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Arguing about justice

Axel Gosseries
Philippe Vanderborght

Real freedom for all turtles in Sugarscape?

Paul-Marie Boulanger


Sugarscape est un monde artificiel imagine par Epstein et Axtell en vue de simuler sur ordinateur l’émergence de propriétés sociales et collectives a partir des interactions d’une population d’agents autonomes et hétérogènes dotes de certaines propriétés et comportements élémentaires places au sein d’un écosystème rudimentaire. Partant du modèle original d’Epstein et Axtell, nous simulons successivement deux modifications fondamentales dans l’existence de ces agents, une existence exclusivement consacrée a la recherche obstinée et purement individualiste d’une nourriture unique consistant en une ressource renouvelable produite par l’écosystème. La première modification consiste a instaurer une sorte d’assurance ≪ perte de revenu ≫ indemnisant les agents dont l’environnement immédiat n’offre (momentanément) aucune possibilité d’activité rémunératrice. L’autre modification consiste a introduire une allocation universelle, un droit inconditionnel pour chaque agent a une quantité donnée de nourriture financée par un impôt proportionnel et versée indépendamment des caractéristiques et du comportement des agents. Nous comparons ensuite les trois mondes sous les critères de la capacité de charge totale (le nombre de survivants après 100 itérations), des inégalités de fortune et des chances différentielles de survie en fonction des capacités et des besoins, ≪ génétiquement ≫ détermines des agents.

Note de l’auteur

I am very grateful to Axel Gosseries and Yannick Vanderborght for their friendly support, remarks and suggestions.

Texte intégral

Everything should be as simple as possible, but not simpler
Albert Einstein

The Sugarscape universe

  • 1 Since Seymour Paperts implementation of LOGO at the MIT, the turtle is a kind of mascot and a tr (...)

1Imagine 400 creatures – let us call them turtles1 – fleeing from their planet devastated by an earthquake and landing in a disorganized way on another planet, quite similar to their native world where they expect going on with their – somewhat dreary – existence. They are very simple beings. Their only activity consists of foraging a renewable resource – let us called it sugar – which constitutes their unique foodstuff. They dont even reproduce themselves, being immortal as long as they have access to sufficient amounts of this food but dying immediately if they fall short of energy. Though simple as a species, they are all different at the individual level in two respects: the foraging capacity and the metabolic rate. The foraging capacity depends on the visual acuity necessary for moving in direction of the most promising area, the one offering the highest yield. Visual acuity is not distributed in a homogeneous way amongst them: some are almost myopic while others can detect the presence of food at distances far remote from where they stand. They differ also with respect to metabolism. While some can survive with small amounts of energy intake, others are more demanding. In sum, they differ in terms of capabilities: the capability to gather food and the capability to transform it into health and welfare (conversion factor). This translates into different survival prospects: having high visual acuity and low metabolism gives better chances of survival than the reverse. Our flock of 400 turtles landing on their new ecosystem – let us call it Sugarscape – constitutes a representative sample of the species diversity of talents, capabilities and needs.

2Furthermore, besides these inborn differences, they don’t start their new existence with equal chances of survival insofar as, if some have been able to carry significant stocks of sugar from home, others didn’t get the opportunity to make comfortable reserves before fleeing away. Needless to say, they will have less time to adapt to their new environment than those who arrive with important food stocks. What will happen to them? How will they adapt to their environment? Who will survive; who will not? What kind of social and spatial structure will emerge?

  • 2 Actually, the history of multi-agents modeling didnt start with Epstein and Axtell's seminal book. (...)

3These are the kind of questions Epstein and Axtell (1996) wanted to explore with their artificial world, named Sugarscape2, a multi-agent simulation model designed to experiment with situations characterized by a plurality of heterogeneous agents to which some properties of interest are randomly assigned (capabilities, preferences, initial social and/or geographical positions, etc.); interacting with one another on an active environment and according to some simple (or less simple) rules of behaviour. Epstein and Axtell's main objective was to understand how complex systems and behaviours can emerge from the stochastic interplay of many quite elementary units (or rules of conduct) in a given environment. Artificial societies, as they called sugarscape-like models, are laboratories where we attempt to grow certain social structures in the computer – or in silico – the aim being to discover fundamental local or micro mechanisms that are sufficient to generate macroscopic social structures and collective behaviours of interest (Epstein and Axtell 1996: 4). On top of the very simple world described below, they add in turn more complex rules (trade, reproduction, additional resources, culture…) and explore their consequences in terms of population growth, wealth distribution, carrying capacity, spatial spreading, and so on. For instance, one of their most exciting experiments consists in introducing a second resource (spice) and opening trading possibilities between turtles (x units of your sugar against y units of my spice). To go back to our 400 turtles in their new world, here is how Epstein and Axtell have pictured them.

Fig. 1. Spatial distribution of the population in Sugarscape 1 at time 0

4The physical environment is made of 2500 location units organized as a 50x50 units grid. Each location has the capacity for a fixed maximum amount of sugar. Some can grow 4 units of sugar, some 0 ones. On figure 1, the darker the spots, the more sugar they can hold (and actually do). The sugar level is highest at what looks like peaks in the northeast and southeast quadrants of the grid and fall off in a series of terraces. Figure 1 shows Sugarscape at time 0, after agents just landed and when each patch of land still holds its maximum capacity of sugar.

  • 3 All statistical distributions used in Sugarscape are uniform, rectangular distributions.

5The agents are pictured as stars and we see that they are randomly scattered on the grid and that no land unit can hold more than one agent at a time. Some agents have been lucky enough to land near one of the peaks of sugar while others have been dropped in areas of lower sugar capacity. Each agent is equipped with a vision (an integer randomly3 picked in the 1-6 range), a metabolism (a randomly chosen integer in the 1-4 range) and an initial wealth ranging from 5 to 25 units of sugar. Vision and metabolism are inherited genetic characteristics fixed for the life but wealth will vary over time. Metabolism refers to the amount of sugar the agent consumes per time step and vision to the number of patches the agent can see, starting from its position in the four directions: north, south, east and west. For instance, an agent equipped with a vision of 4 is able to see 4 patches ahead of its current location, in the four directions (but not in diagonal).

6The rules of life on Sugarscape are simple. At each time step, every turtle looks around (in the limits of its visual acuity) to detect the unoccupied location offering the most sugar to collect and then jumps to this site. If several locations hold the same maximum quantity, the agent selects the nearest one. All the sugar existing on the patch is then harvested and added to the turtle’s endowment. This being done, the turtle eats the amount of sugar it needs to survive (according to its metabolism) by drawing on its ”wealth” (which is accordingly decreased). In case there were not enough left, the agent would die. Then, sugar grows at a rate of one unit per time up to the maximum capacity of the patch.

  • 4 From now on, all data will come from our own version of the Sugarscape model. It is written in Netl (...)

7Let us now give life to all the turtles and observe what happens as time goes by. Figure 2 show the state of our settlement after 100 time steps4. We see that:

Fig. 2. Spatial distribution of the population in Sugarscape 1 at time 99

    • 5 In fact, with agents-based simulation, no two runs will give exactly the same results because of th (...)

    The population has decreased. In fact, from the 400 agents at start, only about 220-230 are still alive. The number 220-2305 corresponds to the carrying capacity of Sugarscape in the context of these behavioural rules.

  • The remaining agents cluster around the sugar peaks. One can even speak of two separated colonies, one on each mountain with a kind of ”no-agents’” land in-between.

8What is not visible in figure 2 is the fact that turtles have accumulated wealth. If at start, the median level of wealth revolves around 15 units of sugar it ends up, after 100 time steps, at a value between 114 and 134 units with a mean (calculated on 30 runs) at 119.

Sugarscape 2 and 3: introducing solidarity mechanisms

9Having reached this point, we will leave Epstein and Axtell at their experiences with migration, sexual reproduction, trade, war, etc. and explore other avenues never explored hitherto as far as we know. Indeed, if Sugarscape 1 is not exactly ”red in tooth and claw” (our creatures are peaceful gatherers, after all) it is nevertheless a world of ”everyone for himself”, where each individual not only pursues his own welfare without caring at all for others but, also, without being aware of the benefit he could get himself from improved cooperation and risk sharing mechanisms. Interestingly enough, if Epstein and Axtell immediately thought of introducing trade in their model, they didn’t consider the possibility of enriching Sugarscape with solidarity mechanisms and look at what they change in terms of carrying capacity, wealth distribution and survival chances of turtles according to their internal as well as external resources.

10In Sugarscape 1, an agent falling short of sugar because trapped in an overexploited area of landscape, and having insufficient endowment and/or having been unlucky in the genetic lottery is necessarily doomed to die. However, in many cases, if he could only wait, stay still during one or two time steps, the time needed for the patches in the neighbourhood to grow more sugar, he could perhaps eventually be rescued. Would it not be nice if he could receive some sugar from others who have plenty of it, for a limited period (ideally), the time necessary for his environment to recover and become more supporting (if possible)? Let us try something like that. Imagine our 400 creatures deliberating together and deciding to set up a kind of insurance system. For instance, instead of collecting all the sugar for himself each time an agent reaches a fertile patch, he would be ”invited” (actually, obliged) to divert a fixed fraction of it in order to fill a collective granary. On the other hand, when in need, he could benefit from a modest allowance in order to help him pass through his ”lean season”.

  • 6 Note that the contribution is levied on the total wealth of the agent, not on the income , the s (...)

11Actually, this is not a small modification with respect to Sugarscape 1 because it changes fundamentally the most important rule of the game, the one that commands agents foraging behaviour. First, the net benefit from every move will be reduced by the amount of the contribution to the common granary. Second, it is to be compared with the benefit of doing nothing which is equal to the amount of the allowance that could be granted in case of unemployment. In short, the agents now have the possibility not to work if the benefit is not worth the effort, without always running the risk of starvation. Introducing this in the Sugarscape program amounts to shifting from a one good world (sugar only) to a two goods world: sugar and leisure. In addition to wealth and metabolism, our agents will now have a minimum requirement in terms of rest and idleness under which they dont want to go as well as the possibility to accumulate free time. On the other hand, working time also has to be taken into consideration now that leisure is a valued good. The simplest way to do so is to consider working time as equivalent to the distance between the current location and the prospective one. So, for instance, a site located at a distance of 3 will take three units of leisure to be reached, and so on. Therefore, before making a move, the agents will calculate the net return of each accessible location taking into account the social security contribution6 and the allowance they would get otherwise, weighted by their marginal rate of substitution of leisure for food.

12In practice, if the net return of all possible moves, taking into account the food supply, the distance (working time), the contribution rate, the prospective allowance and the current state of satisfaction of both income (wealth) and leisure, is null or negative, the agents will just stay put. Then, provided the collective security stock is not empty, they will be granted the level of sugar fixed as ”unemployment compensation”, so to speak. Obviously, the dynamic of the situation will heavily depend on two parameters: the level of the compensation and the contribution rate. In fact, our experiences with Sugarscape 2 show that it is extremely sensitive to these initial conditions, some dramatic changes in the history of our settlement being brought by small variations in the ”institutional parameters”.

Fig. 3. Spatial distribution of the population in Sugarscape 2 at time 99

13Figure 3 shows what happened to our agents after 100 time steps under the conditions of a contribution rate of 0,14 and a dole of 2,2 units of sugar, which is the combination providing the higher carrying capacity. Comparing with figure 2, we see that the agents (now under the form of triangles) are more evenly distributed on the landscape. Though there are still more agents clustered near the sugar peaks than elsewhere, we don’t observe the kind of ”two colonies” settlement of Sugarscape 1. On the contrary, many agents are now located in less productive areas.

14There are other significant differences with Sugarscape 1 but we will discuss them later on, after having considered another social and institutional arrangement, i.e. the basic income scenario.

  • 7 It is fascinating to observe that in both Sugarscape 2 and Sugarscape 3 this mechanism allows a ver (...)

15Our third version, called Sugarscape 3, is close to the second one except that every agent is granted at each time step an unconditional amount of sugar, irrespective of his wealth, vision, metabolism, location and jobs opportunities (accessible and unoccupied patches with sugar to collect). The scheme is financed by a flat tax levied on all wealth above the basic income level, which is therefore always tax-free. It follows that while the wealth of any agent cannot be inferior to the basic income level, it can still be inferior to its metabolism requirements. However, as in Sugarscape 2, the provision can be temporarily suppressed (the amount granted becoming null) if the granary gets empty.7

If you were a turtle, which world would you chose?

16Multi-agents models are inherently stochastic. At the beginning of each simulation, the values of the turtles and patches’ properties are re-assigned on a random basis – with a different random seed – so that all initial conditions are necessarily different from one another. And, of course, the same holds also for any future state. Therefore, in order to get some confidence in the outcomes of the simulation, it is good practice to launch several runs for each simulated scenario and take as result the mean of the variables we are interested in. A scenario is just a set of specific values assigned by the modeler to some parameters of the model. As already indicated, the two crucial parameters here are the amount of the grant on one hand, and the tax or contribution rate on the other. The difficulty is to find the right values for these parameters.

17Table 1 summarizes the main outcomes of the most favorable scenarios for Sugarscape 2 and Sugarscape 3 in terms of overall survival probabilities. All the figures refer to the mean situation a t+99 calculated on 30 runs.

18Among the hundreds of possible pairs of values for the contribution rates and the allowances’ amounts, those reported in table 1 below are the ones that give the highest probability of survival at t+100 for the whole population though not necessarily for every subgroup. The second column shows the probability for an average turtle to survive at time t+100. The third column gives the same probability, but only for the ”lucky” ones. We consider as ”lucky” the turtles endowed with a vision greater than 3 and a metabolism less than 3. The fourth column presents the survival probabilities of the ”unlucky”, i.e. turtles with a vision inferior to 3 and a metabolism greater than 2. The ”middles” are the agents who are neither lucky, nor unlucky. Their probabilities of survival are given in the fifth column. The Gini coefficient, a measure of the degree of wealth inequality in each scenario, is in the sixth column. Finally, the two numbers in the first column refer respectively to the allowances’ amounts and to the contribution rates.

19We see that Sugarscape 2 doesn’t seem to give better prospects for the average turtle than the world without solidarity. But it is clearly more advantageous for the ”unluckies” whose survival chances are higher in almost every scenario than in Sugarscape 1. Note however how their chances drop between the scenario 2,2/0,14 and the 2,2/0,15 one. A difference of only 0.01 in the contribution rate is sufficient to entail a fall of their survival probabilities of 26%.

Table 1. Comparison between the three worlds

  • 8 Confirmed: when a result is too different from expected, taking account of adjacent values, we conf (...)

20The same phenomenon occurs in Sugarscape 3 where a change in the tax rate from 0,15 to 0,16 (holding the basic income fixed at 1,6) or from 0,18 to 0,19 at a value of 1,7 for the grant entails dramatic drops (up to 96%) in the life chances8 of the disadvantaged. This demonstrates how non-linear the behaviour of the system can be, despite its apparent simplicity. It also shows that for any given level of the grant, there is only a very narrow range of values of the tax rate which is favourable to turtles welfare.

21On the contrary, Sugarscape 3 offers better life chances for the whole population and also for every subgroup. It is also the most wealth-equalitarian. Under a veil of ignorance on how they are likely to fare in this new world they are flying to – e.g. as to of what use would be a sharp vision in a world where the sugar grows under the ground – a rational turtle would prefer to land on Sugarscape 3 than on any of the two others.

22How can we explain these better performances of Sugarscape 3 with respect to Sugarscape 2? Note that if the differences in probabilities between the best scenario for Sugarscape 2 and the best one for Sugarscape 3 look significant, the actual difference in raw numbers doesn’t exceed 10-12 average individuals and only about 3 unlucky ones. This makes difficult the search for ex post explanations. However, figs 4 and 5 give us some clues.

Fig. 4. Evolution of the ”GDP” per capita

Fig. 5. Evolution of total savings (wealth)

23Figure 4 shows the evolution of what can be called the ”GDP” (per capita) in the two worlds. By ”GDP”, we mean the total amount of food gathered by the turtles at each time step. We see that it is almost always higher in Sugarscape 3 than in Sugarscape 2. There is probably something like an ”unemployment trap” in Sugarscape 2. Remember that the turtles look around in order to find the most rewarding patch to jump in, but stay still and take the dole if there is no patch in their vision range that provides a net benefit, taking into account the contribution rate and the foregone allowance. This renders less attractive the patches with a low food potential (clearer areas in fig. 1 and fig. 2). On the contrary, in Sugarscape 3, because the grant is unconditional, less productive patches remain attractive and more economic activity take place.

24Another explanation has to do with the use of savings. In Sugarscape 1, agents keep accumulating in excessive, unusable amounts. Things differ in Sugarscape 2 and 3, as we see in fig. 5. In both cases, far from keeping growing with time, total savings decrease and then stabilize more or less. Of course, taxation and redistribution make the difference. However, wealth stabilizes itself at a lower level under the basic income hypothesis than in the social security one. We interpret this as a more efficient allocation (in terms of lives saved) in Sugarscape 3 than in Sugarscape 2.


25To sum up, in the Sugarscape universes, at least, a basic income would justify its characterization by Van Parijs as a marriage of justice and efficiency: ”For the introduction of a basic income would both boost the national product and distribute resources in a more equitable way”. (Van Parijs 1990:14). In our simulations, it competes successfully with a conditional allowance scheme on the ”economic growth” playground as well as on the social welfare and equity battlefield. However, this is not true for every possible pair of values of the income and tax levels. As table 1 shows, for any given amount of the grant, there is a quite limited range of tax rates for which the scheme is sustainable. Moreover, the higher the grant, the narrower the range of viable tax rates. However, this is not particular to basic income. In Sugarscape 2 as well, efficiency is guaranteed only within a narrow range of hypotheses concerning the dole and contribution levels. In the end, is Sugarscape 3 the best of possible worlds for our Logo turtles? This would be a hasty conclusion, especially knowing that we have forgotten another, simplest and more natural scenario: the possibility of individual altruism, generosity and care.

26Multi-agents models are metaphors of the real life, not representations of it. Or, if representations, only in the dramatic sense of the term. Each scenario simulation is a new re-presentation of a play for which roles are not written in advance but improvised according to the circumstances. The art of multi-agent modelling is somewhat like the art of playwriting in the Commedia dell'arte tradition. It consists of creating a situation, a scenery, populating it with characters (agents) to which capabilities, goals and motives are attributed, putting some means at their disposal, leting them act and seeing what happens. However, what makes the show enjoyable or interesting, is what it has to say about the ”real life”. This depends on the evocative power of the scenery, on the verisimilitude of the motives, on the identification potential of the characters.

27It is up to the spectator, not the stage director, to assess the quality of the play. Could the spectator empathize with the turtles’ fate and recognize something of his own existence in their destiny? Did the audience find Sugarscape’s landscape an evocative representation of our labour market with its hierarchy of differently accessible and rewarding jobs? Is the diversity of talents and needs something we, human beings, are sharing with those artificial turtles? Is our life also a competition for places and positions? Is not the impossibility to satisfy its basic needs by itself leading to a kind of social and psychological death? If the answer is "yes", then the spectator will have enjoyed the show. If not, he/she will probably find our turtles’ artificial life "a story, full of sound and fury, told by an idiot, and signifying nothing".



EPSTEIN, J.M. & AXTELL, R. (1996), Growing Artificial Societies, Cambridge, MA: the MIT Press.

GILBERT, N. (2008), Agent-Based Models, London: Sage Publications.

LI, J. and WILENSKY, U. (2009), NetLogo Sugarscape 2 Constant Growback model, Northwestern University, Evanston, IL: Center for Connected Learning and Computer-Based Modeling.

RESNICK, M. (1997), Turtles, Termites, and Traffic Jams, Cambridge, MA: MIT Press.

SCHELLING, T.C. (1971), 'Dynamic models of segregation”, Journal of Mathematical Sociology 1: 143-186.

VAN PARIJS, P. (1990), 'The second marriage of justice and efficiency', Journal of Social Policy, 19 (1): 1-25.

WILENSKY, U. (1999), NetLogo, Northwestern University, Evanston, IL.: Center for Connected Learning and Computer-Based Modeling.


1 Since Seymour Paperts implementation of LOGO at the MIT, the turtle is a kind of mascot and a trademark of many versions (notably the agent-oriented ones) of this programming language.

2 Actually, the history of multi-agents modeling didnt start with Epstein and Axtell's seminal book. Schelling (1971) for instance is an important landmark in the domain. For more information see Resnick (1997) or Gilbert (2008).

3 All statistical distributions used in Sugarscape are uniform, rectangular distributions.

4 From now on, all data will come from our own version of the Sugarscape model. It is written in Netlogo 5.0 - a special brand of the Logo programming language especially designed for agent-based modeling - and constitutes an enrichment and adaptation of Wilenskys Constant Growback Sugarscape program (Wilensky 1999, LI and Wilensky 2009).

5 In fact, with agents-based simulation, no two runs will give exactly the same results because of the randomness of agents characteristics at initialization and of agents time of activations at each time step. For instance, in thirty successive runs of the simple Sugarscape model described so far, the final population after one hundred time steps varied between 243 and 210 with a mean at 234 agents and the mode at 233. Also, the Gini coefficient of wealth distribution varied between 0,358 and 0,475 with a mean of 0,392.

6 Note that the contribution is levied on the total wealth of the agent, not on the income , the sugar gathered when moving to another location. This is a significant difference with institutional practices in most welfare states.

7 It is fascinating to observe that in both Sugarscape 2 and Sugarscape 3 this mechanism allows a very quick adjustment of the two quantities: contributions and transfers. However, the matching is quicker and smoother in Sugarscape 3.

8 Confirmed: when a result is too different from expected, taking account of adjacent values, we confirm it by running the scenario a hundred times instead of the usual thirty.

Table des illustrations

Légende Fig. 1. Spatial distribution of the population in Sugarscape 1 at time 0
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Légende Fig. 2. Spatial distribution of the population in Sugarscape 1 at time 99
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Légende Fig. 3. Spatial distribution of the population in Sugarscape 2 at time 99
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Légende Table 1. Comparison between the three worlds
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Légende Fig. 4. Evolution of the ”GDP” per capita
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Légende Fig. 5. Evolution of total savings (wealth)
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Paul-Marie Boulanger is an independent social scientist with degrees in sociology (Strasbourg & Louvain). He has been active in the fields of sustainable development, demography and social security (in developed countries), as well as food security and famine prevention in Africa. Regarding the latter, he supervised and designed the methodology of the Early Warning Systems (SAP) of famines in Mali, Chad, Mozambique and Madagascar. He heads the IDD (Belgium), a research institute that focuses on sustainability and well-being indicators, sustainable consumption, transition management, energy efficiency, etc. As a member of the Collectif Charles Fourier, he has been heavily involved together with Ph. Van Parijs in conceptualizing, analyzing and disseminating the idea of basic income.

© Presses universitaires de Louvain, 2011

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