Baumard et
   GEOFFROY Et al.
al., 2013; E_erson, 2016; Raihani & Smith, 2015; Stovel & Chiang,
2016; Sylwester & Roberts, 2010, 2013; Wu, Balliet, & Lange, 2016).
Anthropological observations show that defection in traditional so
cieties is mostly met with a passive abandonment rather than with
more defection in return (see Baumard et al., 2013 for a review).
Also, several theoretical studies have shown that partner choice can
account for the evolution of other important properties of human
cooperation, such as the fact that its benefits are often shared in
proportion to ever yone's respective effort in producing them (André
& Baumard, 2011a, 2011b; Chiang, 2008; Debove, André, et al.,
2015a; Debove Baumard, & André, 2015b, 2017; Takesue, 2017).
Regarding the quantitative level of cooperation, observations
show that humans have precise preferences regarding the amount of
effort that shall be put into helping others. Daily life contains ample
examples of these preferences. For instance, we hold the door for
others in subway stations, but only when they are sufficiently close
to the door already, not when they are very far from it. And this is
have preferences for specific amounts of cooperation, neither too
little nor too much (L ange & Eggert, 2015; Santamaria & Rosenbaum,
2011). Sometime s this prefere nce is expres sed in a purely q uanti
tative manner. At other times, the same preference is expressed in
a more qual itative way, determining the kinds of co operative ac
tion that we are willing, or unwilling, to perform. In any case, our
cise level of effort we are willing to put in cooperation seems to be
constrained by considerations of social efficiency. Individuals help
one another only when it is mutually advantageous, that is when the
cost of helping is less than the benefit of being helped. Additionally,
recent evolutionary modellings of risk pooling have revealed the
socially optimal nature of helping behaviours (Aktipis et al., 2016;
Aktipis et al., 2011; Cronk, 2007; Hao, Armbruster, Cronk, & Aktipis,
2015; Campenni et al., 2017). They have shown that people's sys‐
tems of mutual help correspond to the most efficient systems of risk
pooling in a volatile environment.
In this paper, we have shown that partner choice can foster the
evolution of such an intermediate and efficient amount of coopera‐
tion, neither too little nor too much. But we have also shown that the
precise evolutionarily stable amount of cooperation should depend
on the fluidity of the biological market and can range from a very
low level of cooperation up to the socially optimal level (Figure 4).
A number of anthropological studies suggest that contemporary
hunter‐gatherer societies exhibit high levels of spatial mobility
(Baumard et al., 2013; Lewis, Vinicius, Strods, Mace, & Migliano,
2014). Therefore, it seems plausible that biological markets were
highly fluid in the social structure that our ancestors experienced.
Our model predicts that in this case, the amount of effort invested
into cooperation should become very close to the social optimum.
Therefore, partner choice can account for the evolution of human
preferences concerning social efficiency.
One could wonder, however, whether other models than partner
choice could account for the evolution of a socially optimal level of
cooperation as well. The most influential model on the evolution of
the iterated prisoner's dilemma (André, 2015; André & Day, 2007;
Killingback & Doebeli, 2002; Lehmann & Keller, 2006; Roberts &
Sherratt, 1998; Wahl & Nowak, 1999a, 1999b). In this game, André
and Day (2007) have shown that the only evolutionarily stable level
of investment is the one that maximizes the total benefit of the in‐
teraction, that is that natural selection does eventually favour the
socially optimal amount of cooperation (see also Binmore, 1990;
Fundenberg and Maskin 1990; Robson, 1990; Binmore & Samuelson,
1992 in a discrete version of the iterated prisoner's dilemma). Yet, in
this approach, selection for efficient cooperation is only a second‐
order force, that is interactions between rare mutants, which plays
a significant role only because André and Day (2007) assumed the
absence of other first‐order effects. For instance, a slight cognitive
cost of conditional behaviour would have prevented the evolution
of efficient cooperation in their model. In another related study,
Akçay and Cleve (2012) have shown that socially optimal coopera‐
tion is favoured when individuals play a specific class of behavioural
responses to others' cooperative actions. They have also shown that
for a specific case of their model, these behavioural responses can
evolve by natural selection under low levels of relatedness. Here,
we have shown that under the effect of partner choice, efficient
cooperation is favoured by first‐order selective effects even in the
total absence of genetic relatedness. This occurs because, unlike
reciprocity, partner choice is a directional enforcement mechanism.
Whereas reciprocity merely stabilizes any given level of cooperation
(a principle called the folk theorem; see Aumann & Shapley, 1994;
Boyd, 2006), partner choice directionally favours the most efficient
One limit of our model is that we did not introduce an explicit
mechanism for reputation. We simply assumed that in a way or an
other, individuals have reliable information regarding the cooper
ation level of others, but we did not model the way in which they
obtain this information. Costly signalling theory proposes that some
cooperativebehavioursarecostlysignalsofanindividual'squalit yor
willingness to cooperate (André, 2010; Barclay, 2015; Bird & Power,
2015; Bliege Bird, Ready, & Power, 2018; Gintis, Smith, & Bowles,
2001; Leimar, 1997). Such signals could, in the ory, be far from socially
efficient (Gintis et al., 2001). However, further analyses are needed
to rigorously model signalling in the context of a biological market.
This work was supported by ANR‐10‐LABX‐0087 IEC and
ANR‐10‐IDEX‐0001‐02 PSL. This is contribution 2019‐127 of the
Institut des Sciences de l'Evolution de Montpellier (UMR CNRS
5554). This project analyses benefited from the Montpellier
Bioinformatics Biodiversity platform services. A preprint ver
sion of this paper has been reviewed and recommended by Peer
Community In Evolutionary Biology (https ://
pci.evolb iol.100063).
The authors of this preprint declare that they have no financial con
flict of interest with the content of this article.
The source code for the simulations is available on the first author's
GitHub repository: https :// froy/coope ration_runa
way and on the Dryad digital repository: https ://
Félix Geoffroy‐00019800‐4728
Nicolas Baumard‐00021439‐9150
Jean‐Baptiste André‐00019069‐447X
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Additional supporting information may be found online in the
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How to cite this article:GeoffroyF,BaumardN,AndréJ‐B.
Why cooperation is not running away. J Evol Biol. 2019;00:1–
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... That is to say that individuals will be matched according to their performance. The best performing individuals will be able to afford to be picky and will end up being paired with other well performing individuals, and vice versa the worst-performing individuals will pair up together (Geoffroy et al., 2018). Therefore, the best performing individuals who interact together will receive benefits from their high level of cooperation. ...
... To our knowledge, all models published so far on the evolution of coopera-tion by partner choice focus on situations where finding a partner is sufficient to create an opportunity to cooperate. In this case, they show that partner choice can drive the evolution of cooperation in a relatively wide range of circumstances (Aktipis, 2004(Aktipis, , 2011André & Baumard, 2011a, 2011bBarclay, 2011;Campennì & Schino, 2014;Debove et al., 2017;Geoffroy et al., 2018;Johnstone & Bshary, 2008;McNamara et al., 2008;Noë & Hammerstein, 1994). Here, we wish to examine what happens on the contrary when resource availability constitutes a constraint on the operation of partner choice. ...
The evolution of cooperation is a paradox from an evolutionary point of view. Indeed, all individuals in the living world should be interested only in their own interests. Helping another individual is therefore a waste of time and resources. How can we explain that some individuals act in a cooperative way? This thesis focuses on the mechanism of reciprocity named partner choice that allows the evolution of cooperative behavior. However, the constraints necessary for the evolution of this mechanism are strong and rarely respected. This thesis aims at extending the knowledge of these constraints through simulations in complex and realistic environments. The first contribution of this thesis extends the pre-existing partner choice models by adding the constraint of resource availability in the environment. In this case, it is no longer only the population density, but also the wealth of the environment that influences partner choice. In our second contribution, we extend the results obtained by the aspatial models. We study the impact of spatial environments on the dynamics of cooperation with partner choice. Partner choice requires individuals to be able to learn from rare events. In our third contribution, we compare the reward sparsity tolerance of a reinforcement learning algorithm and an evolutionary strategy algorithm. Our work shows the immense difficulty that reinforcement learning algorithms have in developing partner choice, unlike evolutionary strategies.
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The effects of partner choice have been documented in a large number of biological systems such as sexual markets, interspecific mutualisms, or human cooperation. There are, however, a number of situations in which one would expect this mechanism to play a role, but where no such effect has ever been demonstrated. This is the case in particular in many intraspecific interactions, such as collective hunts, in non-human animals. Here we use individual-based simulations to solve this apparent paradox. We show that the conditions for partner choice to operate are in fact restrictive. They entail that individuals can compare social opportunities and choose the best. The challenge is that social opportunities are often rare because they necessitate the co-occurrence of (i) at least one available partner, and (ii) a resource to exploit together with this partner. This has three consequences. First, partner choice cannot lead to the evolution of cooperation when resources are scarce, which explains that this mechanism could never be observed in many cases of intraspecific cooperation in animals. Second, partner choice can operate when partners constitute in themselves a resource, which is the case in sexual interactions and interspecific mutualisms. Third, partner choice can lead to the evolution of cooperation when individuals live in a rich environment, and/or when they are highly efficient at extracting resources from their environment.
Cooperation among non-kin is well documented in humans and widespread in non-human animals, but explaining the occurrence of cooperation in the absence of inclusive fitness benefits has proven a significant challenge. Current theoretical explanations converge on a single point: cooperators can prevail when they cluster in social space. However, we know very little about the real-world mechanisms that drive such clustering, particularly in systems where cognitive limitations make it unlikely that mechanisms such as score keeping and reputation are at play. Here, we show that Trinidadian guppies (Poecilia reticulata) use a 'walk away' strategy, a simple social heuristic by which assortment by cooperativeness can come about among mobile agents. Guppies cooperate during predator inspection and we found that when experiencing defection in this context, individuals prefer to move to a new social environment, despite having no prior information about this new social group. Our results provide evidence in non-human animals that individuals use a simple social partner updating strategy in response to defection, supporting theoretical work applying heuristics to understanding the proximate mechanisms underpinning the evolution of cooperation among non-kin.
We show that altruism can evolve as a signaling device designed to solve commitment problems in interactions with outside options. In a simple evolutionary game-theoretic model, uncertainty about agents' incentives to stay in a relationship can cause the relationship to collapse, because of a vicious circle where being skeptical about one's partner's commitment makes one even more likely to leave the relationship. When agents have the possibility to send costly gifts to each other, analytical modeling and agent-based simulations show that gift-giving can evolve as a credible signal of commitment, which decreases the likelihood of relationship dissolution. Interestingly, different conventions can determine the meaning of the signal conveyed by the gift. Exactly two kinds of conventions are evolutionarily stable: according to the first convention, an agent who sends a gift signals that he intends to stay in the relationship if and only if he also receives a gift; according to the second convention, a gift signals unconditional commitment.
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Acts of prosociality, such as donating to charity, are often analysed in a similar way to acts of conspicuous advertising; both involve costly signals revealing hidden qualities that increase the signaller’s prestige. However, experimental work suggests that grand gestures, even if prosocial, may damage one’s reputation for trustworthiness and cooperativeness if they are perceived as prestige enhancing: individuals may gain some types of cooperative benefits only when they perform prosocial acts in particular ways. Here, we contrast subtle, less obviously costly, interpersonal forms of prosocial behaviour with high-cost displays to a large audience, drawing on the example of food sharing in subsistence economies. This contrast highlights how highly visible prosocial displays may be effective for attracting new partners, while subtle signals may be crucial for ensuring trust and commitment with long-term partners. Subtle dyadic signals may be key to understanding the long-term maintenance of interpersonal networks that function to reduce unanticipated risks.
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Toward understanding assortative matching, this is a self-contained introduction to research on search and matching. We first explore the nontransferable and perfectly transferable utility matching paradigms, and then a unifying imperfectly transferable utility matching model. Motivated by some unrealistic predictions of frictionless matching, we flesh out the foundational economics of search theory. We then revisit the original matching paradigms with search frictions. We finally allow informational frictions that often arise, such as in college-student sorting.
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Equity, defined as reward according to contribution, is considered a central aspect of human fairness in both philosophical debates and scientific research. Despite large amounts of research on the evolutionary origins of fairness, the evolutionary rationale behind equity is still unknown. Here, we investigate how equity can be understood in the context of the cooperative environment in which humans evolved. We model a population of individuals who cooperate to produce and divide a resource, and choose their cooperative partners based on how they are willing to divide the resource. Agent-based simulations, an analytical model, and extended simulations using neural networks provide converging evidence that equity is the best evolutionary strategy in such an environment: individuals maximize their fitness by dividing benefits in proportion to their own and their partners’ relative contribution. The need to be chosen as a cooperative partner thus creates a selection pressure strong enough to explain the evolution of preferences for equity. We discuss the limitations of our model, the discrepancies between its predictions and empirical data, and how interindividual and intercultural variability fit within this framework.
Sexual competition is associated closely with parental care because the sex providing less care has a higher potential rate of reproduction, and hence more to gain from competing for multiple mates. Sex differences in choosiness are not easily explained, however. The lower-caring sex (often males) has both higher costs of choice, because it is more difficult to find replacement mates, and higher direct benefits, because the sex providing more care (usually females) is likely to exhibit more variation in the quality of contributions to the young. Because both the costs and direct benefits of mate choice increase with increasing parental care by the opposite sex, general predictions about sex difference in choosiness are difficult. Furthermore, the level of choosiness of one sex will be influenced by the choosiness of the other. Here, we present an ESS model of mutual mate choice, which explicitly incorporates differences between males and females in life history traits that determine the costs and benefits of choice, and we illustrate our results with data from species with contrasting forms of parental care. The model demonstrates that sex differences in costs of choice are likely to have a much stronger effect on choosiness than are differences in quality variation, so that the less competitive sex will commonly be more choosy. However, when levels of male and female care are similar, differences in quality variation may lead to higher levels of both choice and competition in the same sex.
Humans—like many other organisms—observe others' interactions to gain useful information about who to challenge, avoid, mate with, or cooperate with. Organisms thus benefit from a reputation for being both able and willing to confer benefits on allies and impose costs on competitors. In humans, the existence of language allows for greater spread of information, and has increased the effects that one's reputation has on one's desirability as a partner or fearsomeness as a competitor. This has created selection pressures for high levels of both cooperation and aggression, as well as for behaviors that function to enhance one's own reputation (or decrease the reputation of one's competitors). A better understanding of reputation will allow us to harness social pressures to promote cooperation and decrease aggression, and help build a more comprehensive science of reputation.