Agent based simulations visualize Adam Smith's invisible hand by solving Friedrich Hayek's Economic Calculus
AAgent based simulations visualize Adam Smith's invisible hand by solving Friedrich Hayek'sEconomic Calculus.
Klaus JafféUniversidad Simón BolívarCaracas, [email protected]
Abstract:
Inspired by
Adam Smith and Friedrich Hayek, many economists have postulated the existence of invisible forces that drive economic markets. These market forces interact in complex ways making it difficult to visualize or understand the interactions in every detail. Here I show how these forces can transcend a zero-sum game and become a win-win business interaction, thanks to emergent social synergies triggered by division of labor. Computer simulations with the model Sociodynamica show here the detailed dynamics underlying this phenomenon in a simple virtual economy. In these simulations, independent agents act in an economy exploiting and trading two different goods in a heterogeneous environment. All and each of the various forces and individuals were tracked continuously, allowing to unveil a synergistic effect on economic output produced by the division of labor between agents. Running simulations in a homogeneous environment, for example, eliminated all benefits of division of labor. The simulations showed that the synergies unleashed by division of labor arise if: Economies work in a heterogeneous environment; agents engage in complementary activities whose optimization processes diverge; agents have means to synchronize their activities. This insight, although trivial if viewed a posteriori , improve our understanding of the source and nature of synergies in real economic markets and might render economic and natural sciences more consilient.
Key words : complexity, emergence, dynamics, bottom up, individual, freedom . Introduction
Adam Smith in his book The Wealth of Nations (Smith 1776) described the operation of themarket as follows: “
Every individual necessarily labours to render the annual revenue ofthe society as great as he can. ... He, however, does not have the slightest intention of promoting thepublic interest or is aware that he is promoting it. He intends only his own gain and is led, as inmany other cases, by an invisible hand that makes him promote a cause that does not form part ofhis intentions. This is not a disadvantage for society. By pursuing his own interest, he frequentlypromotes that of the society more efficiently than if his interest were the latter. I do not know ofmuch good dispensed by those who strive to represent the common good. It is not from thebenevolence of the butcher, the brewer, or the baker, that we can aspire to our dinner, but from theirattention to their own interests ”. In another part of the book he writes "
The greatest improvement inthe productive powers of labor, and the greater part of the skill, dexterity, and judgment with whichit is anywhere directed or applied, seem to have been the effects of the division of labor .... It is thegreat multiplication of the productions of all the different arts, in consequence of the division oflabor, which occasions, in a well governed society, that universal opulence which extends itself tothe lowest ranks of the people " These are beautiful descriptions of phenomena where theinteractions at the individual level bring as a consequence dynamics significant only at the sociallevel, without individual activity being conscious of it. It is a fascinating phenomenon but difficultto study using traditional experimental techniques. The discovery of the invisible hand of the market is a major achievement of humankind. Itrecognizes the absence of centralized social cohesive forces and discovers forces of the market thatexplain our social dynamics. More detailed studies of the effects of division of labor have beenpublished (Becker and Murphy 1994, for example), but all failed to grasp analytically in waysacceptable to the natural sciences, the emergence of synergies in economic markets due to divisionof labor. This inability to grasp numerically these phenomena has led some economists to concludeabout the analytical intractability of all details in complex economies. Prominent among these thinkers is Friedrich Hayek (1948), who coined the term "Economic Calculus" when referring to this fundamental analytical limitation of economic analysis. He said (Hayek 1961) “ [economics]has become too ambitious by applying standards of rigorousness ... to the empirical science ofconomics where there are definite limits to what we can positively now; that we shall see moreclearly what economics can do if we separate that logical groundwork – the economic calculus as Ihave called it – from its use in the empirical science of economics; and that, though this science isof great help in all-important issues of the choice of an economic order and of the generalprinciples of economic policy, its power of specific prediction is inevitably limited – limited by thepractical impossibility of ascertaining all the data – those very data whose utilization in theallocation of resources is the great merit of the market system ”.Beyond economics, the effect of the behavior of the individual on the performance of thesocial aggregate and how these interactions might led to the emergence of novel properties, can bestudied from the point of view of Complex System Science (Jaffe 2014). Specifically “artificialsocieties” or computer simulations of social dynamics (Tesfatsion 2006, Magliocca et al. 2014 forexample) have shown their worth in illuminating how the aggregate of various simple interactionsmight produce phase transitions and the emergence of novel properties of the system and even novelphenomena. These modern computer simulations, specifically agent-based simulations, allow us toexplore complex economic phenomena. Examples include the complexity of exchanges (Axtell2005), and money dynamics and banking catastrophes (Brummitt 2014). However, agent basedsimulations have not been incorporated in mainstream economics (Leombruni and Richiardi 2005),nor have they unveiled until now in detail the working of the invisible hand of the markets. Agentbased simulations are a powerful tool in clarifying fundamental aspects of the working of complexeconomic phenomena (Jaffe 2014). Its potential in visualizing fundamental concept in very simpleeconomies will be explored here so as to avoid the limits " of ascertaining all the data whoseutilization in the allocation of resources is the great merit of the market system" (Hayek 1911), andwhich are not easy to determine analytically in more complex economic settings.Simulations with Sociodynamica allow for exploring abstract virtual economies that are farsimpler than real ones but already so complex that the experimenter may looses the integral viewover the interactions between environment, agent behavior, pricing mechanisms, and environmental heterogeneity in the market. This might happen in simulations of economies were realistic price dynamics were included that showed that division of labor was the strongest predictor of successfuleconomic performance (Jaffe 2015). However, it was not clear in these simulations, if this effect ofivision of labor was exerted through the price dynamics of the economy or through other means. Inorder to pinpoint the source of the synergies achieved by division of labor, the model was simplifieduntil the emergent effect of division of labor disappeared. Stripping out effect of pricing on themarket dynamics did not eliminate the effect of division of labor. This allowed us to follow in detailthe features that make division of labor work, making the system amenable to analytical analysis,solving the required "Economic Calculus" (Vaughn 1980) for this simple virtual economy.
2. The Model
The agent based computer simulation model Sociodynamica is a freely available agentbased simulation model written in Visual Basic that has previously been used to study the effect ofaltruism and altruistic punishment on aggregate wealth accumulation in artificial societies (Jaffe2002a, 2004a, 2008, Jaffe and Zaballa 2009, 2010) and to grasp the dynamics of complex markets(Jaffe 2002b, 2004b). These models are completely mechanical in nature, and individual incentivesmay emerge trough an evolutionary process that makes agents with the right combination ofincentives or behaviors survive, and those with the wrong combination, to become eventuallyextinct. The features revealed by Sociodynamica are very similar, and in cases identical, to thoserevealed by Sugarscape, an agent based model developed independently by Axelrod (1997); or themodel developed by Axtell (2005). In all three cases, Walrasian solutions in which an auctioneercentrally computes prices cannot be made more efficient than the decentralized alternatives basedon free and heterogeneous agents making these decisions. These results supports the proposition ofAdam Smith's that markets are ruled by an Invisible Hand that coordinates the different kind oflabor rendering markets efficient. Specifically, simulations in complex economic setting showedthat omnipotent agents performing all tasks, produced less aggregate wealth than simulations wherethree different agents performed different tasks, such as farming, mining and trading (Jaffe 2015).This counter-intuitive result was partly due to the fact that optimal prices and conditions for tradewere different for each agent, depending on its spatial position in the virtual world. Omnipotentagents had to assume average solutions to balance their different tasks. Therefore, they never traded at optimal prices and optimal quantities according to their spatial position. Here the model was simplified, until the effects of prices dissipated, to reveal fundamental economic features that allowthe emergence of synergies from division of labor.he model simulates a virtual society of agents who farm and mine for foods and mineralsrespectively, analogous to the model "Sugarscape” by Axelrod (1984), and also trade their surplusaccording to different economic settings. The agents inhabit in a continuous flat two-dimensionaltoroidal world (see Figure 1) that was supplied with patches of agricultural land (“sugar” or “food”)and separate non-overlapping patches of mines (“spices” or minerals). Diverse agents weredistributed at random on a fine-grained virtual landscape with resources. Simulations depended onthe type of movement of agents, and thus, to simplify interpretation of results, agents weresimulated as immobile entities. Their individual utility function was defined by two resources. Eachtime step, any agent that happened to be located over one of these resources, acquired a unit of thecorresponding resource, accumulating its wealth, either as sugar or food (G ) and/or as spices orminerals (G ). Agents spend a fixed amount of each resource in order to survive, consuming each ofthem at a basal constant rate (default value was set to 0.1 units of the corresponding resource at eachtime step). Both resources were consumed and metabolized similarly, but food was 3 times moreabundant than minerals (the size of the patch for minerals was set to 100 x 100 pixels and for foodwas 300 x 300 pixels). Each patch remained in the same place during each simulation run and theresources inside them were replenished continuously. Agents perished when they exhausted any ofthe two resources. Success in gathering and trading resources was defined by variables thatproduced behaviors that made them unable to compete successfully for resources. These variablesincluded type of movement, spatial positioning, price thresholds for selling each of the resources,price threshold for buying the resources, and type of agent. During the simulation, natural selectionweeded out unsuccessful combinations of these variables. The total population of agents wasmaintained constant by creating the required amount of new agent necessary, each with randomlyassigned initial parameters. Initial parameters were the type of agent, the random spatial positionand the initial amount of money used start trading resources (the default initial value was set to 10units of money). The amount of money for each agent varied according to its trade balances. Agentsgain money when selling food and/or minerals and lose money when buying them. Agents traded the resources they possessed with other agents. In order to trade, they had to find a partner with the desired resource, and they had to have agreement over prices. The tradecould be among any agent in a population of omnipotent agents without “division of labor”. Whenimulating division of labor, agents specialized in collecting food or collecting minerals, orcollecting neither but engaging only in trade. Here, agents were subdivided into three categories.Farmers which specialized in collecting only resource 1; Miners which extracted only resource 2;Traders specialized in trading minerals for food when encountering a farmer, and food for mineralswhen encountering a miner. Food collectors traded only with mineral collectors and traders, mineralcollectors traded only with food collectors and traders, and traders could interchange resources withall types of agents. Trades were allowed only between agents spaced at a distance not larger than the“contact horizon” of the trading agent. Each time step, all buyers searched for potential sellers of therequired good by contacting randomly up to 10 agents in the area defined by this contact horizon. Iffinding a seller with the wanted goods at or below the price defined by the buyer, a trade wasexecuted using the price of the seller. Trades were limited to the amount of money available to thebuyer and the amount of goods possessed by the seller, unless credit was simulated. Variation of thiscontact horizon allowed to simulated different levels of globalization or integration of economicagents. The effect of the degree of globalization (or the size of the market) on the economy can thusbe measured quantitatively, a feature that is not possible with real economies (but see Campos et al.2014). Prices were initially assigned to each agent for each resource at random from a range ofvalues defined by the experimenter, and then varied according to supply and demand as experiencedby each individual agent. That is, at the end of every time step, after finishing a tournament of tradesin the market, each selling agent attempting to sell parts of its excess of resource that could not finda willing buyer because of the price it asked for, reduced its reference price by an unit. And eachbuyer that could not find a seller willing to sell the desired resource at the desired price increased itsreference price for that resource. In this way, each agent maximized its self interest by selling eachresource at the maximum price possible and buying at the lowest.Various processes were simulated. A first process of the simulation was the balance between income (I) of resources (r ) and their consumption (C). For survival, agents were required to conform to Ir > Cr (1)Income can be either by direct gathering (G) or by trade (T)r = Gr +Tr (2)Here each agent has to balance two resources in order to survive. I simulated a utility function (U) so that U had to remain positive for the agent’s survival and:Ur = (Gr + Tr) – Cr (3)A second process of the simulation was the dynamics of traded resources. These resources can increase or decrease, according to the balance of resources bought (B) and sold (S)Tr = Br – Sr (4)The amount of resources bought and sold depends on the availability of money (M) and the price (P) paid for the resource by the agent (a)Br = M a / Pr a (5)Sr = M a / Pr a (6)The amount of money of agent (a) depends on the amount spend buying (Mbr) and the amount gained selling (Msr) resourcesM a = M a a0 stands for the initial amount of money supplied to each new agent jUr was calculated every time step for the population of agents (a) so that the total accumulated of wealth for each resource (Wr)Wr = Σ a Ur (8)Agents with U <= 0 or U <= 0 were eliminated and substituted by new ones with default properties, as an analogy of broken companies that are replaced by new start-ups.Here we focus on the age of the agents as the most relevant variable for assessing the benevolence of an economic system. The average age is a measure of the probability of survival of individuals in the population, but other measures are possible (Jaffe 2015). The aim was to pinpoint the features that allowed the emergence of the synergies of the market due to division of labor. Simulations of virtual worlds with one type of agents (Omnipotent agents), two types (Farmers + Miners), and 3 types (Farmers + Miners + Traders) allowed determining the effects of increasing omplexity of labor structure. Simulation with homogeneous and heterogeneous distribution of resources allowed to asses the effect of the environmental complexity, and simulations with different contact radius provided insights to the importance of synchronization between trading agents. A longer and more detailed description of the simulations is provided in Jaffe (2015) and the detailed program in Visual Basic is available in the help feature of the program. Simulations can be run with parameters choose at will by downloading Sociodynamica at [http://atta.labb.usb.ve/Klaus/Programas.htm]. Default values used here were: Contact horizon for transaction = 200. For both resources, Initial prices = 3 units, Reserve units not traded = 1. Amount of resources metabolized per time step = 0.1, Amount of resources collected per time by agent = 2. Number of agents = 500, maximum number of trades per time step = 10.
3. Results
Figure 1 shows two examples of the output of simulations with free prices after 200 time steps. The upper figure shows the virtual world when simulating omnipotent agents; the second figure reflects the outcome when division of labor (Farmers + Miners) was included in the simulations. The figures reflect the effects on the economic dynamics of introducing division of labor. In the figure with omnipotent agents, agents over mineral fields are smaller (have less wealth)than those over fields with food. In contrast, the figure from simulations including division of labor showed that miners over field of minerals were very wealthy, and so where many farmers over field with food. The price agents were willing to pay for minerals was higher among farmers (red bordersin Figure 1B) and lower among miners (blue borders in Figure 1B) when division of labor was simulated. In the case of the omnipotent agents, prices agents were willing to pay for minerals or food seemed to be randomly distributed (mix of colors in borders of agents in Figure 1A). This example reveals that omnipotent agents made sub-optimal trading decisions. They sold the resource hey had accumulated in more abundance to any other agent willing to take it; whereas specialized agents (Figure 1B) traded only the resource they were collecting; that is, Miners only sold minerals to Farmers and Farmers sold only food to Miners. The trading patterns of omnipotent agents produced less wealth in the long term that that of specialized agents, even though the cognitive complexity of the algorithm omnipotent agents used was more complex.
Figure 1 : Representation of the landscape of two virtual economies. Figure 1A shows a result from a simulation with free prices in an economy collecting food and minerals by omnipotent agents; whereas Figure 1B shows the same but for agents specialized either in mining or farming. AB Bright green field is covered with “Food”; darker green field is covered with “Minerals”; thelightest green is devoid of resources. Each agent is depicted as a colored sphere. The color of the body of the sphere describes the type of agent: Farmers are yellow, Miners are red, and Omnipotent agents are black. The width of the bubble is proportional to the amount of food and minerals accumulated by the agent and the height by the amount of money the agent possesses. The thickness of the border of the sphere is proportional to the perceived cost of living calculated as Food Price + Mineral Price and the color of the border rage from blue to yellow. The more reddish or even yellow the higher the ratio between the Food price and Mineral price. Agents with red and yellow borders pay more for minerals, whereas those with blue or black borders pay less for minerals compared to what they are willing to pay forfood.
Table 1 : Average age accumulated by agents after 200 time steps in simulations exploring the effect of fixed or free prices, with omnipotent agents or with agent dividing labor. Maximum contact radius of agents was 200 pixels. Each data is the mean of 100 simulation runs.
Omnipotentagents Division of labor 2Farmers + Miners Division of labor 3Farmers+Miners+TradersFixed Prices
Free Prices
Table 2:
Average age accumulated by agents after 200 time steps in simulations exploring the effectof homogeneous economic environments. Maximum contact radius of agents was 200 pixels. Each data is the mean of 100 simulation runs.
Omnipotent agents Division of labor 2Farmer+Miner Division of labor 3Farmer+Miner+Trader
197 ± 4 198 ± 4 176 ± 7Introducing the possibility of different motility among agents also affected the difference between between simulations of only omnipotent agents and simulations where division of labor occurred: Selection tended to favor mobile traders and immobile farmers and miners. Results suggested that the division of labor, in order to work properly, required an adequate coordination of actions or synergy between the agents. For example, omnipotent agents sold whatever resource theyhad, independently of what they collected, whereas farmers and miners only sold the product they collected and bought the one they did not collected. Also, traders in simulations with no mobile agents seemed just to introduce noise in the economy as they were not allowed to behave differentlyfrom miners and farmers. In Figure 2 the effect of an improved ability to trade is shown. Here, the maximum contact radius determining the distance at which potential traders could be spatially separated was varied. As expected, results show that at greater maximum contact radius, the economy performed better. This trend, however, was not linear. Prices had a very strong non-linear relationship with the contact radius. This relationship is strongly depended on the topology of the resource distribution simulated, as was shown before (Jaffe 2015).
Figure 2 : Effect of the contact radius on the economic performance of the virtual economy, measured by the average age (blue circles, left scale) and average price of food red squares, right cale) accumulated by agents after 200 time steps in simulations with free prices and with division of labor. Conclusions
The results presented here showed how this relatively simple simulation model of a virtual economy, identified features that are indispensable for making the emergence of synergies due to division of labor possible. The most important Conditions for synergy to arise are:1- Spatial or temporal heterogeneous environment and/or behavior2- Complementary activities with divergent optimization3- Synchronization of one or more heterogeneities The first feature is interesting in that it recognizes that the complexity of labor structuremirrors the complexity of the economic environment where it works, and vice versa . This feature isa consequence of economic activity being molded by the environment to which it has to adapt. Inhuman societies economic wealth of a country and economic complexity are linked (Hausmann andHidalgo 2014). Economic complexity, of course, can only be achieved with complex division of labor. he second feature is illuminating as it allows predicting when division of labor mightimprove economic activity and when not. Division of labor might prevent inefficient trades and/ormight make more efficient trades possible. Tasks, which converge in skills, might not requirespecializations, whereas tasks that require very different types of skills will benefit more of divisionof labor. It can be argued that more intelligent agents might be capable of performing several tasksand thus, rather that division of labor, economies benefit from more complex or intelligent agents.This might be true but complexity and intelligence have their costs and might be sub-optimal ifdifferent simple agents can handle the problems with higher efficiency. This seems to be the case inthe social evolution of ants, where a negative correlation between brain development of individualsand social complexity was evidences (Jaffe and Perez 1989). The third feature is possibly the more difficult to manage in real situations. Experienceshows that on-time synchronized productive chains allow specialization of tasks to be moreproductive overall; whereas low division of labor is more tolerant to inefficient supply chains. Thesefeatures explain many a difference between highly developed economies and ones with incipientindustrialization and poor services. The identification of these 3 features as fundamental in allowing division of labor to eliciteconomic synergies might seem trivial. But browsing the literature, a great number of reasons havebeen postulated to explain the synergies created by economic markets. The problem seems far fromsolved (see Kochugovindan & Vriend 1998), Even if found to be trivial a posteriori , the simulationshelped to identify the relevant features and discard superfluous ones. Bowles (2009) for example,defined the invisible marker mechanism as a Nash equilibrium and its Pareto optimal, where the selfinterest of each actor yields an outcome that maximizes the well being of each. Here we reveal inmore detail how this can be achieved. The three features unveiled here seem to be very general,relevant to system dynamics, biology, human society, and real economies. Possible empiricallyfalsifiable predictions based on these tree features are: 1- Division of labor should be more developed in societies that exploit a greater variety of resources.
2- Better communication and economic instruments are provided by more sophisticated financialsystems which in turn provide better opportunities for synergies between economic actors in moreomplex economies. Novel communication technology, such as the Internet, can also broaden thecontact radius of economic agents improving synchrony. 3- More division of labor leads to more incompatibilities between skills required to perform themand thus to more diverse specialized education.4- Larger contact horizons or more globalization improves the synergies unleashed by division oflabor as they broaden the scopae for more diverse interactions between economic agentsEmpirical evidence found so far would support these predictions (examples for each of thethree point are respectively: Hausmann and Hidalgo 2014, Mantegna and Stanley 2000, Dale 2005).Though research purposefully designed to answer these questions should be designed. We know thatdivision of labor is related to synergies associated with fundamental aspects of social systems inbiology: Thermodynamic studies showed that the amount of entropy of ant societies and the levelsof division of labor are related (Jaffe and Heblin-Beraldo 1993). In human society, economicsynergy and division of labor have important relationships. Research showed that more complexeconomies requiring more division of labor accumulate more wealth and produce higher economicgrowth (Hausmann and Hidalgo 2014). Empirical data showed that an even better predictor thaneconomic complexity for future economic growth in developing countries is the scientificknowledge estimated by the amount of academic activity (Jaffe, Rios, and Florez 2013). Even morestriking, the type of division of intellectual activity in a country is a much better predictor than thetotal complexity or the absolute amount of academic research performed (Jaffe et al. 2013). That is,division of academic labor that prioritize basic natural sciences over applied sciences and socialsciences, is much more efficient in producing future economic growth. These results, in the light ofthe findings of the present simulations, show that much remains to be learned about the quality andquantity of division of labor and its effect on economic activity. More interdisciplinary research isneeded to improve our understanding of this very fundamental phenomenon.This exercise shows that computer simulation of simple economic agents can generate anon-linear dynamics that resembles real life features of known economic system. Simulations of very complex systems produce complex results that may become intractable even with sophisticated statistical analysis. Here we overcame this limitation by focusing on very specific and fundamentalproblems. The simulations presented revealed fundamental features that allow division of labor toreate economic synergies. This insight was possible by solving some aspects of the "EconomicCalculus" (Hayek 1991) in a very simple system. This feat is impossible in complex real situations,but the insights gained in simple systems help in understanding synergies in more complex ones.Simulation models, besides having a potential in experimental economic research, are a fantastictool to make complex phenomena visible to human understanding and thus should have a potential,if properly adapted for that purpose, in didactic games for teaching economics at all levels ofeducational and academic specialization. Science learned through games based on simulationsmight reduce self-serving cognitive biases among lay people, professional practitioners and decisionmakers, improving the rationality of our society and thus, hopefully, it’s economic performance.
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Acknowledgments:
Thanks are due to Stephen Davies and Juan Carlos Correa for helpful comments on previous versions of the manuscript ppendixSociodynamica creates a virtual society where a gents exploit and compete for resources and share resource 1 among them, according to the settings defined by the internal parameters and the externalparameters. The agents may acquire renewable and non-renewable resources trough work; they mayaccumulate those resources and commercialize them. At the same time, agent may acquire resourcesthrough commerce. Global Parameters
POP:
Number of agents (no)
TAR:
Aggregate total wealth accumulated by all agents
Simulation logic
Each time step:
Do simulation loopMatrix: Eliminate variable types previously defined Eliminate agents with wealth = 0 (par 11) Increment age agent(i, 7) = agent(i, 7) + 1 Use of resource 1 and 2 agent(i,11)- BRC1; agent(i,12) – BRC2 Assessment of GDP GDP = GDP + agent(i, 11) Show and Plot
Plot
Shows the agents according to their total resources (Food+Money) indicated as the sqr of the diameter. The high of the agent is proportional to the total wealth of the agent's money.The color of the bubble depends of the type of agent as indicated at the left bottom of the screenThe thickness of the border is proportional to the perceived cost of living (Prize for food + Price for minerals).
The color of the border is more reddish or even yellow the higher the ratio MinPrice/FoodPrice.
Blue borders indicate that food prices are higher than mineral prices.Black bar at the bottom indicates a length of 100 pixel
Internal parameters:
General parameters (number in parenthesis indicates the column in the master matrix)
X (0) Spatial dimension1 Y (1) Spatial dimension2 CRa (2)
Contact Radius or Contact Horizon
Maximum distance at which interchange between agents may occur (Altruistic interchange for example)Mo (4)
Type of Movement
Type of spatial displacement: NO MOVEMENT
Characteristics of agents
Age (7)
Age
Age of agentWT (10)
Wealth-Money
Total capital in liquid moneyWFo (11)
Wealth-Food
Amount of resource 1 (Renewable). If WFo(i) = 0 then agent i starves (i is eliminated)WCo(12)
Wealth-Commodity
Amount of resource 2 (Minerals or Non-Renewable resource)
Dept (13)
Dept
Accumulated Dept
Well (19)
Well-being
Amount of resources 3 = r1 * r2 * GainTAg (20)
Type of Agent
Specialization or task of agent
External Parameters
General
Initial Nr. of Agents (ino)
Optimum Population Size (ops): Maximum number of agents aimed at through ssconst
Simulation Scenario : production of new agents (ssconst):0: New agents are created each time steps, until the number indicated by ops is achieved. New agents are assigned internal parameters at random
Proportion Culled (PC). The proportion of agents killed randomly when population in excess of ops
Dangers , other than starvation danger. Large values increase random selection; large WCo reduces this.
Fitness function : Agents, in order to continue in the virtual word, had to satisfy each time step the rule: 100 * Rnd / (amount of resource 2) / (mean wealth of resource 2) < 1000 * Rnd /
Dangers: probability of being eliminated in random selection events
Resources 1 and 2
Resource 1 (provides WFo) and 2 (provides WCo)Number of patches of Resource (
RNR) Number of resource patches
Size of patch of Resource (SNR) Maximum sizes of each patch (but see Mutation)
Degradation of Resource due to consumption (DNR) Amount lost due to consumption (RD)
Distribution Pattern of Resource (DPR) Resource is distributed: 1: Fixed size, randomly distributed2: Fixed size, centeredElse Random size, randomly distributed
Basal rate of metabolism (BRC) Amount of resource passively used-up (b)
Efficiency of consumption (EfC) Amount of resource assimilated. When EfC>10 then productivity is simulated: Agent collects = (EfC-10)*price (either for resource 1 and/or 2)
Frequency of change in distribution (
FCh) Frequency in t-steps distribution changes
Consumption of resource : Rate of exploitation: resource = resource – DNRBRC: Wearing or passive use of resource agent- BRCResource 1 can be modeled as a renewable resource (agriculture for example), whereas resource 2 as a non renewable resource (mining for example), by assigning DNR = 0 and DNR = 1 respectively
Food Reserve (FR): Minimum amount of food needed for agent to engage in transactions ofany kind
Min Food for Reproduction (MFR): The amount of food that need’s to be accumulated before reproduction can start when Simulation Scenario is 1 or 4
Type of economy (EconoT) : No Barter nor any other interactions except taxes : Barter : with no money > 1 : Money as Species. If
Price adjust = 0 then Fixed pricesIf
Price Adjust > 0 the Prices are determined by demand: agents not selling decrease price by one unit; agents not finding seller from which to buy increase price by one unit. : + Financial: Traders lend money. : + Agents finishing a successful sale, increase price by one unit : + Successful buyers decrease their future asking price by one unit : + As in EconoT 4 and 5 : + As in 2, 3, 4 and 5: As in 2 and 3 Agents pay Taxes: Taxes collected are increased synergistically by Taxpool * SSTax prior to their distribution.
Food price : in integer units
Mineral price : Price of commodities in integer units