Evolution of Cooperation in N-player Social Dilemmas:

The Importance of being Mobile

Maud D. Gibbons, Colm O’Riordan and Josephine Grifﬁth

Discipline of Information Technology, National University of Ireland Galway, Galway, Ireland

Keywords:

N-Player Social Dilemmas, Evolution of Cooperation, Contingent Mobility.

Abstract:

This paper addresses issues regarding the emergence of cooperation in evolutionary, spatial game-theoretic

simulations. In the model considered, agents participate in a social dilemma with their neighbours and have

the ability to move in response to environmental stimuli. Both the movement strategies and the game strategies

(whether to cooperate or not) are evolved. In particular, we present results that compare the outcomes using the

classical two player prisoner’s dilemma and a generalised N-player prisoner’s dilemma. We also explore the

effect that agent density (the number of agents present per cell in the world) has on the evolution of cooperation

in the environment. Finally, we discuss the movement strategies that are evolved for both cooperative and non-

cooperative strategies.

1 INTRODUCTION

Questions relating to cooperation and its emergence

have been studied in a range of domains including

economics, psychology, theoretical biology, and com-

puter science. Researchers have explored the con-

ditions necessary for cooperation to emerge among

groups or societies of self-interested agents. Social

dilemma games, such as the Prisoner’s Dilemma (Ax-

elrod, 1984), have been adopted as a succinct rep-

resentation of the conﬂict between individually self-

ish behaviours and collectively rational behaviours.

Evolutionary game theory has been studied since the

1980s when ideas from evolutionary theory were in-

corporated into game theory (Maynard Smith, 1982).

A variety of social dilemmas have been studied

with the majority of attention afforded to the 2-player

prisoner’s dilemma. Many variations of this game ex-

ist, which allow researchers to explore questions re-

garding cooperation in the presence of noise, trust,

spatial mechanisms and other extensions. One inter-

esting extension that has been explored in the liter-

ature is that of N-player social dilemmas (Yao and

Darwen, 1994) where N agents participate simultane-

ously in the interaction. Each agent can cooperate or

defect, and receives a reward based on the number of

cooperators present. Additionally, cooperators incur

a cost to interact while defectors do not.

In this work, we consider populations of agents

participating in both the 2-player and N-player ver-

sions of the prisoner’s dilemma. We adopt a spatial

model where agents’ interactions are deﬁned by some

topological constraints. Much recent work has fo-

cused on the effect of such constraints (Szolnoki et al.,

2009; Ohtsuki et al., 2006; Lieberman et al., 2005).

We use a toroidal lattice where agents may interact

with their immediate eight neighbours, if any. We fur-

ther imbue the agents with the ability to move based

on environmental stimuli. The role of mobility in the

evolution of cooperation has grown in importance and

recognition in recent decades with several researchers

demonstrating its use in the promotion of cooperation

in artiﬁcial life simulations (Aktipis, 2004; Vainstein

et al., 2007). We adopt an evolutionary framework

where successive populations are evolved; the strat-

egy for interacting in the games and the mobility strat-

egy are both subject to evolution.

The N-player prisoner’s dilemma has not been

widely studied in evolutionary models where agents

are spatially situated with the inclusion of mobility.

We wish to explore if any signiﬁcant differences are

prevalent between 2-player and N-player dilemmas in

this context. Furthermore, we wish to examine the

effect of varying the density of the agents in the en-

vironment, and ﬁnally we wish to analyse the move-

ment strategies evolved in these conditions.

In this paper, we show through simulation that

there is in fact a substantial difference between the

2-player and the N-player scenarios in terms of the

likelihood of cooperation emerging for varying den-

Gibbons, M., O’Riordan, C. and Grifﬁth, J.

Evolution of Cooperation in N-player Social Dilemmas: The Importance of being Mobile.

DOI: 10.5220/0006052700780085

In Proceedings of the 8th International Joint Conference on Computational Intelligence (IJCCI 2016) - Volume 1: ECTA, pages 78-85

ISBN: 978-989-758-201-1

sity levels. We demonstrate that for a range of density

levels, cooperation emerges in the N-player case.

The paper outline is as follows: the next section

discusses some related work in the ﬁeld, section 3 out-

lines our model and approach, and section 4 presents

and discusses our results. Finally conclusions and

some potential future directions are presented.

2 RELATED WORK

In this section we review some of the relevantresearch

in the literature; we introduce some concepts pertain-

ing to social dilemmas and discuss some work on spa-

tial and evolutionary game theory and the role of mo-

bility.

2.1 Social Dilemma Games

Social dilemma games (most famously the prisoner’s

dilemma and its variants) have been studied in a wide

range of domains due to their usefulness in capturing

the conﬂict between individual and collectively ratio-

nal behaviours. The prisoner’s dilemma in the clas-

sical game is described as follows: two players make

a choice simultaneously to either cooperate or defect.

Mutual cooperation yields a reward R for both par-

ticipants. However, unilateral defection results in a

greater payoff, T, for the defector and a worse pay-

off, S, for the cooperator (the sucker’s payoff). If

both defect, both receive P as a payoff such that:

T > R > P > S.

It has been argued that the N-player variant cap-

tures a wider set of dilemmas (e.g. donating to char-

ity organisations, environmental issues etc.). In the

N-player dilemma game there are N participants, and

again, each player is confronted with a choice: to

either cooperate or defect. In one formalism of the

game (Boyd and Richerson, 1988), all players receive

a beneﬁt based on the number of cooperators present.

Cooperators have to pay a cost. No such cost is borne

by defecting players. For instance, let B represent

some ﬁxed beneﬁt, N the number of players, c the

cost and i the number of cooperators. Participants re-

ceive (B × i)/N. Cooperators must pay c and thus

receive a net reward of ((B×i)/N) −c. This, or simi-

lar, formulas have been adopted in several other works

(O’Riordan and Sorensen, 2008; Yao and Darwen,

1994; Suzuki and Arita, 2003).

We represent the payoff obtained by a strategy

which defects given i cooperators as D(i) and the pay-

off obtained by a cooperativestrategy giveni coopera-

tors as C(i). Defection represents a dominant strategy,

that is, for any individual, moving from cooperation to

defection is beneﬁcial for that player in that they still

receive a beneﬁt without the cost:

D(i) > C(i) 0 < i ≤ N − 1

However, if all participants adopted this domi-

nant strategy, the resulting scenario would be a sub-

optimal, and from a group point of view, irrational

outcome:

C(N) > D(0)

If any player changes from defection to coopera-

tion, the society performs better:

(i+ 1)C(i+ 1) + (N− i− 1)D(i+ 1) >

(i)C(i) + (N − i)D(i)

In multi-person games, the problem of avoiding

exploitation, or free riders, is more difﬁcult, and coop-

eration may be harder to achieve. In 2-player games,

reciprocity has been explored as a means to engender

cooperation (Nowak, 2006). However, in N-person

games reciprocity may be less advantageous. In order

for an agent to punish a defector by defecting in re-

taliation, the agent must also punish all those that did

cooperate.

2.2 Evolutionary N-player Games

There have been several other notable approaches

to exploring the N-player prisoner’s dilemma using

the tools and approaches in evolutionary game the-

ory. Yao and Darwen (Yao and Darwen, 1994) ex-

plore the effect of group size in the evolution of co-

operation. Strategies are represented using a gener-

alised form of the representation employed by Axel-

rod and Dion(Axelrod and Dion, 1988). In their ex-

periments, it is shown that cooperation can be evolved

in groups but that it becomes more difﬁcult with in-

creasing group size.

The effects of spatial inﬂuences on the evolution

of cooperation among strategies participating in the

N-players prisoner’s dilemma is explored by Suzuki

and Arita (Suzuki and Arita, 2003). The two spatial

factors under investigation are on the scale of interac-

tion (determines which neighbours to play with) and

scale of inﬂuence (speciﬁes which neighbouring can-

didates to choose for offspring). Results for simula-

tions involving a tit-for-tat like strategy showed that

cooperation becomes most wide-spread for a modest

value of scale of interaction and that, as the cost of

cooperation increases, the levels of cooperation de-

crease and a higher value of the scale of interaction is

found. Results also indicate that higher cooperation

levels are achieved for higher values of the scale of

inﬂuence.

Evolution of Cooperation in N-player Social Dilemmas: The Importance of being Mobile

2.3 Mobility

Traditional spatial models promote the evolution of

cooperation by constraining agent interactions to a

particular static topology. Previous work has inves-

tigated structures such as lattices (Nowak and May,

1992), small-world graphs (Santos et al., 2006), and

scale-free graphs (Poncela et al., 2009). However, the

inclusion of movement creates a more realistic model

by allowing agents to respond to their current neigh-

bourhood by moving within their environment.

Mobility is a form of network reciprocity (Nowak,

2006), which has gone from being perceived as a hin-

drance to the emergence of cooperation to a key con-

cept in its promotion. While unrestrained movement

can, and does, lead to the ‘free-rider’ effect (Enquist

and Leimar, 1993), allowing highly mobile defectors

to go unpunished, using simple strategy rules (Ak-

tipis, 2004; Ichinose et al., 2013) or using mobility

rates (Meloni et al., 2009; Vainstein et al., 2007) sig-

niﬁcantly curb the free-rider phenomenon allowing

self-preserving cooperator clusters to form, and co-

operation to proliferate.

Several mechanisms for the emergence of coop-

eration exist, but all essentially express a need for co-

operators to either avoid interactions with defectors or

increase and sustain interactions with other coopera-

tors. Research in this domain is largely divided into

two categories based on authors’ deﬁnition of mobil-

ity; all movement should be random (Vainstein et al.,

2007; Meloni et al., 2009; Sicardi et al., 2009; Anto-

nioni et al., 2014), or should be purposeful or strate-

gically driven, but may indeed contain random ele-

ments (Aktipis, 2004; Helbing and Yu, 2008; Helbing

and Yu, 2009; Jiang et al., 2010; Yang et al., 2010;

Tomassini and Antonioni, 2015). Random mobility

can be used to describe the minimal conditions for

the evolution of cooperation. Alternatively, contin-

gent mobility has the capacity to be proactive. This is

where individuals deliberately seek better neighbour-

hoods, rather than simply reacting to stimuli and ran-

domly relocating.

The majority of the contingent mobility strate-

gies in the literature are hand crafted or guided by

heuristics. However, there has been some research

(Joyce et al., 2006; Gibbons and O’Riordan, 2014;

Gibbons et al., 2016) using evolutionary models to

evolve movement strategies that are conducive to the

emergence of cooperation. Ichinose et al. (Ichinose

et al., 2013) also use an evolutionary model and in-

vestigates the coevolution of migration and cooper-

ation. Agents play an N-player Prisoner’s Dilemma

game after which they move locally according to an

evolved probability vector. All agents are evolved to

collectively follow or chase cooperators. The authors

highlight the importance of ﬂexibility in the direction

of migration for the evolution of cooperation.

Chiong et al. (Chiong and Kirley, 2012) describe a

random mobility model where a population of agents

interact in an N-player Prisoner’s Dilemma set in a

fully occupied regular lattice. Pairs of agents move

by exchanging grid positions. Mobility in this envi-

ronment is a probability function based on the time

an agent has spent in a location, and the relative ﬁt-

ness of the agent at the destination. The agents have

a limited memory of past interactions, and past coop-

erator and defector levels. Cooperation is shown to

be promoted under a limited small set of parameters

including the cost to beneﬁt ratio of cooperation and

the movement radius.

Most recently, Suarez et al. (Suarez et al., 2015)

present a contingent mobility model, using the N-

Player game, in which agents move toward locations

with higher potential payoff. While cooperation does

emerge, the authors do not elaborate on the speciﬁc

effects of mobility, focusing more on the impact of

the neighbourhood size.

3 METHODOLOGY

3.1 Environment & Agent

Representation

The population of agents A inhabits a toroidal shaped

diluted lattice with L × L cells, each of which can

be occupied by up to one agent. The interaction

and movement radii of agents is determined using the

Moore neighbourhood of radius one. This comprises

the eight cells surrounding an individual in a cell on

the lattice. The agents can only perceiveand play with

those within this limited radius.

Each agent is represented by a genotype, which

determines their strategy to interact with other agents

and to move in the environment. The ﬁrst section of

the gene describes their strategy for playing the game:

that is to cooperate or defect and the remaining sec-

tions determine how an agent will move. The remain-

der of the genotype encodes actions for a range of

scenarios that may arise within the environment, in-

cluding: encountering a cooperator, encountering a

defector, or encountering both at once. If an agent

meets a cooperator, they have a set of potential ac-

tions. These actions are as follows: remain where

they are, move randomly,follow the cooperator or ﬂee

from it. Similarly these potential actions are mirrored

when an agent meets a defector. The ﬁnal section is

ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications

used to determine actions when an agent meets both a

defector and a cooperator. The actions are: ﬂee from

both cooperator and defector; follow both cooperator

and defector; follow the cooperator and ﬂee from the

defector and the converse action (ﬂee from the coop-

erator and follow the defector). During a simulation

run, each potential action of an agent is determined

by its genotype.

At each time step, agents participate in a single

round of the Prisoner’s Dilemma with each of their

neighbours, if any. The strategy with which agents

play is ﬁxed; either always cooperate or always de-

fect. We choose to implement pure strategies in or-

der to reduce the strategy space allowing us to more

clearly examine the effect of mobility in these experi-

ments. Agents are aware of the actions taken by their

neighbours in a single round, but these memories do

not persist. Following this interaction phase, agents

have the opportunity to take one step into an adjacent

free cell according to their movement strategy. Move-

ment will not occur if there is no adjacent free space,

or if their strategy dictates that they remain in their

current location. Isolated agents will take one step in

a random direction.

3.2 Evolutionary Dynamics

The movement strategies adopted by the population

are explored by using an ALife inspired evolution-

ary model. In a single generation, agents accumu-

late their payoffs received from playing the Prisoner’s

Dilemma with their neighbours. This is used as a

measure of ﬁtness, and at the end of each generation,

the agents are ranked according to this score. The

bottom 20% are replaced with copies of the top 20%.

This replacement strategy was chosen as it has been

previously shown to produce a fair sampling of the

population’s ﬁtness while still allowing for conver-

gence in a reasonable time frame. No other genetic

operators are utilized. These offspring are randomly

placed on the grid, and the other agents remain in the

same place, thus maintaining any spatial clustering

between generations. Following reproduction, the ﬁt-

ness score of the whole population is reset and a new

generation begins.

3.3 Interaction Model

In keeping with previous work, we adopt a

well known formalism for the N-player prisoner’s

dilemma. Letting B be a constant representing social

beneﬁt, c be the cost of cooperation and i the number

of cooperators from a group of N agents, the follow-

ing payoffs are used:

C(i) =

B× i

− c

D(i) =

B× i

The following constraints hold: B > c and both B

and c are positive values.

Considering the N-player dilemma, when N=2

and attempting to align with the classical interpreta-

tion of the 2-player prisoner’s dilemma, we also re-

quire that B < 2c. Values chosen in this research that

are in keeping with previous studies in the ﬁeld are:

B = 5,c = 3.

For example, in mapping this back to the two

player games, we use the following payoff matrix:

Table 1: Prisoner’s Dilemma game matrix.

C D

C 2,2 −

,−

0,0

In our simulations, we contrast scenarios with 2-

player interactions and N-player interactions. In the

N-player case, an agent particpates in the dilemma

with all of its immediate neighbours; the number of

such neighbours determines the number of partici-

pants. In the 2-player case, an agent participates in

individual 2-player games with each of its immediate

neighbours.

4 SIMULATION RESULTS

4.1 Experimental Setup

In these experiments, we run two sets of similar simu-

lations, one with 2-Player interactions the other with

N-Player interactions, comparing the respective out-

comes. It is generally accepted that when compar-

ing the two interaction models inducing cooperation

in the N-Player games is considerably harder.

The population of A = 100 agents is placed ran-

domly on the L × L torus with L = 30, the strate-

gies (whether to cooperate or to defect) are assigned

in equal proportion, and the movement strategies are

assigned randomly. A single simulation lasts 1,250

time-steps, in which the agents take 25 steps in each

of 50 generations. The distribution of spatial strate-

gies, level of cooperation, time taken for the simula-

tion to convergeon cooperation (or defection), and the

total number of interactions will all be recorded. Each

simulation will be run over a 1000 times to generate

statistically valid results.

Evolution of Cooperation in N-player Social Dilemmas: The Importance of being Mobile

4.2 2-Player vs. N-Player

4.2.1 Cooperative Outcomes

On average in these environmental settings, the 2-

Player interaction model is more effective at induc-

ing the spread of cooperation in a larger percent-

age of simulations. We see in Table 2 that in

roughly one third of evolutionary simulations using

2-player interaction, cooperation emerges as the out-

come, whereas when agents participate in an N-player

interaction, cooperation emerges in roughly one quar-

ter of the simulations. On average, simulations using

the 2-Player interaction model tend to converge more

quickly, and with less variance. The simulations re-

sulting in the emergence of defectors exhibit a faster

convergence and less variability in convergence speed

regardless of the interaction model.

Table 2: 2-Player vs. N-Player : % Cooperator Wins.

Avg Std Dev

2-Player 33.2% 4.2%

N-Player

25.8% 4.7%

These results are in keeping with the general con-

sensus that evolving cooperation in the N-player pris-

oner’s dilemma can be more difﬁcult. This previous

research did not allow movement of agents, but still

captured the difﬁculty with N-player dilemmas where

an agent can exploit multiple participants and achieve

a considerable gain in payoff per interaction.

4.2.2 Evolved Movement Strategies

Tables 3, 4 and 5 show the movement behaviours that

are evolved for 2-player and N-player situations re-

spectively in those runs when cooperation emerges.

One hundred simulation runs resulting in cooperative

outcomes are considered.

Upon seeing a cooperator in their neighbourhood,

agents evolve to either stay where they are or to fol-

low the cooperator; this occurs in both 2-player and

N-player scenarios. When a defector is encountered,

agents have evolved to ﬂee or adopt a random move-

ment in 75% of cases in the 2-player game and 97% of

cases in the N-player game. For the scenarios where

agents see both cooperators and defectors we see sim-

ilar behaviours being evolved. Movement behaviours

Table 3: On seeing Cooperator : % Genes Evolved.

2-Player N-Player

Random 0% 0%

15% 27%

Flee 0% 0%

Stay

85% 73%

Table 4: On seeing Defector : % Genes Evolved.

2-Player N-Player

Random 34% 22%

Follow 16% 2%

Flee

41% 75%

Stay 9% 1%

Table 5: On seeing Cooperator & Defector : % Genes

Evolved.

2-Player N-Player

FollowCFollowD 27% 3%

FollowCFleeD 44% 52%

FleeCFollowD

9% 11%

FleeCFleeD 20% 34%

that promote cooperation and avoid exploitation are

selected. We can see that cooperators who interact

using the N-Player interaction model have a greater

evolutionary incentive to be adverse to defectors.

In all cases agents learn movementbehaviours that

allow them to continue cooperative interactions and,

to a lesser extent, to avoid interactions with defectors.

Behaviours that continue defector interactions die off,

although at a slower rate. Following cooperators is

selected more quickly than ﬂeeing from defectors.

It is important to note that the selective pressure

to avoid defectors is removed when the defectors are

replaced in the population with cooperators and hence

we do not see convergence to 100% for the genes that

promote avoiding defector interactions. Adopting a

random movement can also often have the same effect

as ﬂeeing from or indeed following an individual.

The population did not always evolve a single

strategy; random ﬂuctuation and lack of relevant stim-

uli resulted in simulations in which agents converged

on several strategies that were genotypically different,

but phenotypically similar.

In non-cooperative runs, defectors learned to (1)

follow cooperators, (2) ﬂee from defectors, and to (3)

follow both cooperators and defectors.

4.3 Variation in Density

In the previous experiments, the percentage of co-

operative outcomes and the evolution of movement

strategies was a function of the agent interactions.

The ratio of cooperative interactions to other types of

interactions inﬂuences the evolutionary trajectories.

In this experiment we aim to investigate the im-

pact of the density of agents in the environment. We

deﬁne the density as D = A/L

where A is the size of

the population, and L is the length of the lattice grid.

Density is a function of the population size and the

size of the grid. We keep the population size constant

ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications

0 500 1,000 1,500 2,000

100

Grid Size (L

)

Cooperator Win %

2-Player

N-Player

Figure 1: 2-Player vs. N-Player: The percentage of simula-

tions resulting in cooperative victories as we vary the grid

density starting from random initialization.

and vary the size of the grid as a means to vary the

density.

The movement strategies of agents are randomly

initialized, the strategies for game interactions are as-

signed in equal proportions and both the movement

and interaction strategies are subject to evolution. In

one set of simulations, the population interacts using

the 2-player interaction model, and the other uses the

N-player model.

As shown in Figure 1, at the highest density level,

there is not enough space within the grid for agents

to move freely and so defection dominates in the vast

majority of simulations. These conditions echo the

traditional spatial models with an agent located in ev-

ery cell where no movement is possible. These ﬁnd-

ings mirror those results with defection spreading and

dominating the population.

As the density is reduced, we see that the evo-

lutionary runs using the 2-Player interaction model

are more readily able to induce higher levels of co-

operation. However, using the 2-Player interaction

model, random initialization in low densities can only

achieve cooperation in just above 50% of simula-

tions. With these same settings the N-Player inter-

action model can induce cooperation in a far greater

percentage (80%) of runs.

For a grid size of 32x32 (1024 cells), the N-player

interactions overtakethe 2-player interaction model in

their ability to induce cooperation. This result demon-

strates that despite the difﬁculty of inducing coopera-

tion, cooperation emerges in N-player games, the ad-

dition of movement capabilities can support the emer-

gence of cooperation in these conditions.

0 500 1,000 1,500 2,000

100

Grid Size (L

)

Cooperator Win %

2-Player Seeded

N-Player Seeded

Figure 2: 2-Player vs. N-Player: The percentage of cooper-

ative victories, as we vary the grid density, seeding the most

prevalent evolved strategies for cooperators and defectors.

4.4 Seeding the Evolved Strategies

In our ﬁnal experiment, the evolved movement strate-

gies for both cooperators and defectors are seeded in

the population and we repeat the density experiment.

In the previous experiment both movement strategies

were randomly assigned and it took several genera-

tions for movement strategies to emerge. A number of

these strategies. were identiﬁed as being favorable to

the emergence of cooperation. The aim of this exper-

iment is to explore the effect of these good strategies

when they are present in the ﬁrst generation. If these

strategies help cooperators to follow each other and

form cooperative clusters, then higher levels of coop-

eration are expected across the various density levels.

Results show in both sets of simulations that the

evolved cooperator movement strategies are able to

induce cooperation for a much wider range of densi-

ties, as illustrated in Figure 2. There is a far greater

level of cooperation than that which was achieved

by either interaction model in the experiment with

random initialization. For the N-player interaction

model, once the grid size reaches 1024 (density

roughly equal to 10%), cooperation is achieved 100%

of the time. For the 2-player interaction model, this

level of cooperation is also maintained for higher den-

sity levels. The agents using the N-player model are

more hindered by the exploitative nature of defectors,

who are also using a previously evolved movement

strategy.

Evolution of Cooperation in N-player Social Dilemmas: The Importance of being Mobile

5 DISCUSSION

Traditionally, it has been difﬁcult to induce cooper-

ation using the N-player Prisoner’s Dilemma. How-

ever, in our model we observe high levels of cooper-

ation in a range of settings. The incorporation of a

contingent mobility allows cooperators to cluster to-

gether, and avoid repeated defector interactions. In

forming these clusters, these agents can increase their

number of mutually cooperative interactions, thereby

boosting their score. However, these cooperative clus-

ters can be exploited by defectors unless they employ

strategies that can avoid repeated exploitativeencoun-

ters. We observe high levels of cooperation coupled

with evolved movement strategies that encourage the

formation of these larger self-preserving clusters free

from the inﬂuence of defectors.

As expected, the 2-Player interaction model was

more successful at inducing cooperation in the higher

grid densities when we evolved from random strate-

gies. This is due to the fact that while the chances

of encountering a defector are higher, they have less

of an exploitative impact on individuals or clusters

of cooperators. Surprisingly, the N-player interaction

model was signiﬁcantly more successful at inducing

cooperation when the grid density was very low. We

attribute this success to the reduced chances of en-

countering a defector, and increased gains made by

mutually cooperative interactions in clusters. Addi-

tionally, single defectors beneﬁt by being in the neigh-

bourhood of cooperators but this beneﬁt is reduced in

the presence of other defectors.

6 CONCLUSION

In this work, we introduced a model wherein agents

inhabit a toroidal world, interact in social dilemmas,

and have the ability to move. We explored a num-

ber of scenarios involving both the 2-player and N-

player Prisoner’s Dilemma. The density of agents in

the grid was varied in a systematic manner, and its ef-

fect on the emergence of cooperation was discussed.

We present results for 2-player and N-player interac-

tion models and discuss the outcomes both in terms of

cooperation levels obtained and in terms of the move-

ment strategies selected.

Through experimentation, we show that the pres-

ence of contingent mobility strategies helps induce

cooperation in environments where the interaction

model uses the N-player Prisoner’s Dilemma. We

show that this cooperation can emerge for a range of

density levels. Furthermore, we show that seeding

a population with the previously evolved movement

strategies results in very high levels of cooperation in

both the 2-player and the N-player interaction models

for a large range of densities. These simple mobile

strategies are extremely adept at spreading coopera-

tion throughout a mobile population without the need

for complex computation, or costly memories.

Future work will involve a more thorough inves-

tigation of the nature of the cooperative clusters that

form throughout the evolutionary runs. We also wish

to explore a larger set of N-player social dilemmas

and explore a more expressive spatial topologies.

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