Evolutionary dynamics of behavioral motivations for cooperation

Abstract

Human decision-making is shaped by underlying motivations, which reflect both subjective well-being and fundamental biological needs. Different needs are often prioritized and traded off against one another. Here we develop a theoretical framework to study the evolution of behavioral motivations, encompassing both philanthropic (cooperating after personal needs are met) and aspirational (cooperating to fulfill personal needs) motivations. Our findings show that when the ratio of benefits to costs for cooperation exceeds a critical threshold, individuals initially driven by aspirational motivations can transition to philanthropic motivations with a low reference point for cooperation, resulting in increased cooperation. Furthermore, the critical threshold depends on the structure of the underlying social network, with network modifications capable of reversing the evolutionary trajectory of motivations. Our results reveal the complex interplay between needs, motivations, social networks, and decision-making, offering insights into how evolution shapes not only cooperative behaviors but also the motivations behind them.

Full text

Article https://doi.org/10.1038/s41467-025-59366-1
Evolutionary dynamics of behavioral
motivations for cooperation
Qi Su
1,2,3
&AlexanderJ.Stewart
4
Human decision-making is shaped by underlying motivations, which reflect
both subjective well-being and fundamental biological needs. Different needs
areoftenprioritizedandtradedoffagainstoneanother.Herewedevelopa
theoretical framework to study the evolution of behavioral motivations,
encompassing both philanthropic (cooperating after personal needs are met)
and aspirational (cooperating to fulfill personal needs) motivations. Our
findings show that when the ratio of benefits to costs for cooperation exceeds
a critical threshold, individuals initially driven by aspirational motivations can
transition to philanthropic motivations with a low reference point for coop-
eration, resulting in increased cooperation. Furthermore, the critical threshold
depends on the structure of the underlying social network, with network
modifications capable of reversing the evolutionary trajectory of motivations.
Our results reveal the complex interplay between needs, motivations, social
networks, and decision-making, offering insights into how evolution shapes
not only cooperative behaviors but also the motivations behind them.
The evolution of cooperation is no longer mysterious or hard to
explain. Although apparently altruistic behavior can seem maladaptive
when viewed in isolation1, when placed in the proper context, it can be
seen to emerge easily from the process of natural selection2,3.The
difficulty we face in trying to understand cooperative behavior is not a
lack, but rather an overabundance of possible mechanisms capable of
producing it. Cooperation can be generated by reciprocity4,5, by social
norms and the need to sustain a good reputation in a community6–10,
by structural forces in social networks that promote cooperative
clusters11–15, by inter-group competition16, or by kinship17,18.Whenwe
observe individuals cooperating in the real world, the question is not
whether it is possible to account for it, but which of many possible
underlying explanations are leading them to engage in this common
behavior.
Understanding the origins of cooperative behavior is important if
we wish to enable prosocial environments to flourish. While it can
often arise quite easily, cooperation is also lost easily due to invasion
by cheaters and free-riders. Reducing the impact of such bad actors on
the overall level of cooperation in a population requires us to
understand the underlying motivations of those who are willing to
cooperate. Furthermore, over long timescales, the motivations for
cooperation can themselves shift and evolve depending on the envir-
onment and on the level of cognitive complexity of the individual
making the decision to cooperate19.
Unlike prior studies that focus on the evolution of behaviors,
where the behavior yielding a higher payoff is more likely to be
adopted, this paper considers the evolution of behavioral motivations
that guide the choices of behaviors. We focus on two types of moti-
vation that can underpin cooperation, depending on whether an
individual increases or decreases their willingness to cooperate with
their own level of wealth. On the one hand, individuals may view
cooperative acts as philanthropic or even altruistic, a cost that they pay
to help others when all their needs are metand they have resources to
spare. On the other hand, as studies of the evolution of cooperation
show, cooperation can also serve as a mechanism for increasing both
individual and population fitness, i.e., cooperation can help individuals
meet their needs in the first place. We study the evolution of motiva-
tions behind cooperative behavior among individuals who can assess
Received: 19 March 2024
Accepted: 17 April 2025
Check for updates
1
School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China.
2
Key Laboratory of System Control and Information Pro-
cessing, Ministry of Education of China, Shanghai, China.
3
Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai, China.
4
Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington, Bloomington, IN, USA. e-mail: qisu@sjtu.edu.cn;
stewalex@iu.edu
Nature Communications | (2025) 16:4023 1
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needs, anticipate outcomes, and adapt their behavior accordingly. We
model motivation as lying on a continuum, with cooperation as an
expression of “self-transcendence”, which is more likely to occur after
basic needs have been met, at one extreme, and cooperation moti-
vatedpurelybyadesiretomeetone’s basic needs at the other.
There is evidence for both “philanthropically motivated”and
“aspirationally motivated”cooperation in humans. Philanthropically
motivated cooperation is most easily seen in the behavior of wealthy
philanthropists who invest in public goods such as public health or
education20. In contrast, aspirationally motivated cooperation may be
reflected in the tendency for individuals whose incomes are relatively
low to behave with greater charity and generosity (as a proportion of
their wealth)21–25 and in the “affluenza”phenomenon in which, as
people gain more wealth, they also tend to become less empathetic
and less likely to help others21–23. There has been a long-standing
debate about the association between socioeconomic status and
prosociality in human society. Some favor a positive association26,
while others highlight a negative association25.Giventheconflicting
evidence and the observed heterogeneity of human behavior25–28,we
have developed a modelling framework that allows for both types of
behavioral motivation. Our goal is to elucidate the conditions under
which different behavioral motivations emerge, which may then be
tested empirically.
We construct a model of cooperative motivations in which we
characterize the short-term dynamics of cooperation resulting from
individual interactions between neighbors on a social network. We
then characterize the long-term co-evolution of cooperative behavior
and the motivational strategies that underpin it, for both weak and
strong selection. Our results offer key insights into the evolution of
behavioral motivations for cooperation. First, we show that when
motivations are fixed, cooperative behavior emerges among two dia-
metrically opposed types of motivation: undemanding philanthropists
(i.e., individuals who use philanthropic motivations and easily meet
thresholds of need) and demanding aspirationalists (i.e., individuals
who use aspirational motivations and hardly meet thresholds of need).
Second, we show that breaking down one big need into many smaller
needs can facilitate greater cooperation. Third, we show that when
individuals’needs and motivations are allowed to co-evolve, there is a
critical benefit-to-cost ratio for cooperation, above which behavioral
motivations assuredly evolve towards either undemanding philan-
thropists or demanding aspirationalists and, as a result, stable coop-
eration. Finally, we provide analytical results for the critical benefit-to-
cost ratio and show how it depends on the structure of the social
network.
Our results correspond with the co-existence of both philan-
thropically motivated and aspirationally motivated forms of coopera-
tion observed in society. We show that, remarkably, the conditions for
both to evolve are the same, and depend on factors such as the costs
and benefits of cooperation and the structure of the underlying social
network. However, our results also suggest that when motivations are
not fixed, cooperation requires philanthropic motivations among
communities of people whose income are relatively high, and aspira-
tional motivations among communities of people whose income are
relative low.
Results
Model
We begin by constructing a framework for modeling the evolution of
cooperative behavior and motivations in a finite population of indivi-
duals interacting via a social network. We consider a structured
population consisting of Nindividuals, denoted by N=f1, 2,  ,Ng.
The population structure is represented by a network consisting of N
nodes, with each individual occupying a node and edge weight deno-
ted by fwijgi,j2N. Here, variations in edge weights account for the fact
that some interactions occur more frequently or last longer than
others, resulting in different payoffs even when the actions of the
participants are fixed, which captures the heterogeneity in interactions
beyond just the number of connections. The total degree for node i
is wi=Pj2Nwij.
Socialinteractions occur between pairs of individuals and take the
form of a donation game (DG), in which each individual in the popu-
lation decides to either cooperate (C) or defect (D). If an individual
chooses to cooperate, they pay a cost cto generate a benefitbto their
neighbor. If they choose to defect, they pay no cost and deliver no
benefit to their neighbor. A “round”of the game consists of all pairwise
interactions between all members of the population. We assume that
at the start of the game, every individual cooperates with probability
0.5. Let s
i
denote individual i’saction,wheres
i
= 1 represents coop-
eration and s
i
= 0 defection. The payoff to individual iat round tis then
uiðtÞ=X
j2N
wij
wi
csi+bsj

,ð1Þ
i.e., the edge-weighted average of all their social interactions with
other members of the population.
We initially assume that each individual has their own fixed
behavioral motivation, which is used to guide them to update their
action (cooperate or defect) after each round. In particular, after each
round of play, one individual is selected to update their action
according to this behavioral motivation. We later show that our results
remain robust if we instead assume that multiple individuals simulta-
neously update. In qualitative terms, behavioral motivations are
assumed to be either aspirational –meaning that the probability of
cooperation is greater when an individual’s payoff is lower (i.e., their
needs are not met) –or philanthropic –meaning thatthe probability of
cooperation is greater when an individual’s payoff is higher (i.e., their
needs are met). In order to capture this we define two variables, the
need threshold αand motivation intensity λ(where λ> 0 corresponds
to philanthropic motivation while λ< 0 corresponds to aspirational
motivation –see Fig. 1). Under this model an individual selected to
update their behavior, who obtained payoff uin the last round,
chooses to cooperate next round with the probability
gðuÞ=1
1+ exp½λðuαÞ ð2Þ
and defect with 1 −g(u). In general, each individual in the population
may have a different b ehavioral motivation, i.e., they may differ in both
their value of αand λ.
Figure 1illustrates the dynamics of an evolving system with two
behavioral motivations, namely motivation Awith α
A
and λ
A
,and
motivation Bwith α
B
and λ
B
.u−αmeasures how much the payoff
obtained by an individual exceeds their need threshold. When the
obtained payoff uequals the need threshold α, the individual chooses
to cooperate with probability 1/2.
Figure 2illustrates the four qualitatively different behavioral
motivations under our model, and their relationship to the need
threshold αand motivation intensity λ. A large value of the need
threshold αindicates a large payoff is requiredfor an individual’sneeds
to be met. In the donation game, if two individuals randomly choose
whether to cooperate or defect, their expected payoff is (b−c)/2.
Therefore, we refer to a need greater than (b−c)/2 as ‘demanding’,and
a need less than (b−c)/2 as ‘undemanding’. The sign of motivation
intensity λdetermines whether the individual’s motivation type is
aspirational or philanthropic. When λis positive, g(u)(i.e.,theprob-
ability of cooperation) monotonically increases with payoff u.When
the payoff exceeds the need threshold, i.e., u>α, the individual is more
likely to cooperate than defect, i.e., g(u) > 1/2. Such individuals are
motivated to help others when their needs are met. An individual is
thus an ‘undemanding philanthropist’if λ> 0 and their need threshold
Article https://doi.org/10.1038/s41467-025-59366-1
Nature Communications | (2025) 16:4023 2
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is low, and a ‘demanding philanthropist’if their need threshold is high.
When λis negative, g(u) monotonically decreases with payoff u.When
the payoff exceeds the need threshold, i.e., u>α, the individual is less
likely to cooperate than defect, i.e., g(u) < 1/2. Such individuals are
motivated to help others when their needs are not met. An individual is
thus an ‘undemanding aspirationalist’if λ< 0 and their need threshold
is low, and a ‘demanding aspirationalist’if their need threshold is high.
The absolute value of motivation intensity, i.e., ∣λ∣,measureshow
strictly the individual follows their behavioral motivation. For example,
for a philanthropist, a large value of ∣λ∣indicates that the individual will
immediately choose to cooperate once their need is met, but w ill never
cooperate before that.
In order to model the evolution of behavioral motivations, we
allow the process of action updating to repeat for Trounds, so that
each individual iobtains an average payoff given by

ui=ð1=TÞPT
t=1 uiðtÞ:We then choose a random individual ito update
their behavioral motivation based on a death-birth updating rule in
which ireplaces their current behavioral motivation with the motiva-
tion used by their neighbor j’s with probability e
ij
where
eij =wij

uj
P‘2Nwi‘

u‘
:ð3Þ
After each behavioral motivation update, the process of action
updating proceeds for another Trounds, and the process repeats.
In the main body of the text, we focus on the parameter region of
weak motivational intensity, specifically when ∣λ∣≪1, and later we
demonstrate the qualitative consistency of results for strong motiva-
tional intensity. Firstly, we examine fixed behavioral motivations and
analyze the cooperation abundance under the condition that each
individual’s behavioral motivation remains constant throughout the
evolutionary process. Next, we move on to the scenario where indivi-
duals’behavioral motivations evolve and investigate the survival of
behavioral motivations. Lastly, we explore several extensions and
generalizations of behavioral motivations.
Evolutionary dynamics of cooperation with fixed behavioral
motivation
Let α
i
and λ
i
denote individual i’s need threshold and motivation
intensity. When individuals’behavioral motivations remain unchanged
throughout the evolutionary process, after a sufficiently large number
of interactions and action updating, the abundance of cooperative
behaviors in the population, i.e., xC=ð1=NÞPi2Nsi,tendstobesta-
tionary, given by (see Methods and Supplementary Note 3)
xC=1
2+1
8NbcðÞ
X
i2N
λi2X
i2N
λiαi
"#
:ð4Þ
Intuitively, from an individual perspective, an undemanding philan-
thropic behavioral motivation is moreconducive to cooperation, while
a demanding philanthropic motivation can lead to the breakdown of
cooperation. This is because individuals with lower needs tend to
cooperate more frequently. In other words, it is easy to see that
increasing the need threshold inhibits cooperation. However, from a
global perspective, particularly in structured populations, an indivi-
dual’s actions depend on the comparison between their need thresh-
old and the payoff obtained from all interactions with neighbors. The
population structure often leads to a complex coupling of individuals’
behavioral motivations and cooperative actions, making the
D
AA
A
C
C
CD
B
B
B
C
D
AA
C
CC
D
B
B
B
C
?
D
AA
A
C
C
CD
B
B
B
?
?
5
2
6
1
3
Player 4
Interaction in round tAction updating
Average payoff
over T rounds
Behavioral motivation
updating
abc
f
Behavioral
motivation
Action
Cooperation Defection
CD
A
B
Payoff,
Need,
Intensity,
Interaction in round t+1
Interaction in round 1
d
g
Payoff,
Need,
Intensity,
0
1
Cooperating probability
Payoff,
Cooperating probability
Payoff,
0
1
D
AA
A
C
C
C
D
D
B
B
B
D
AA
A
C
CC
D
B
B
B
C
B
C
B
B
D
AA
C
CC
D
B
B
B
e
Fig. 1 | Evolutionary dynamics of behavioral motivation. a The population
structure is described by a network, and each individual (node) in the population
has a behavioral motivation A or B (circle) and adopts action cooperation (C) or
defection (D) (square). The figure illustrates two examples of behavioral motiva-
tions: one with need α
A
and motivation intensity λ
A
, and the other with need α
B
and
motivation intensity λ
B
. With the shown behavioral motivation A, the individual is
more likely to cooperate when his payoff exceeds the need, i.e., u>α
A
.Conversely,
with the shown behavioral motivation B, the individual tends to defect when he
fulfills his needs, i.e., u>α
B
.bIn every round t, every individual adoptscooperation
or defection to play games with each neighbor and obtain an edge-weighted
averagepayoff u
i
(t). Herewe consider a network where all edge weights are set to 1.
cAn individual (markedby “?”) is selected uniformlyat random to update his action
based on hisown behavioral motivation, namely, to cooperate next round with the
cooperating probability and to defect otherwise. dGame playing and action
updates repeat in the next round, t+1.eAfter Trounds of interactions, individuals
obtain an average payoff, 
ui=PT
t=1 uiðtÞ=T.fAn individual (marked by “?”)is
selected uniformly at random to update his behavioral motivation, and all neigh-
boring individuals, indicated by black circles, compete to be imitated by the focal
individual, with probability proportional to their average payoff. gAfter the
behavioral motivation updating, game playing, and action updates restart from
round 1.
Article https://doi.org/10.1038/s41467-025-59366-1
Nature Communications | (2025) 16:4023 3
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prediction of theglobal cooperation level more challenging than at the
individual level.
This effect can be even more unpredictable when individuals have
different need thresholds. For example, consider two cases within the
same heterogeneous structured population. In the first case, indivi-
duals occupying the largest 50% of highly connected nodes have a
higher threshold, α+ϵ, while those in the least 50% have a lower
threshold, α−ϵ. In the second case, the thresholds are reversed: indi-
viduals in the largest 50% of highly connected nodes have a lower
threshold, α−ϵ, and those in the least 50% have a higher threshold,
α+ϵ. Although the average threshold is identical in both cases,it is not
intuitive which case will lead to higher cooperation levels. The varia-
tion in individuals’motivation intensity further complicates the
outcome.
In Fig. 3e, we depict the cooperation abundances in a population
of philanthropists and aspirationalists, where individuals are dis-
tributed in a structured population and differ in their need thresholds.
We find that for the homogeneous setup of motivation intensity, the
average need threshold of the whole population, i.e., α=ð1=NÞPi2Nαi,
determines the cooperation abundance. Therefore, in a population of
philanthropists, an increase in the average need threshold leads to a
decrease in cooperation abundance. Conversely, in a population of
aspirationalists, an increase in the average need threshold leads to an
increase in cooperation abundance. It’s noteworthy that philan-
thropists are not inherently more prosocial than aspirationalists when
it comes to helping others. Generally, a population of demanding
aspirationalists sustains a higher cooperation abundance than a
population of demanding philanthropists. This is because demanding
philanthropists tend to defect more often due to their high need to be
satisfied, while demanding aspirationalists tend to cooperate more
frequently. These results are consistent across all six types of networks
analyzed. Put simply, altering the average need threshold (α)produces
an overall outcome that aligns with the expected results based on the
model’sdefinition.
We also investigate multi-action donation games that account for
situations where an individual can break down their willingness to
cooperateintomultiplestepsor“levels”such that they only cooperate
at higher levels if they have already successfully cooperated with
others at lower levels. One way of understanding this type of multi-
level cooperation is to think about each level as a “need”. An individual
may choose to help others only if they have both food and shelter,
corresponding to the two-action donation game discussed above. With
multiple levels of needs, the individual may choose to provide some
help if their food need is satisfied, and give more help if both food and
shelter needs are met, resulting in a three-action game with two
thresholds between them. We formalize multi-action linear donation
games as follows: Let Ldenote the number of actions, and each action
ℓ∈{1, 2, …,L} involves paying a cost of c(ℓ−1)/(L−1) to generate a
benefitofb(ℓ−1)/(L−1) (see Fig. 3b for an example of the three-action
linear donation game). Action 1 corresponds to defection, and action L
corresponds to cooperation in the classic donation game. The
threshold between actions ℓand ℓ+ 1 is set to be ℓα/(L−1), and the
threshold to action Lis α. We also select the switching function
appropriately to obtain the classic two-action donation game as a
specific case (see details in Methods). Let s
i
∈{1, 2, ⋯,L}denote
individual i’s action. The cooperation abundance for such multi-action
donation games is xC=ð1=NÞPi2Nðsi1Þ=ðL1Þ.
Once again, we find that undemanding philanthropic and
demanding aspirational behavioral motivations promote cooperation
(see Eq. (16) in Methods for the analytical cooperation abundance and
Fig.3f for simulation results). In addition to the multi-action linear
donation games, wealso study multi-action nonlinear donation games,
where donating a cost of c(ℓ−1)/(L−1) yields a benefitofb(1 −ωℓ−1)/
(1 −ωL−1), nonlinearly related to the cost. Above ωis the benefit factor,
where ω> 1 corresponds to synergistic donation games and ω<1 cor-
responds to discounting donation games (see Eq. (18)andFig.3cd,
respectively). The results remain robust.
Multi-action donation games provide a better model than two-
action games to describe complex needs. However, a natural question
arises regarding how increasing the number of action options affects
the global cooperation abundance. Our analysis of Eq. (16)demon-
strates that for philanthropists with low needs, i.e., α<(b−c)/8, an
increase in the number of actions Lresults in a decrease in the coop-
eration abundancex
C
(see Fig. 4a). Conversely, forphilanthropists with
high needs, i.e., α>(b−c)/2, x
C
monotonically increases with increas-
ing L. An intermediate need level yields maximal cooperation abun-
dance at L*=1=ð1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2α=ðbcÞ
pÞ. Intuitively, an increase in the
number of actions provides individuals with more donation options,
such as partially cooperative behavior in addition to the options of
fully cooperative and defective behavior in a two-action donation
game. For high need thresholds, individuals have the option to engage
in partially cooperative behavior, which avoids the high cost of full
cooperation and maintains cooperation at a certain level. In particular,
Fig. 4a shows that in a population of demanding philanthropists, i.e.,
α>(b−c)/2, even when cooperation is disfavored for two-action
donation games, i.e., x
C
< 1/2, an increase in the number of actions can
make cooperation more favorable, i.e., x
C
> 1/2. Conversely, when the
need threshold is low, individuals can easily fulfill their needs and opt
for cooperation in two-action games. Introducing more actions, such
as partially cooperative behavior, encourages a substantial fraction of
individuals to engage in partially cooperative behavior instead of full
cooperation, thereby reducing the overall cooperation abundance. For
intermediate need thresholds, an intermediate number of actions
ensures the possibility of partially cooperative behavior while avoiding
individuals getting trapped in the low cooperative level.
Cooperating probability,
Payoff,
0
1
0
1
0
1
0
1
Need threshold,
Motivation intensity,
0
Undemanding
philanthropist
Demanding
philanthropist
Undemanding
aspirationalist
Demanding
aspirationalist
PhilanthropicAspirational
Undemanding Demanding
Fig. 2 | Four representative behavioral motivations. A behavioral motivation is
described by a pair of variables,namely need threshold (α) and motivation intensity
(λ), corresponding to a point in the (α,λ) plane. In a donation game, if both parti-
cipants choose cooperation (or defection) with probability 0.5, each player’s
expected payoff is (b−c)/2. If a player’s need thresholdis greater than(b−c)/2, th ey
are referred to as ‘demanding’, whereas they are referred to as ‘undemanding’if
their need threshold is less than (b−c)/2. If a player’s motivation intensity λhas a
positive value, this indicates that they are more likely to cooperate if their need is
met, which we call ‘philanthropic’behavioral motivation. If λis negative, they are
more likely to cooperate if their need isnot met, which we refer to as ‘aspirational’
behavioral motivation. As such, there are four qualitatively different types of
players: undemanding philanthropist, demanding philanthropist, undemanding
aspirationalist, and demanding aspirationalist.
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Figure 4b displays the global cooperation abundance x
C
as a
function of the benefitfactorωand the number of actions L. Generally,
for ω< 1, an increase in the number of actions is beneficial to coop-
eration, leading to a cooperation abundance above 1/2. One possible
explanation for the cooperation-promoting effect is that for ω< 1, both
the cost and the need threshold increase linearly with the number of
actions, while the benefit generatedby an action is concave. As aresult,
a small additional cost yields a disproportionately large benefit, which
exceeds the increase in the need threshold. Therefore, the ratio of
benefit to need threshold is greatly higher for actions with low cost.
The gradual increase in the number of actions encourages players to
become more cooperative. Conversely, for ω> 1 (a convex curve), the
opposite outcome occurs. Increasing the number of actions leads to a
decrease in the cooperation abundance x
C
. This is because the benefit
generated by actions with low cost is insufficient to offset the cost of
cooperative actions and the need threshold. As the number of actions
increases, the ratio of benefit to need threshold for actions with low
cost decreases, making it harder to adopt cooperative behavior. These
intuitions also support the observation that the global cooperation
abundance decreases as the benefitfactorωincreases. Besides, we
observe similar non-monotonicity in a population of aspirationalists
(see Supplementary Fig. 1).
Evolutionary dynamics of behavioral motivation
In this section, we investigate the evolution of behavioral motiva-
tions. Suppose a population consisting of a single individual using
behavioral motivation A and N−1 individuals using B. When there is
no exploration of new motivations in the motivation updating
stage, the population is expected to eventually reach an absorbing
state where either all individuals use behavioral motivation A or use
B. Let ρ
A
denote the fixation probability that an individual using
behavioral motivation A, when initially placed in a random node,
eventually causes a population of individuals using behavioral
motivation B to switch to using A. For motivation intensity λ=0,
every individual chooses cooperation and defection equitably (see
Eq. (2)), resulting in fixation probability 1/N. Selection favors the
evolution of behavioral motivation A if it is more likely to fixthana
neutral mutant, i.e., ρ
A
>1/N. Under weak motivation intensity, i.e.,
∣λ
A
∣≪1 and ∣λ
B
∣≪1, we have the condition for behavioral motivation
A to be favored over B, given by (see Methods and Supplementary
Cost of action
0c
no
i
tcafotifeneB
0
b
Cost of action
0c
0
b
Cost of action
0c
0
b
Cost of action
0c
0
b
c/2 c/2
2b/5
b/2
c/2
2b/3
Two-action DG Three-action linear DG Three-action DG with Three-action DG with
abcd
efgh
RR ER Analytical
Aspirationalist
SW
Philanthropist Positive
Negative
Positive
Negative
BA-SF GKK-SF HK-SF
Fig. 3 | Undemanding philanthropic and demanding aspirational behavioral
motivatio ns promote coop eration. We considerfour types of games,namely two-
actiondonation games (a,e), three-action linear donation games (b,f),three-action
nonlinear donation games with benefit factor ω=1.5 (c,g), and with benefit factor
ω=0.5 (d,h). Dots in (a–d) illustrate the optional actions in the game, with the
action cost shown in the x-axis and thegenerated benefitinthey-axis. e–hpresents
the abundance of cooperation as the average need threshold 
αvaries from unde-
manding to demanding levels. In each game, we investigate both philanthropic
(blue, λ= 0.01) and aspirational (red, λ=−0.01) behavioral motivations on six
classes of networks (random regular networks (RR), Erdös-Rényi networks (ER)57,
Watts-Strogatz small-world networks (SW)58 with rewiring probability 0.1, Barabási-
Albert scale-free networks (BA-SF)59, Goh-Kahng-Kim scale-free networks (GKK-
SF)60 with exponent 2.5, and Holme-Kim scale-free networks (HK-SF)61 with triad
formation probability 0.1). Dots in (e–h) indicate the results of Monte Carlo
simulations, and lines are analytical results. The results show that in a population of
undemanding philanthropic and demanding aspirational behavioral motivations,
cooperation is favored, consistent in all population structures. Each dot in (e–h)is
the result averagedover 5000 simulations, andeach simulationlasts for 105rounds.
We consider two initial configurations: individuals occupying the largest 50% of
highly connected nodes have a higher threshold, α+ϵ, while those in the least 50%
have a lower threshold, α−ϵ(positive correlation, solid dots); individuals in the
largest 50% of highly connected nodes have a lower threshold, α−ϵ, and those in
the least 50% have a higher threshold, α+ϵ(negative correlation, open dots).
Parameter values: network size N= 100, average degree d= 6, benefitb=6,cost
c=1, andϵ=0.5.
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Note 3)
λAbc2αA

λBbc2αB

cη2+bðη3η1Þ

>0:ð5Þ
Above, η
n
is a quantity depending on the population structure13,15,29
(see “Methods”).
We consider two philanthropic behavioral motivations with the
same intensity λ
A
=λ
B
> 0 but different need thresholds α
A
>α
B
.
Rewriting Eq. (5) yields αBαA

cη2+bðη3η1Þ

> 0, indicating
that selection favors philanthropists with high needs when the benefit-
to-cost ratio is small. However, when the benefit-to-cost ratio b/c
exceeds a critical value η
2
/(η
3
−η
1
), denoted as (b/c)*, philanthropists
with low needs are favored. This finding suggests that in a population
full of demanding philanthropists, where individuals’needs are hard to
meet and the global cooperation abundance is low initially, an unde-
manding philanthropist can promote the transition to a cooperative
population as long as the cooperative act is sufficiently profitable per
unit of cost. We confirm the theoretical predictions in both homo-
geneousandheterogeneousnetworksinFig.5. In particular, the cri-
tical benefit-to-cost ratio (b/c)*is determined by the population
structure, which has two important implications. Firstly, in the well-
mixed setting, (b/c)*=−(N−1), indicating that undemanding philan-
thropists are disfavored for any large benefit-to-cost ratio. However,
placing individuals in the proper spatial structure, such as the lattice,
yields (b/c)*=4(N−2)/(N−8), enabling the evolution of undemanding
philanthropists. Secondly, in structured populations, modifying the
34567891011
0.91
0.94
0.97
1.00
1.03
1.06
1.09
10-2
a
4567891011
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04 10-2
b
(1,0.01) - (3,0.01)
Simulation
Analytical
(2,0.03) - (2,0.01)
Random regular network BA scale-free network
Fig. 5 | Selection favors undemanding philanthropists over demanding phi-
lanthropists when thebenefit-to-cost ratio exceedsa critical value. Presented is
the fixation probability of an individual using behavioral motivation A, i.e., (α
A
,λ
A
),
in the population of individuals using behavioral motivation B, i.e., (α
B
,λ
B
), as a
function of benefitbin the two-action donation game, with cost c=1. Weconsider
random regular networks (a) and BA scale-free networks (b). Selection favors
behavioral motivation A over B if fixation probability ρ
A
exceeds the horizontal line,
i.e.,ρ
A
>1/N. Squares indicate fixationprobabilitiesby Monte Carlo simulations, and
solid lines are analytical results. Red lines and squares represent the fixation
probability of philanthropic motivation A, i.e., (1,0.01), in a population of B, i.e.,
(3,0.01), which shows that selection favors undemanding over demanding indivi-
duals as long as the benefit-to-cost ratio exceeds the critical ratio, i.e., b/c>(b/c)*.
Nonetheless, for motivations with α
A
=α
B
, the evolution of the motivation intensity
is non-monotonous with benefitb--- both the small and large b/cfavor a strong
motivati on, while the interme diate b/cfavors weak motivation, as blue lines and
dots show (the evolution of (2,0.03) in a population of (2,0.01)). The fixation
probability of beneficial motivation A, ρ
A
, is determined by the fractions of simu-
lations where the b eneficial motivation A reached fixation out of 2 × 107genera-
tions. Parameter values: population size N= 100 and average degree d=6.
ab
Fig. 4 | Breaking down a high level of need into small pieces can make coop-
eration favorable. a Abundance of cooperation x
C
as a function of the need
threshold αand the number of available actions Lin the multi-action linear dona-
tion game. In the red zone, the cooperation abundance x
C
decreases monotonously
with L,andalargeLcan make cooperation less favorable. In the blue zone, the
increasing Lmonotonously increases the cooperation abundance x
C
.Thesolid
dashed line marks the level of x
C
= 1/2. Thus, for behavioral motivations with a high
need threshold α> 1/2, increasing the number of available actions can make
cooperation favorable, i.e., x
C
> 1/2. bAbundance of cooperation x
C
as a functionof
the benefit factor ωand the number of available actions Lin the multi-action
nonlinear donation game. Generally, the cooperation abundance increases with L
for ω< 1 and decreaseswith Lfor ω> 1. Similarly, for ω< 1, increasing the number of
available actions can make cooperation favorable, i.e., x
C
> 1/2. Parameter values:
b=6, c=1, λ=0.01, andα=3 (b).
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population structure could be a potential solution to alter the
evolutionary outcome of behavioral motivations, such as transitioning
from heterogeneous networks (Fig. 5b) to homogeneous net-
works (Fig. 5a).
We now consider two behavioral motivations with the same need
threshold α
A
=α
B
=α, but different motivation intensities λ
A
>λ
B
.
Rewriting Eq. (5) gives the condition for the evolution of behavioral
motivation A, i.e., λAλB

bc2αðÞcη2+bðη3η1Þ

>0. Fig-
ure 5shows that the evolutionary fate of behavioral motivation A is
non-monotonous with the benefit-to-cost ratio b/c: both a small and
large b/csupport motivation A, but an intermediate b/cmakes moti-
vation A disfavored. To gain insight into this, we consider the example
of λ
A
>0>λ
B
. The evolution of behavioral motivation A depends on
two aspects: (i) whether or not behavioral motivation A is cooperation-
promoting (i.e., whether the cooperation abundance in a population of
individuals using A is higher than the defection abundance), which is
captured by x
C
>1/2inEq. (4), as determined by λ
A
(b−c−2α); and (ii)
whether or not the population structure supports cooperation and
accordingly cooperation-promoting motivations, as captured by
−cη
2
+b(η
3
−η
1
). If the benefit-to-cost ratio is small enough such that
b−c−2α
A
< 0, motivation A leads to x
C
< 1/2 and is thus defection-
promoting. Furthermore, if the small benefit-to-cost ratio also satisfies
−cη
2
+b(η
3
−η
1
) < 0, the population structure favors defection-
promoting motivation, resulting in the evolution of motivation A. On
the other hand, if the benefit-to-cost ratio is large enough such that
λ
A
(b−c−2α)>0 and −cη
2
+b(η
3
−η
1
)>0, motivation A is
cooperation-promoting (i.e., x
C
> 1/2), and the population structure
favors cooperation-promoting motivation, resulting in the evolution
of motivation A. However, if the population structure and the moti-
vation intensity are not aligned, motivation A can either promote
cooperation while the population structure favors defection-
promoting motivation or promote defection while the population
structure favors cooperation-promoting motivation. In both cases,
motivation A will shrink.
Fig. 6 | Evolution of behavioral motivation. a The theoretical prediction of the
evolutionary direction of behavioral motivations for (b/c)<(b/c)*. The evolution
resultsin individualstransitioningaway from undemanding philanthropists (region
II) and demanding aspirationalists (region IV), and towards demanding philan-
thropists (region I) and undemanding aspirationalists (region III), as indicated by
the arrows. This transition leads to a decrease in the abundance ofcooperation x
C
.
The blue (respectively red) regions represent the behavioral motivation that con-
tributes to a larger abundance of cooperation than defection (respectively defec-
tion than cooperation). bThe Monte Carlo simulations show the evolutionary
trajectories of behavioral motivations for (b/c)<(b/c)*using 300 simulations in
random regular networks. Each simulation starts from a monomorphic population
with behavioral motivations (α,λ) in one of (0.75,0.05), (0.25,0.05), (0.25,−0.05),
and (0.75,−0.05), represented by open black dots, and undergoes 5 × 107motiva-
tion updating steps, where interactions and action updates repeat for T=100
rounds before each motivation updating. During each behavioral motivation
update,with a probabilityof 0.01, the imitated behavioral motivation is subjectto a
random fluctuation in need α(randomly sampled from the range [−0.1,0.1]) and
motivati on intensi ty λ(randomly sampled from the range [−0.01,0.01]). Each thin
red line represents a resulting trajectory (i.e., the average behavioral motivation of
the population), and each open red dot represents an ending behavioral motiva-
tion. The thick red line represents the linear regression of all final behavioral
motivations, which is highly consistent with the evolutionary direction predicted
analytically in (a). cThe cooperation abundance throughout the evolutionary
process (b/c)<(b/c)*by simulations. The highlighted line represents the average
cooperation abundance over the 300 simulations. dThe theoretical prediction of
the evolutionary direction of behavior al motiva tions fo r (b/c)>(b/c)*shows that
individuals evolve towards undemanding philanthropists (region II) and demand-
ing aspirationalists (region IV). eThe evolutionary trajectories of behavioral moti-
vations for (b/c)>(b/c)*by simulations. fThe cooperation abundance throughout
the evolutionary process for (b/c)>(b/c)*by simulations. Parameter values: N= 100,
d=6, whichgives (b/c)*≈6.7, b=2,c=1 (bc)andc=0.2(ef).
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Furthermore, we consider the exploration of new motivation in
the motivation updating stage and investigate the evolution of beha-
vioral motivations in the entire (α,λ) space, ensuring that the system
never becomes trapped in an absorbing state. Let x
C
(A)(respectively
x
C
(B)) denote the global cooperation abundance when all individuals
use behavioral motivation A (respectively, motivation B). By applying
Eq. (4)toEq.(5), we obtain the condition favoring behavioral moti-
vation A over B,
xCðAÞxCðBÞ

cη2+bðη3η1Þ

>0:ð6Þ
Thus, when the benefit-to-cost ratio falls below a critical value, i.e.,
b/c<(b/c)*, the evolution leads to the adoption of cooperation-
inhibiting behavioral motivations, resulting in a continuously decreas-
ing cooperation abundance. As shown in Fig. 6a, even if initially all
individuals are undemanding philanthropists (region II) or demanding
aspirationalists (region IV), and the population exhibits a high
abundance of cooperation, i.e., x
C
> 1/2, as long as the benefit-to-cost
ratio is below the critical value, all individuals gradually transition to
being either demanding philanthropists (region I) or undemanding
aspirationalists (region III). Ouranalytical predictions are supported by
extensive Monte Carlo simulations, which include the evolutionary
direction of behavioral motivations (see Fig. 6b) and the collapsing
cooperation (see Fig. 6c). It is important to note that we investigated
the largest possible motivation range by considering an adequate
number of motivation updating steps and by not imposing any limit on
the need threshold or motivation intensity. As a result, the need
threshold exceeds the feasible range, namely [−c,b], and the
evolutionary trajectories subsequently oscillate within the domain of
demanding philanthropists and undemanding aspirationalists (as
shown in Fig. 6b).
On the contrary, when the benefit-to-cost ratioexceeds the critical
value, i.e., b/c>(b/c)*, even if initially all individuals are demanding
philanthropists or undemanding aspirationalists, and the population
presents more defection than cooperation, i.e., x
C
< 1/2, the evolution
of behavioral motivations gradually leads all individuals to become
undemanding philanthropists or demanding aspirationalists (see
Fig. 6d). Extensive simulations confirm the analytical prediction of
motivation evolution (see Fig. 6e) and the continuous increase in the
abundance of cooperation (see Fig. 6f).
Extensions
Finally, we consider various model extensions and generalize our
conclusions to different scenarios, including (i) any game with an
arbitrary number of actions and general payoff structures, which
includes two- or three-action donation games as a specificcase(see
Supplementary Note 2); (ii) any need threshold setting between mul-
tiple actions and general action switching functions, beyond the linear
threshold setting and sigmoid functions as in Eq. (2)(seeSupple-
mentary Note 2); (iii) state-dependent action updating, where the
probability of cooperating next round depends not only on the
obtained payoff but also on the current action, as in the case of ‘hys-
teresis’(see Supplementary Note 3); (iv) individualized need thresh-
olds and action updating functions for each individual (see
Supplementary Note 3). In all these extensions, we demonstrate that
the population structure has no impact on the cooperation abundance
for a fixed behavioral motivation, but plays a critical role in influencing
the evolutionary direction when behavioral motivation evolves. So far,
our analysis has relied on the assumption of weak motivational
intensity, i.e., ∣λ∣≪1. We also demonstrate that all our findings are
qualitatively consistent when the motivational intensity increases up
to 1 (see Supplementary Fig. 2 for the robustness of the cooperation
abundance against the population structure, Supplementary Figs. 3
and 4 for the evolutionary trajectories of behavioral motivations, and
Supplementary Fig. 5 and Supplementary Note 4 for theoretical results
based on adaptive dynamics analysis30–32) and results remain robust
when multiple individuals simultaneously update their actions (see
Supplementary Fig. 6).
Discussion
Most studies of cooperation focus on the idea that the strategies
individuals use in deciding whether to cooperate are the product of a
process of natural selection or learning that seeks to maximize the
payoff they (or their lineage) receive from cooperative acts. In reality,
human beings face many opportunities to engage in minor acts of
cooperation every day, and the decision whether to help another
person is typically guided by a few simple heuristics, rather than a
carefully optimized behavioral strategy. And so we have asked the
natural question: what happens if natural selection acts at the level of
the heuristics people use when deciding to cooperate? To answer this,
we characterize individual decisions to cooperate in terms of an
internal behavioral motivation.
Our results show that the underlying behavioral motivations for
cooperation have a large impact on how muchcooperation occurs. We
show that undemanding philanthropists and demanding aspir-
ationalists are more likely to sustain a high level of cooperation,
whereas demanding philanthropists and undemanding aspirationalists
are more likely to defect, regardless of population structure. Inter-
estingly, we also discover that when choices are not limited to binary
options —fully cooperative when the entire need is met, and fully
defective when it is not —and needs are divided into several smaller
parts, a group of demanding philanthropists tends to use cooperation
rather than defection. For instance, if an individual has a single
demanding need for food and shelter, this tends to lead to a low
cooperation rate. However, if the need is divided into food and shelter,
the individual can choose to be partly cooperative once the food need
is met and then fully cooperative after both food and shelter needs are
met. This results in more cooperation within the population. On the
other hand, if the need is already undemanding and easy to meet,
breaking it down into multiple smaller needs may decrease coopera-
tion. This is because some individuals may remain partly cooperative,
even though it is easy to be fully cooperative in a two-action game.
Akeyfinding of our analysis is that need intensity tends to evolve
to either be large and positive or large and negative (Fig. 6), corre-
sponding to a motivation that comprises a sharp, switch-like behavior
in whichcooperation shifts from occurring at low rates to occurring at
high rates once a need threshold is reached. From an empirical view-
point, this kind of behavior corresponds to individuals using an
internal reference point to decide whether to cooperate. This kind of
sharp response to an internal reference point has frequently been used
to model motivations in both human and animal behavioral ecology.
Indeed, this pattern serves asthe foundation for numerous theoretical
studies on aspiration-based action updating and cooperation33–39.Our
work shows how such reference points can arise via evolution.
We also note a number of other key differences between our study
and previous work. Prior studies assume that all individuals are self-
interest motivated and only have two actions to choose from —one
keeps using the current action if the aspiration is met, and otherwise
switches to the other action. This limits the interactions between
individuals. Secondly, these studies still follow the idea of comparing
actions, without mentioning behavioral motivations on action updat-
ing at all. Lastly, these studies do not consider the evolution of indi-
viduals’behavioral motivations or action updating rules. As a result,
they fail to reveal the important effects of population structure. In
contrast, our model endows each individual with an individualized
behavioral motivation, which guides their decision-making among an
arbitrary number of actions. Our model can recover the prior studies
as a specific case (see Supplementary Note 3), but also goes beyond by
considering the evolution of individuals’behavioral motivations and
the effects of population structure on their decision-making.
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Particularly, we study the evolution of aspiration-based action updat-
ing in a population of philanthropists and aspirationalists. We find that
in the interacting environment with b/c>(b/c)*, both undemanding
philanthropists and demanding aspirationalists, by fostering a high
level of cooperation, can resist the invasion of mutants using
aspiration-based action updating (see Supplementary Fig. 7).
Our study also offers a few insights into how population structure
impacts cooperation. Theoretical studies which focus on the evolution
of cooperation in one-shot games have demonstrated that population
structure, including the density and distribution of connections, has a
profound impact on evolutionary outcomes11,13–15,40–42. However, several
experimental studies have shown that a heterogeneous population
structure does not provide additional advantages for the evolution of
cooperation43. While there may be many reasons for this, we note that
these findings are consistent with our study, in which heuristics in the
form of behavioral motivations drive the decision to cooperate. In our
study, when individuals’behavioral motivations remain fixed, the global
cooperation abundance remains robust against population structure,
regardless of the density and distribution of connections. Several prior
studies focusing on aspiration-based action updating have found that
the abundance of cooperation on random regular networks is identical
to that in a well-mixed setup34,35. Analyzing the σrule for strategy evo-
lution reveals a structural coefficient σ= 1, indicating the absence of
cooperation clusters under aspiration-based action updating, similar to
the well-mixed scenario34,35. We offer an alternative intuition applicable
to any threshold-based action updating: the frequency of an individual
taking any action is fully determined by the payoff structure, their
motivation intensity, and their need threshold, but is independent of
their connections with other individuals (see Eq. (7) in the Supplemen-
tary Information). However, we also note that once individuals’beha-
vioral motivations begin to evolve, population structure again plays a
critical role in determining the evolutionary direction of these motiva-
tions. This is because undemanding philanthropists and demanding
aspirationalists can lead to a higher level of cooperation, and particu-
larly, the death-birth updating process favors cooperation for certain
b/cratios, which in turn supports the evolution of undemanding phi-
lanthropists within a population of demanding philanthropists.
In studying the evolution of behavioral motivations, we find that
the trajectory of individuals’heuristics is influenced by a critical benefit-
to-cost ratio (b/c)*, which determines the evolutionary trajectories and
outcomes. Specifically, if the benefit-to-cost ratio is low, i.e., b/c<(b/c)*,
even if the population is initially composed of undemanding philan-
thropists or demanding aspirationalists, and cooperation is more pre-
valent than defection, over time all individuals gradually abandon their
prosocial preferences and switch to demanding philanthropists or
undemanding aspirationalists, resulting in a sharp decline in the coop-
eration abundance. Conversely, if the benefit-to-cost ratio is just above
the critical ratio, i.e., b/c>(b/c)*, in a population consisting of
demanding philanthropists or undemanding aspirationalists, where
defection is more prevalent than cooperation, we observe the emer-
gence and expansion of undemanding philanthropists and demanding
aspirationalists, creating a conducive environment for cooperation.
Notably, the critical benefit-to-cost ratio is greatly influenced by the
population structure. These findings have two important implications.
Firstly, for the classic well-mixed population, where any two individuals
are equally likely to interact, the critical ratio is −(N−1), implying that
undemanding philanthropists and demanding aspirationalists are
unable to evolve for any benefit-to-cost ratio. By considering population
structures, particularly those with sparse connections, we can achieve a
positive (b/c)*that facilitates the evolution of prosocial behavioral
motivation. Real-world networks are often much sparser than well-
mixed setups, which may explain the prevalence of cooperation. Sec-
ondly, if the (b/c)*value is too large to attain, a potential solution is to
modify a few connections, which can reduce the (b/c)*value to below
the actual benefit-to-cost ratio.
There is a natural connection between our work and the study of
cooperation in iterated games4,44–50, in which players update their
behavior based on the outcome of previous interactions. Indeed,
strategies such as tit-for-tat4can be thought of as heuristics for
determining when to engage in cooperation. However, iterated game
strategies describe decision-making as conditional on the history of
play with a specific interaction partner, whereas the behavioral moti-
vations we study operate at the level of the cumulativepayoff received
by an individual over many interactions. Which kind of heuristics
people use in reality may depend on the relationship between the
individuals interacting and the cognitive demands on decision-
making19.
In this work, we focus on the two-action donation game and its
multi-action variations as they capture the cooperation dilemmas
where pursuing a short-term larger payoff leads to cooperation col-
lapse and collective tragedy. However, our treatment can be applied to
other interaction scenarios, such as snowdrift games and stag-hunt
games (see Supplementary Note 3 and Supplementary Fig. 8).
Although a few recent studies incorporate the idea of indirect evolu-
tion - where individuals update their actions according to an objective
function different from the actual payoffs51–53 - theoretical exploration
in this area is relatively underdeveloped compared to the direct evo-
lution of actions. Therefore, we suggest that the application of evo-
lutionary game theory to the study of human behavior should focus
more strongly on the evolution of decision heuristics and the under-
lying motivations for cooperation.
Our work does not attempt to describe a new mechanism for the
evolution of cooperation, but rather assumes that all individuals are
willing to cooperate under some circumstances, and then explores
how those circumstances evolve in terms of behavioral motivations.
And so our model does not attempt to capture the emergence of
baseline social norms of cooperation, but variation in an individual’s
behavior against that baseline. However, it is clear that social norms
may influence the evolution of behavioral motivations for cooperation
in ways not explored here. For example, a transition from philan-
thropic to aspirationally motivated cooperation may be constrained if
aspirational cooperators are perceived as norm violators. We propose
that integrating our modelling framework with models of reputation
management via social norms6–10 will be a productive avenue for
exploring this type of interaction in future work.
An overarching goal of this work is to develop a modelling fra-
mework that address questions relating to the evolution of cooperation
in humans in ways that better connect to the empirical literature. In
particular, our model addresses the relationship between individual
wealth and willingness to cooperate, and reveals an intriguing sym-
metry, in which similar levels of cooperation can emerge along with
opposite motivations for engaging in that cooperation. This finding
helpsmakessenseofsomeoftheapparentlyconflicting evidence in the
literature25–28, which sees some support for both aspirationally and
philanthropically motivated cooperation. Our key results (Fig. 6)sug-
gest that the key factor distinguishing populations may not be whether
they are aspirationally or philanthropically motivated, but the direction
of the correlation between motivation intensity and need threshold, i.e.,
whether people are demanding or undemanding philanthropists or
aspirationalists. Furthermore, as our framework focuses on the evolu-
tion of behavioral motivations, it naturally extends to other domains
beyond cooperation. For example, in the evolution of risk preferences,
individuals may shift toward riskier, higher-reward behaviors once their
payoffs exceed a critical threshold. This broader applicability highlights
the potential of our approach in studying the evolution of diverse
decision-making strategies across social and economic contexts.
While our theoretical approach provide s insights into the evolution
of motivations for cooperation, it has certain limitations. First, human
motivational heuristics are far more complex and diverse than the two
factors —need threshold and motivation intensity —considered in our
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model. Second, although our findings build on classical evolutionary
dynamics and offer a few theoretical perspectives, empirical validation
remains essential. Future experimental studies could examine how
environmental fluctuations shape cooperative behavior and how
cooperation adapts to periods of scarcity and abundance19,28,54.Incor-
porating additional factors could further enhance our understanding of
human behavior and the motivations that drive it. From a theoretical
standpoint, our study assumes a fixed functional form for decision-
making (Eq. (2)) while allowing the evolution of two free parameters:
need threshold and motivation intensity. A promising direction for
future research is to explore the evolution of the entire decision-making
function itself55.
Methods
In this section, we outline a derivation of the global cooperation
abundance and the critical condition for a behavioral motivation being
favored (i) for general two-action games and (ii) for multi-action
donation games. Complete mathematical details and the results for
general multi-action games, action-dependent need threshold, and
action updating function, are provided in Supplementary Notes 1 and 2.
Two-action game
We consider the classic two-player two-action game with payoff struc-
ture
CD
C
D
RS
TP
 ð7Þ
We use the population structure and notation described in the Model
section. We define πi=wi=Pj2Nwj,p
ij
=w
ij
/w
i
,andpðnÞ
ij to be the
probability that an individual starting from node iterminates in node j
after an n-step random walk. Let α
i
denote individual i’sneedthreshold
and λ
i
individual i’s motivation intensity. For fixed behavioral motiva-
tions, we obtain the global abundance of cooperation
xC=1
2+1
16NX
i2N
λiR+S+T+P4αi

ð8Þ
and the condition for cooperation being more abundant than defec-
tion, i.e., x
C
>1/2, givenby
X
i2N
λiR+S+T+P4αi

>0:ð9Þ
When it comes to the evolution of behavioral motivations, we can
obtain ρ
A
,thefixation probability of an individual who uses motivation
A (with need threshold α
A
and motivation intensity λ
A
) in a population of
individuals that use motivation B (with need threshold α
B
and motiva-
tion intensity λ
B
). First, we obtain the correlation of behavioral moti-
vation in two nodes iand j, by solving the following O(N2)equations
ηij =1δij
2+1
2X
k2N
pð1Þ
ik ηkj +pð1Þ
jk ηik

,ð10Þ
where δ
ij
=1 for i=jand 0 otherwise. Let ηn=Pi,j2NπipðnÞ
ij ηij,wecan
express the fixation probability ρ
A
as
ρA=1
N+βAβB
8NðR+S+T+PÞðR+STPÞη2

+ðRS+TPÞðη3η1Þ,
ð11Þ
where βX=λXR+S+T+P4αX

and X∈{A,B}. The condition for
selection favoring motivation A over B, i.e., ρ
A
>1/N,is
βAβB

R+STP
R+S+T+Pη2+RS+TP
R+S+T+Pðη3η1Þ

>0:ð12Þ
Let x
C
(A)andx
C
(B) respectively denote the global cooperation abun-
dance when all individuals use behavioral motivation A and B, com-
paring β
X
and x
C
in Eq. (8), we can rewrite Eq. (12)tobe
xCðAÞxCðBÞ

R+STP
R+S+T+Pη2+RS+TP
R+S+T+Pðη3η1Þ

>0:ð13Þ
Multi-action game
We consider the linear donation game with Llevels of donation (or say
Lactions), labeled by {1, 2, ⋯,L}, where level ℓmeans paying a cost
c
ℓ
=c(ℓ−1)/(L−1) to bring the opponent a benefitb
ℓ
=b(ℓ−1)/(L−1). As
such, level 1 corresponds to defection, and level Lmeans paying a cost
cto yield a benefitbto the opponent, referred to be “fully coopera-
tive”. The other actions are referred to be “partly cooperative”, i.e.,
payinga fraction of costs to generate a fraction of benefits. For a L-level
donation game, there are L−1 need thresholds, denoted by {α/(L
−1), 2α/(L−1), ⋯,α}, where the need threshold to the ℓ-level donation
is α(ℓ−1)/(L−1). By taking into account the fact that the satisfaction of
a need is not an “all-or-none”phenomenon, even if the individual uses
k-level donation in the current round and his payoff udoes not meet
the need threshold to ℓ-level donation, he is still likely to choose the ℓ-
level donation. In other words, regardless of the current action, an
individual is likely to choose any action next round but with a different
probability. Let αdenote the total need and λthe motivation intensity.
We introduce αkℓto mark the need threshold when an individual
transits the current k-level donation to the ℓ-level donation next round,
given by
αk‘=
‘α
L1‘<k,
ð‘1Þα
L1‘>k:
(ð14Þ
For given payoff u, the probability of updating action kto ℓ(k≠ℓ)is
given by
gk‘uðÞ=
2
L1 + exp λuαk‘
ðÞ
½
ðÞ
‘<k,
2
L1+ expλuαk‘
ðÞ
½
ðÞ
‘>k:
8
<
:
ð15Þ
And the probability of remaining to take a k-level donation is
gkk(u)=1−∑
ℓ≠k
gkℓ(u). Action updating function Eq. (15)achieves(i)for
philanthropic behavioral motivation, i.e., λ> 0, the increasing payoff u
makes individuals more likely to choose highly cooperative actions,
i.e., ℓ>k, rather than the lowly cooperative actions, i.e., ℓ<k;(ii)when
an individual uses action kto obtain a sufficiently high payoff u,evenif
the payoff ugreatly exceeds the threshold for a much higher level of
donation, the individual is more likely to transit to an adjacent higher
level of donation, such as the k+ 1 level, rather than jumping too
far ahead.
We have the global cooperation abundance of L-action linear
donation games, given by
xC=1
2+L+1
12NL ðbcÞX
i2N
λiL
L1X
i2N
λiαi
"#
ð16Þ
Article https://doi.org/10.1038/s41467-025-59366-1
Nature Communications | (2025) 16:4023 10
Content courtesy of Springer Nature, terms of use apply. Rights reserved

and the condition for selection favoring behavioral motivation A over
B, given by
βAβB

cη2+bðη3η1Þ

>0, ð17Þ
where βX=λXbcαXL=ðL1Þ

and β
X
∈{A,B}. The condition can
also be expressed as Eq. (6). For the multi-action nonlinear donation
game, depending on the interaction scenario modeled, there are many
formalizations of the relevant payoff structure. Here, we set the benefit
generated by ℓ-level donation to be b(1 −ωℓ−1)/(1 −ωL−1)andprovide
details in Supplementary Note 3. Benefit factor ω= 1 corresponds to the
former linear donation game, and 0 < ω< 1 (respectively ω> 1) describes
the discounting effect, see Fig. 2c (respectively, synergistic effect, see
Fig. 2d). We have the global cooperation abundance given by
xC=1
2+L+1
12NL
2σ
Lbc

X
i2N
λiL
L1X
i2N
λiαi
"#
,ð18Þ
where σ=Lð1ωÞð1ωLÞ

=ð1ωÞð1ωL1Þ

.
Reporting summary
Further information on research design is available in the Nature
Portfolio Reporting Summary linked to this article.
Data availability
All results can be reproduced from the code56.
Code availability
All numerical calculations and computational simulations were per-
formed in Julia 1.5.3. All data analyses were performed in MATLAB
2023b.Allcodeshavebeendepositedintothepubliclyavailable
repository at https://github.com/qisu1991/BehavioralMotivation56.
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Acknowledgements
Q.S. acknowledges support from the National Natural Science Foun-
dation of China (No. 62473252) and Shanghai Pujiang Program (No.
23PJ1405500). A.J.S. acknowledges support from the John Templeton
Foundation (No. 62281).
Author contributions
Q.S. and A.J.S. conceived the project. Q.S. derived analytical results and
performed numerical calculations. Q.S. and A.J.S. analyzed the data.
Q.S. wrote the main text and the Supplementary Information. A.J.S.
reviewed and edited the main text.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s41467-025-59366-1.
Correspondence and requests for materials should be addressed to
Qi Su or Alexander J. Stewart.
Peer review information Nature Communications thanks Simon
Columbus and the other anonymous reviewer(s) for their contribution to
the peer review of this work. A peer review file is available.
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