© Copyright JASSS
O. Thébaud and
B. Locatelli (2001)
Modelling the emergence of resource-sharing conventions: an agent-based approach
Journal of Artificial Societies and Social Simulation
vol. 4, no. 2,
To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary
This paper presents an agent-based simulation framework for the analysis of the emergence of resource-sharing conventions. The model is based on Sugden's article entitled "Spontaneous order", which looks at the conditions under which
conventions regarding access to a natural resource become
established. The aim of the model is to explore the potential of agent-based modelling for the analysis of these questions. First, the structure of a simulation model based on
the example of driftwood collection used by Sugden is presented. Second, simulations of various scenarios about the behavioural rules followed by agents are described, and simulation results are presented. The paper concludes with a brief discussion of the advantages of agent-based models for analysing social processes such as the emergence of conventions regulating access to natural resources.
- Conventions, natural resources, multi-agent systems
In a fishing village on the Yorkshire coast
there used to be an unwritten rule about the gathering
of driftwood after a storm. Whoever was first onto a stretch of
the shore after high tide was
allowed to take whatever he wished, without interference from later
arrivals, and to gather it into piles
above the high-tide line. Provided he placed two stones on the top
of each pile, the wood was regarded
as his property, for him to carry away when he chose. If, however,
a pile had not been removed after two
more high tides, this ownership right lapsed (...). We can be sure
that the inhabitants of a fishing village
would not have appealed to law courts or police to enforce a custom
Somehow this rule was self-enforcing
R. Sugden (1989: 90)
In his article entitled "Spontaneous order", Sugden (1989)
analyses the conditions under which collective rules regulating access
to a natural resource can evolve and maintain themselves without conscious
design, and without external enforcement. The author adopts a critical
perspective with respect to classical game-theoretic approaches to this
issue. According to Sugden, the problem of access rules is a typical case
of co-ordination games with more than one uniquely rational outcome, with
the ensuing difficulties for classical game-theory in predicting which
outcome may obtain: agents following a particular rule will be guided by
something more than the axioms of rational choice as normally understood
As an illustration, he cites the example of a self-enforcing resource-sharing
arrangement on the coast of Yorkshire, in England, where people compete
for the gathering of driftwood brought to the shore by storms. The arrangement, he stresses, can be looked at from the perspective
of its efficiency properties. The allocation of a stretch of the shoreline
to the first who gets there avoids the allocation of too much labour to
the wood collection activity; the ownership rights to properly marked wood
piles avoids people having to monitor and protect their piles. In effect,
the arrangement thus enhances the efficiency of driftwood collection, relatively
to a free-for-all situation.
Such efficiency properties, however, are not much help in explaining why
and how this particular arrangement - or convention - became established.
Among the other possible arrangements that could have come about for
allocating access to driftwood, the author mentions taking turns based
on days of the week or using a lottery. Either of these, he notes, could
have proved more efficient, as it would avoid people wasting resources
in the race-to-shore competition.
Sugden is interested in the processes leading to the emergence of such
conventions in a collective, without resorting to the hypothesis of an
external, over-arching, agent capable of enforcing a particular rule. He
considers that this question can be cast in terms of a co-ordination problem
in an evolutionary game, which allows him to define a convention as an
evolutionary stable strategy:
The idea here is that a convention is
one of two or more rules of behaviour, any one of which, once established,
would be self-enforcing. (p. 96)
He then focuses his analysis on the
process by which conventions evolve in a collective, raising the questions
of (i) how a convention starts to evolve, i.e. significantly more people
follow it than follow any other convention; and (ii) what self-reinforcing
processes lead the convention to become established in the collective.
Sugden analyses various factors which may help to respond to these two
questions, including the prominence of certain forms of co-ordination and
the role of common experience in this respect, as well as the versatility
of particular conventions.
The aim of this paper is to present an agent-based simulation framework
which was developed in order to explore the potential of agent-based modelling
for the analysis of these questions. Agent-based modelling of social phenomena
has developed rapidly in recent years (Gilbert
and Doran, 1994; Epstein and Axtell, 1996; Kohler and Gumerman, 2000). The approach appears particularly well-suited
to the type of issues considered by Sugden. It allows one to tackle explicitly
questions of process and emergence in the economy (Gilbert, 1995), which have presented difficulties to traditional modelling
in economics. In particular, it allows the explicit representation of a
heterogeneous collective of agents of variable sizes, and the analysis
of its evolution at both individual and collective levels.
The paper is organised as follows. First, the structure of a simulation
model based on the metaphor of driftwood collection described by Sugden
is presented. Second, to illustrate the type of dynamics that this model
can represent, simulations of various scenarios regarding the behavioural
rules followed by agents are described, and simulation results are presented.
The paper concludes with a brief discussion of the advantages of agent-based
models for analysing social processes such as the emergence of conventions
regulating access to natural resources.
The simulation model uses CORMAS (Common-Pool Resources and Multi-Agent
Systems), a multi-agent simulation platform specifically designed for
the simulation of renewable resource management systems (Bousquet et al., 1998). The platform, based on the programming environment
VisualWorks, was used because it is dedicated to the modelling of interactions
between individuals and groups using natural resources, and because it
includes a spatial dimension.
The model has three main components (see Figure 1) :
a spatial grid (" the beach ");
a passive object (" driftwood ") which is distributed in the grid,
any single cell having the capacity to store an unlimited number of pieces
social agents (" driftwood collectors ") having the capacity to
move over the spatial grid, and to collect driftwood.
|Figure 1. The spatial grid with driftwood (black dots), wood
piles and collectors (with different colours reflecting varying behaviour
General structure of the model
The general structure of the model is as follows.
|Figure 2. General structure of the model
Initially, the supply of wood is distributed randomly on the grid, with
no more than one piece of wood per cell. Each agent has a limited capacity
to carry wood. As long as his carrying capacity is not reached, an agent
will look for wood and, when he finds some, will collect it. When he reaches
his maximum carrying capacity, the agent creates a pile in the cell in
which he picked up his first piece of wood. He can then go on collecting,
and will keep stacking wood on the same pile for the rest of the simulation.
To study the way in which conventions regarding the sharing of wood can
evolve, rules of individual behaviour are specified at two different stages
in this process:
at the stage of search, assumptions are tested regarding the way
in which agents define the set of possible actions in terms of moving towards
at the stage of collection, assumptions are tested regarding the
way in which agents behave when they meet on a cell containing driftwood
to be collected.
A basic model of search and collection behaviour
First, a basic model of search and collection behaviour is specified,
in which no particular rule concerning access to driftwood is postulated.
Basic behavioural rules are as follows.
|Figure 3. Behavioural rules
Agents are given a capacity to observe their surroundings within
a given range. They can identify driftwood, both stranded pieces and existing
piles, as well as other agents in their vicinity. When observing wood in
a cell, agents can distinguish between a pile and a single piece of driftwood
The range of visibility can be fixed anywhere between zero and the
entire grid, in order to allow for variable levels of individual information
about the availability of wood and the actions of other agents. While no
driftwood is observed, an agent will move randomly to a neighbouring cell
in the grid. As soon as driftwood comes within sight, the agent will move
as quickly as possible to the cell in which the wood is located. The only
constraint on possible movements is that no more than two agents may meet
on the same cell in any time step.
As long as he is alone on a cell containing wood, and as long as
he has not reached his carrying capacity, the agent will pick up wood piece
by piece. The only rule specified in this version regarding collection
is for cases where two agents meet on a cell containing wood. When this
is the case, it is assumed that the agents play a " Game of Chicken
", with the following structure. Each player has a choice between an aggressive
strategy (to pick up a piece of wood) and a conciliatory strategy (to seek
compromise, but to let the other player pick up the wood if he looks determined
to do so). The payoff matrix for this game is a follows:
|Table 1: The payoff matrix of the game
|1 = get a full piece of wood; 0 = get nothing; 0.5 = share
the piece of wood|
The value of 0.5 in the payoff matrix means that there is an equal chance
for both agents to collect the piece of wood when both are conciliatory.
A random procedure in the model determines which agent wins the piece
of wood in any particular encounter.
The key assumption here is that, while each player prefers being
aggressive if he knows that the other player will be conciliatory, he will
prefer being conciliatory if he can be sure that the other player will
be aggressive, i.e. agents will prefer backing off to avoid conflict. This
is modelled by assuming that each agent's payoff in case of conflict is
The choice of this game structure in the model is motivated by its
use in Sugden's article as a basis for the understanding of the emergence
of conventions. Indeed, games of this type are specific in that they have
more than one Nash equilibrium, i.e. more than one pair of strategies
which are simultaneously best replies to the opponent's strategy. Sugden
argues that the only stable equilibria in an evolutionary game of this
kind are the ones in which the two players behave differently. This implies
that the players be distinguished in a way leading them to reach different
conclusions regarding their own best strategy in a particular interaction.
In the initial version of the model presented here, it is assumed
that agents confronted with a wood-sharing conflict adopt an aggressive strategy
with a given probability equivalent to the "degree of aggressiveness", specified
when initialising the model. If located on a wood-pile, the agents repeat
the game until no wood remains to be collected, or until either of them
has reached his carrying capacity.
The arrangement Sugden describes in his work can in fact be separated
into three different rules: (i) a first come - first served rule for the
allocation of access to a stretch of the shore; (ii) a property rule for
wood gathered into marked piles; and (iii) a first come - first served
rule for the collection of wood on abandoned piles.
The simulation framework was used to analyse these three rules based
on variations in the assumptions used to simulate agent behaviour. The
emphasis in this article is on simulating various processes by which the
convention regarding the property of marked wood-piles could become established
in this metaphorical model. The main focus is thus on strategies of avoidance
of wood piles, and their diffusion in the collective. For this reason,
relatively little use is made here of the rules regarding collection behaviour
and the resolution of conflicts, other than as a means to allocate wood
where these conflicts occur (following the principles described above).
In this, the analysis presented here departs from Sugden's article.
This section presents some of the simulation experiments which were
carried out using the model. After introducing the basic version of the
model, two general mechanisms are simulated with variants in their definition:
(i) peer pressure as a control on individual behaviour; (ii) imitation
a determinant of individual strategies. The conditions under which a property
convention may become established in this metaphorical model are discussed
in the following section of the paper, based on the simulation results.
The basic model
In the basic model, no particular rule regarding the property of
wood-piles was postulated. Simulations were used to understand the role
played by different parameters of the competition for wood thus modelled,
e.g. the impacts of varying wood availability, the effects of relative
distances between wood piles, or the consequences of various assumptions
regarding agent behaviour (range of vision, degree of aggressiveness).
In order to test for the performance of aggressive versus conciliatory
strategies, simulations were run with 25 agents and 300 pieces of wood
on a 900-cell grid. Agent strategies were
held constant during the simulation, i.e. each agent had a strategy fixed
at the beginning (aggressive or conciliatory). 20 simulation runs using
different distributions of agent strategies were then implemented, and
the average size of wood piles in the system was tracked.
In this version of the model, the rule for search behaviour was modified
in two different ways:
Agents head towards existing wood piles only if no one is observing them.
If another agent is visible (i.e. if he can also observe them), they will
avoid cells in the grid which contain wood piles, hence they will not pick
wood from existing piles.
Agents become identified as wood pile owners if the size of their pile
is above a given limit. It is then assumed that it becomes in their interest,
as pile owners, to enforce the rule of property. This is modelled by assuming
that all agents will avoid cells containing wood piles if a pile owner
is visible. It amounts to assuming that pile owners have the means to deter
other agents from cheating (for example through the imposition
of monetary or psychic costs).
Two variants of this second rule were simulated. In the first variant,
pile owners enforce the property rule, but do not respect it when no other
owner is watching. This version of the model illustrates problems of imperfect
enforcement of a collective rule. In the second variant, pile owners respect
(and enforce) the property rule in all cases. This is more akin to a moral
norm or a code of conduct among a group of pile owners. In effect, members
of this group adopt a particular rule of conduct whatever the consequences
for them in terms of resource collection.
As simulations showed that the initial location of agents induced
large variability in the results, it was decided to start all simulations
with the same geographical configuration in order to study the effects
of varying parameter values. This variant of the model was run 10 times
for each set of parameter values (see table below), with 10 agents and
a total supply of 300 pieces of wood.
With both variants, changes in the numbers of property-respecting agents
and non-respecting agents were tracked during simulation runs.
|Table 2: Effects of varying parameter values
|Group of simulation runs
|Minimum pile size for being pile-owner
|Range of vision
In this version of the model, two variants of the rule for search
behaviour were simulated:
Agents compare the wood piles they observe while searching for wood with
their own pile, and if the observed pile is larger than their own (including
the wood they are currently carrying), they adopt the strategy of its owner
with regards to the property rule, i.e. they decide to respect it or not.
As in the previous version of the model, agents become identified as pile
owners if the size of their pile is above a given limit. As pile owners,
they will enforce the rule of property, hence all agents will avoid cells
containing wood piles if a pile owner is visible. In this variant of the
model, pile owners will initially respect property in all circumstances
(see the second variant of the peer pressure model above).
However, they will also observe the behaviour of the other agents
around them. If it appears to them that more than one half of the agents
they can see (themselves included) is not respecting the property rule,
agents will change their strategy to non-compliance with the rule (except
if forced to comply by a neighbouring pile owner). Pile owners may thus
disregard the property rule if they feel that only a minority respects
it. Furthermore, they will change their strategy if, while emptying their
basket on their pile, they notice that enough wood has been stolen from
it for its size to be below the pre-determined threshold for pile-ownership
In both variants, the initial population of agents was randomly mixed,
with some agents respecting property and some collecting wood without respect
for other's piles, and the system was allowed to evolve. Again, changes
in the numbers of property respecting agents and non-respecting agents
were tracked during the simulation runs.
The basic model
As expected, a general feature observed in all simulations was the
central role of the initial size of the wood resource in the system. In
terms of average performance of the wood collection activity (measured
as the variance of wood pile sizes in time), the system became increasingly
unstable when the initial availability of wood relative to the number of
collectors was reduced.
Simulation runs showed that there was no significant difference between
the size of wood-piles of aggressive and conciliatory agents in this first
version of the model (see figure below), the exact results depending on
the initial allocation of wood piles in space.
|Figure 4. Evolution of average pile size of conciliatory and
aggressive agents during 20 simulation runs (25 agents, wood resource =
300, range of vision = 3)
The range of vision of agents proved to be a key parameter in the
first variant of the peer-pressure version of the model. With agents able
to observe the entire area, full compliance with the property rule was
obtained. But as soon as the range of vision of agents was less than the
entire area, there were situations in which agents could move to wood piles
without being observed, and less than full compliance was then observed.
In the second variant, the initial distribution of agents and their
number relative to the availability of wood played a key role, as they
determined the length of time which agents had to accumulate wood (and
become members of the group of pile owners) before someone started stealing
from their piles while they were absent, leading them back to a situation
in which they could no longer claim to be pile owners (their pile being
An example of the results obtained is presented below, for the second
variant of the peer-pressure version of the model, and for different values
of two parameters (range of vision, and threshold pile size for becoming
a pile owner). As all agents became property respecting after a certain
length of time, the simulations were stopped when the property rule had
become fully established in the collective. Analysis of the results is
in terms of the average value of this length of time.
|Figure 5. Influence of two key parameters on the mean and the
standard deviation of length of simulations (10 agents, wood resource =
The results show that the wider the range of vision, the quicker the simulation
ran (see Figure 5). This can be explained by the fact that a wide range of
vision allows greater enforcement of the property rule, thus leading to
quicker accumulation of wood by individual agents in the collective. Also,
when the pile size threshold is low, agents can easily create piles larger
than the minimum necessary for becoming respectful of the property rule.
But results showed that the duration of simulations increased with this
threshold; and that if the threshold was too high (i.e. more than 40),
a stable state was never achieved.
In the first variant of the imitation rule, simulations showed that
all agents ended up respecting the property rule (see Figure 6), except
in some extreme cases (e.g. with just one property-respecting agent at
the beginning). This can be explained by the way search behaviour
was specified. As non-respecting agents tried to take wood from existing
piles, they passed near piles which belonged to property-respecting agents.
If this pile was larger than their own, they became property-respecting.
On the contrary, since property-respecting agents excluded cells containing
wood piles from their range of movement, they had less chance of
going near to wood piles belonging to non-respecting agents, and thus
less chance of shifting to non-respect of the property rule.
|Figure 6. Evolution of rule respect during one simulation run
(10 agents, wood resource = 300, range of vision = 3)
The second variant of the imitation rule was used in particular to assess
the role played by the threshold limit for becoming a pile-owner, and a
property-respecting agent, when imitation also plays a part in determining
With a low threshold (e.g. 20 in this version of the model), the
system quickly stabilised, with all agents respecting the property of wood
piles (see Figure 7). This occurred after an initial reduction
in the number of respecting agents due to the spatial interactions allowing
some imitation of cheating behaviour, while none of the agents had accumulated
enough wood to acquire pile-ownership status. After a certain length of
time, with their piles increasing, agents became owners and shifted to
property-respecting behaviour, and imitation re-enforced this process.
|Figure 7. Evolution of rule respect during one simulation run
(10 agents, wood resource = 300, cells = 900, range of vision = 3, threshold
With higher levels of this threshold (e.g. 40 in this version of the model),
the system never achieved a stable state of either all-cheating or all-respecting
behaviour. The two strategies co-existed, with most agents changing
their behaviour many times in any simulation run. The consequence of raising
the threshold was in fact to increase the resource-scarcity constraint
to which agents were confronted: because of the limited availability of
wood, all agents could not become pile owners at the same time, and imitation
made it possible for cheating behaviour to subsist durably in the system.
Introducing imitation as a determinant of individual behaviour also
made the range of vision of agents a key parameter in the evolution of
the system. Extending the range of vision of agents in this case played
against the property rule, as it favoured observation of non-respectful
behaviour, hence increasing the shift to non-respect. Another way to see
this was to change the size of the grid while maintaining the number of
agents, their range of vision, and the supply of wood. This amounted in
particular to increasing the range of vision of agents. Results of such
a simulation run for a low property threshold (20) are presented in
Figure 8. In this case, the system remained unstable, with frequent
shifting of individual behaviour from respect to non-respect of the property
|Figure 8. Evolution of rule respect during one simulation run
(10 agents, wood resource = 300, cells = 400, range of vision = 3, threshold
The rules governing access to natural resources play a central role
in the economic analysis of resource management issues. The reasoning is
that where access rules are lacking, or if existing rules are deficient,
there is a tendency for resources to be misallocated between economic agents
and between alternative uses in the economy. An important component of
resource economics has focused on the way in which changing the structure
of access rights to a resource, usually by the State, could correct these
inefficiencies. On the other hand, the processes by which particular access
rules, including sub-optimal ones, become established and are enforced
have attracted less research in economics, possibly due to the difficulties
in taking explicitly into account the dynamic properties of social systems
in analytical models.
The aim of developing the agent-based simulation framework described
in this article was to explore the potential of agent-based modelling for
the analysis of such processes. The model is based on a metaphorical example
used by Sugden to discuss the issue of self-organisation in social systems,
and the limitations of classical game-theoretic approaches to this issue.
As already noted, our model makes relatively little use of the rules regarding
the resolution of conflicts, other than as a means to allocate resources
where these conflicts occur. In this, the analysis presented here departs
from Sugden's article.
Simulation experiments show that agent-based modelling provides a
rich framework for the study of social dynamics. The preliminary results
of this simple model of resource-sharing conventions illustrate the many
possibilities associated with such an approach. For example, issues discussed
in the literature with respect to the role of sanctions and norms in the
collective management of natural resources can be given an explicit treatment.
The model as it stands is highly simplistic in its description of
individual behaviour. This was in fact one of the aims pursued by the authors,
in anticipation of the difficulties that can appear in the interpretation
of simulation results in complex - and more realistic - models. Despite
this simplicity, the agent-based approach already allows for a degree of
complexity in that it offers the possibility of modelling interactions between
a large number of agents, heterogeneous in terms of individual behaviour
and resource constraints.
Further developments based on this simulation framework could include:
The analysis of the conflict resolution mechanisms to which Sugden gives
specific attention in his article. Analysing the impact of various assumptions
regarding agent behaviour in repeated resource-sharing conflicts should
allow testing of some of the factors proposed by the author to explain why
certain conventions emerge rather than others. Agents developed in our
model could have a capacity for memory and could act according to their
representation of past events.
The specification of economic constraints on individual behaviour. The
entire analysis is based on a simplistic model of wood collection behaviour.
A possible way to use the model would be to include costs (including opportunity
costs) and benefits as determinants of search and collection behaviour,
with a profit-maximising or cost-minimising objective function for agents.
The model would then allow the comparison of various scenarios from an
perspective, as well as from the perspective of which collective arrangement
- The authors would like to thank F. Bousquet and C. Lepage for
their support in developing the modelling platform.
1 See http://cormas.cirad.fr for more information.
2 Code for the model is available from
3 This size of grid was also used for
all the following simulation experiments.
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GILBERT N. (1995). Emergence in social simulation.
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© Copyright Journal of Artificial Societies and Social Simulation, 2001