Juliette Rouchier, Martin O'Connor, François Bousquet (2001)

The creation of a reputation in an artificial society organised by a gift system

Journal of Artificial Societies and Social Simulation vol. 4, no. 2,
<https://www.jasss.org/4/2/8.html>

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Received: 01-Nov-00      Accepted: 01-Feb-00      Published: 31-Mar-01

Abstract

This paper describes simulations in an artificial society in which autonomous agents exchange gifts. In this society agents perform simple acts that are looked at by the others and are analysed so that a common image is created for each agent (a reputation). The model is based on numerous descriptions of non-merchant exchange systems, which are very interesting for ethnologists as well as for economists: they appear to be important for circulation of goods and to insure the reproduction of social links and values. In the system built the agents must make a gift at each time-step. There exist two kinds of gifts and two corresponding kinds of reputation: the agents either give to share or to be prestigious. Since gifts are received according to status, receiving a gift is as important for a reputation as making one. Each agent is characterised by its ''motivation'' to acquire the reputation of being a sharing agent or a prestigious agent. It is also characterised by its ''esteem'', to decide if it will be able to do the gift it wants to do for a time-step. These two characteristics of an agent can be stable during the simulation, but can also evolve according to its history. We study here the different patterns that can appear in the societies, in terms of generation of reputation, and of histories over time. A huge range of these patterns can be observed, depending on the choice made for the parameters. In some cases the agents cannot be individually distinguished, in other cases they can: but, in any case any individual behaviours that emerge have to be sustained by a collective specification that points out more or less the way agents value each reputation.

Keywords:

Gift, reputation, multi-agent systems

Introduction

1.1

Ethnologists are usually very interested in the study of gift exchanges which structure society in a deep way and are good tools for the reproduction of habits and values (Godelier, 1996). As a first consequence, the gift creates a link between people and it is accepted in almost all cultures that a gift has to be given back. The individual who gives shows that he is willing to engage in a relation and that he trusts the other to understand the message and give back to keep the interaction going. The reciprocation creates a never-ending loop of encounters that establishes a stable relation. In some societies, one has to give more than one received and the relation can then turn out to be competitive. Each individual wants to prove that he cares so little about material goods that he gives them away with no regret. This leads to a prestige fight where each individual challenges the others to prove that he is more able to give (Boas, 1966). Another aspect is the fact that the gift is a good means of redistributing goods: more specifically it is very often the role of the chief and of rich people or rich members of the family to be generous so that poor people can survive, and this is recognized by the one who knows about the gift (Nicolas, 1986). In that context, giving back is not necessary^[1].

1.2

The work presented here was aimed at studying the creation of reputation in an artificial society where agents perform giving. The reputation of an agent is here the common image that the group has of it. We decided to use multi-agent systems as a way of building our artificial society. This kind of systems appears to be effective in representing interacting agents and for observing the result of the repetition of their interactions in time (Ferber, 1999; Bousquet, 1994). Moreover, it has been widely recognised as a good tool to question the link between individual actions and the society's global organisation (Doran et al., 1994; Gilbert, 1995; Bousquet et al., 1998; Rouchier et al., 1998).

1.3

We decided not to focus on the reciprocal characteristics of the gift since we have studied this previously. In that study we analysed interdependences in a group due to gifts and counter-gifts, observing the hierarchies that can be induced by inter-individual links (Rouchier, 1996). In the society we created, the information that agents have about each other are gathered only through their own interactions. When an agent gives to another one, the receiver is indebted and has to give back a gift of higher value. At each time step the agent first makes counter-gifts and then can give to new agents to force them to give back. There, the relation is never-ending, since once an agent gives back more than it received, the other turns out to be its debtor. At each time-step an agent knows just who are its debtors, to whom it is indebted, how much is owed and the time the debt has existed. Using this information it builds an image of all agents known and can deduce an ordered relation among them, which is its image of the society. It knows then its own position in the group. The debt is then the foundation of a structure, in which each individual is interested mainly in having a great number of dependents (Weber, 1985). There also exists an "objective" observation of the group that exhibits another hierarchy by comparing the real number of regular dependents and of money owned over a certain time period. In this study, it was striking to discover the huge differences between the global "objective" hierarchy and the individual representation. Indeed, the encounters being randomised, and indebted agents trying first to get rid of their debts, some of them would know a very limited number of others. One conclusion of the work was that we had to find a way to have the agents be able to use global representations to build their image of themselves.

1.4

In the present work, we wanted thus a common representation of each other to be shared among agents (here called a reputation). As we said, the gift is important in terms of redistribution of goods and in terms of prestige for each individual in a society and here we tried to capture these two aspects. In the society the agents share the same information (all acts are known by all) and the same process of evaluation of actions. The only activities are giving (one gift at each time-step) and working to get enough money to give. The evolution of reputation depends on several parameters of the group that can be tested through simulations. An agent is characterised individually by that reputation, but also by the way it chooses its actions. Two elements help define that process: its motivation (make gifts either to get prestige or to share), and its esteem (belief in the ability to make gifts that are acceptable to the group). The agents can evolve by learning from their former results and their reputation in the group, and change their motivation or their self-esteem. The individual history of each agent is defined by the evolution of its reputation, its motivation and its esteem.

1.5

When choices are fixed for each agent, it is possible to build a reputation that does make sense: one can for example observe societies with stable distinct groups, like elites constituted of agents that clearly have higher prestige than the others. A link was made between reputation and motivation for prestige and between a local perception of success and failure and the esteem. This double loop seems to give an even greater coherence to the society although some surprisingly complex patterns can still be observed.

Model and implementation

Aims and method

2.1

We wanted here to follow the idea of ethnologists who state that exchanges of goods create symbolic values in a group. We elaborated an artificial society to study the creation of a reputation for individuals thanks to the existence of exchanges. The inspiration comes from the numerous examples of societies where reputation is essential to individuals: they try to renew it through ostentatious behaviours, giving being the most often found (Mauss, 1968; Boas, 1966; Malinowski, 1922; Nicolas, 1986; Godelier, 1996).

2.2

The choice was to use a multi-agent system to create the artificial society. A multi-agent universe is constituted of an environment with characteristics of evolution that contains objects and agents. Classically, in a multi-agent simulation, one defines agents as entities that are autonomous and active and have a representation of their environment. Each agent is then defined by the way it perceives its environment and builds a representation of it, the actions it can perform and the process through which it chooses its actions according to its knowledge. Among the actions that the agents perform, some are interactions with others (for example sending messages, giving, asking, acting upon). A simulation is a series of time-steps during which the universe evolves and the agents act and have their representation evolve by perceiving their changing environment. When one builds that kind of system, one also has to wonder, usually, about the relevant information to observe in order to characterise the dynamics at a global level.

2.3

To observe a differentiation that could be analysed like a structure, a multi-agent system has already proved to be a good tool, not only in our previous research project. In the EOS project (Doran et al., 1994), in a society of hunter-gatherers (one of the first actually built to study societies), the position of chief is attributed to the one to whom the others directly ask to associate with (Doran, 1995). Some agents can be chief forever, some form different groups over time, some groups absorb others and thus the hierarchies add to each other. The agents in that case did not consciously make the evaluation of a hierarchy. Here, the evaluations that the agents have of the others and of themselves only exist through comparisons in the group. All agents have thus a clear and conscious understanding of the order of the society.

2.4

In our society the universe is constituted of agents that make gifts and work when they lack money to make a gift. An agent acts according to two parameters: the "esteem", or self-confidence (an image, or internal representation, of its ability to act like the others), and its "motivation" to get prestige or rather to show its sharing ability. As a result of acts performed in the group, reputations evolve. The agent perceives the reputation of everyone and this perception has an influence on its characteristics for choice.

2.5

As we saw before, one important assumption here is that each agent does not worry about to whom its gift is going to go or whether it will get one in return, but is just motivated to participate in the system. Since the gift is seen as compulsory and agents try to conform to that, there is anyway an important circulation of goods. In real societies, when giving is important, the value of an individual in the society is not related to his possessions but to his ability to give away (Weber, 1985), and this is why it was chosen here that only the participation in the common dynamics grounds the evaluation of the agents.

2.6

In this study, we wanted to stress the circularity between the choices made individually and the social situation in which the agent is. The hierarchy reveals the recent history of exchanges that took place in the society; conversely each act is strictly influenced by the social order. The multi-agent system was established in order to perform simulations that would enable the creation of that circular process.

Assumptions of the model

2.7

We emphasize here some elements that are expressed in the definition of the dynamics:

• When an agent makes a gift, it gives all the money it has at the beginning of the time-step. For the next time-step, its possession is the amount it received from gifts. There are two kinds of gifts that the agents offer, "sharing gifts" and "prestige gifts". The "sharing gifts" make goods circulate and people feel part of a group. The "prestige gift" show that one is not interested in possession at all and (as described by Boas for the Potlatch) and must be an important loss for the one who performs it. There is a minimal amount that agents have to give away for each kind of gift, which is either the common "consumption value" or twice that value, which is constant for a simulation.
• Since agents make prestige gifts to those that they consider as prestigious, receiving a prestige gift indicates that one is recognised as having prestige. Sharing with another agent also indicates that one recognises its integration in the group. Hence when a reputation is set, the ability to act with the others is evaluated (the ability to make gifts) as well as the reception of gifts. Each kind of exchange in which the agent is involved is translated into a different kind of reputation.
• The ability to make a gift is influenced by how the agent considers itself in the group and some agents consider themselves as less able than others to give. More precisely, it seems unlikely that a very badly integrated agent should often be allowed to make a gift to the most prestigious ones. A priori, the more integrated, the more an agent may participate in the social dynamics: this is why the esteem was linked to the reception and emission of gifts.
• All the agents do not have the same interest in prestige and integration. Hence some are more motivated to share with the others, whereas others look for prestige. Here, the motivation was considered as dependent of the position in the group in a very direct way that tends to reinforce the actual situation.
• All the assumptions about choices for the agents are not absolutely deterministic. We wanted the rules of behaviour to be constraints, that could be very strict or not, but that would leave some opportunity for the agents to "misbehave" according to their social position. To express that tendency a random element was introduced in all decision processes. It is equivalent for all, hence all agents are supposed to behave the same way towards social rules.

2.8

Taking inspiration from all these conceptual processes, we implemented the model (in Smalltalk, using Visual Work 3.0).

Agent and definition of a time-step

2.9

The society consists of a group with 50 agents, each characterised by:

• its prestige reputation
• its integration reputation
• its rank (from 1 to 50: the rank 1 being the agent with the highest reputation for prestige)
• its motivation to get prestige (first choice parameter), a value between 0 and 10 (its motivation for sharing that can be directly deduced: motivation for prestige + motivation for sharing = 10).
• its esteem (second choice parameter) between 0 and 10.

2.10

All of these parameters are defined socially as well as individually, and correspond to the criteria already described.

Figure 1. Attributes and actions of the agents, the group and the universe to which they all belong

2.11

In this system, all agents consume the same minimal amount of money at each time step. They earn money by working (which gives twice the minimum value for consuming) and/or by receiving gifts. They choose what they want to give depending on their choice parameters (motivation for prestige and esteem) (Figure 2). The esteem is the ability that the agent feels it has to participate in the exchange dynamic: it is what makes it decide whether the gift is acceptable to the group or not.

Figure 2. How the agent tests all its attributes to decide which gift it is eventually going to give. "Rd" means a random number between 0 and 1. The two motivations are always such that: motivation for prestige + motivation for sharing = 10. Each agent calculates according to its characteristics.

2.12

Agents spend all their money at each step, retaining none for the subsequent time-step. The amount and the receptor of the gift both depend of the kind of gift made. The agent chooses the amount:

• For a sharing gift, the agent shares what it possesses in two equal parts and keeps half for its own consumption.
• For a prestige gift, the agent divides its money into three, two thirds being for the gift. An agent may give a prestige gift only if it already has enough money: if it has to work it will have to turn to a sharing gift. A direct consequence is that it must have received enough gifts at the previous time step.

2.13

The group designates the receptor:

• A sharing gift is given randomly to an agent with a rank greater than (rank of the giving agent - 2): they are agents with less prestige or equivalent.
• A prestige gift is given randomly to an agent whose rank is less than (rank of the giving agent + 2): they are agents with more prestige or equivalent.

2.14

Once the gifts have been made, the new reputation of each agent is calculated locally: the prestige reputation (integration) is the sum over 25 time steps of all reputation (integration) tokens that are accumulated at each time step by an agent (Figure 3). Then the group establishes the ranks by comparing the reputations: the first rank has the highest prestige reputation, and the last rank has the lowest. The memory of the group and of the agents was chosen to be 25 steps for all the simulations.

Figure 3. How the group calculates the increase or decrease of reputation for each agent before calculating ranks

2.15

The two choice parameters can evolve over time, since we want the agent's rationality to depend on its social position. They thus evolve depending on the acts of the time step and on the reputation:

Motivation for prestige / motivation for sharing = motivation change constant * (prestige reputation / integration reputation )

Motivation for prestige + motivation for sharing = 10.

The evolution of the esteem is such that:

• if the agent makes any kind of gift, its esteem increases by 0.1,
• if the agent receives no gift its esteem decreases by 0.2.

2.16

During one simulation step, all the agents make one gift: they go through all the process of decision; then the group distributes the gifts and updates the values of all the characteristics (Figure 4).

Figure 4. One time step in the universe

Simulations and definition of observation

2.17

Before doing simulations where the esteem and the motivation evolve (which interested us the most), we did a few simulations where the choice parameters were fixed, called here "Basic simulations". It gave us the opportunity to find good characterisation of the patterns in the society and find the most interesting elements to observe. Most of the simulations were run for 1000 steps. They were defined as follow:

Table 1: the different types of simulations.
Type of simulation	Motivation for prestige	Esteem
Basic	The same for all agents, motivation for prestige between 0 and 10	The same for all agents, value between 2 and 8
Motivation evolves	Motivation evolves with reputation	The same for all agents, value between 2 and 8
Esteem evolves	The same for all agents, motivation for prestige between 0 and 10	Esteem evolves with gifts made and received

Table 2: parameters that define one simulation.
Type of simulation	Parameters stated at the beginning
Basic	Fixed esteem, fixed motivation
Motivation evolves	Fixed esteem, motivation constant
Esteem evolves	Initial esteem, fixed motivation

2.18

The aim in building the system was to be able to build reputation and to see if it could characterise one individual agent itself. We thus observed differences between the agents in terms of reputation, and the regularity of the ranking. We were also interested in studying globally the number of gifts and their type for each turn, to be able to characterise a society with a lot of exchanges or, on the contrary, societies with little circulation of goods. The criteria used could thus be individual or global.

Individual criteria

• Evolution of both reputations and rank
• Evolution of the motivation
• Evolution of the esteem
• Number of gifts received in 25 steps
• Number of gifts made in 25 steps

2.19

One can note that studying the number of gifts received by an agent is an indication of the stability of its rank. In the system the distribution of the gifts is decided in a randomised way, and:

1. if an agent receives a number of prestige gifts that is much higher than the others', it means that his rank was higher than most of the agents for the last five steps.
2. conversely, if it receives many more sharing gifts, it means that it had quite a low prestige reputation for the last five steps.

2.20

To characterise an agent, we wanted to capture not only its reputation but its choice parameters as well, since they are what we regard as its representation of itself. We defined an agent as being attracted by prestige if its motivation for prestige is higher than 6 and to be not interested in prestige whenever motivation for prestige is less than 5. Since esteem is a social criterion that in part determines if one is able to perform an act or not, an agent that has an esteem higher than 5 is said to be "self confident ".

Global criteria

• Number of agents that possess each given value of reputation
• Integration reputation as a function of prestige reputation (this helps us to identify agents that would have a very different rank from the others at a given time step).
• Number of gifts of each category at each time step

2.21

We considered that a society "goes well" if there are a lot of exchanges. The elements were observed for 1000 steps. For each case, all the criteria were directly observed, and then some of simulations were repeated 30 or 50 times to make averages. The results were almost always similar for the same initial setting, except for some cases that are indicated.

Patterns of reputation repartition: types of societies and differentiation

2.22

For the cases where the esteem and the motivation are fixed, we do not describe the simulations precisely, but only some of the very clearly recognisable patterns that we shall refer to later. There exist three main types of societies that appear depending on the initial conditions:

• either the prestige reputation is equivalent for all the agents and they can hardly be distinguished
• or a group is clearly identified that we call an elite. The members have a prestige reputation that is much higher than the rest of the group
• or an elite does appear, but there exists also another separated group where the agents are either entering the elite or leaving.

2.23

The society can then be globally characterised by the difference of reputation between the highest ranks and the lowest, and the time during which an agent can stay in the elite.

Table 3: types of initial settings (characterised as thresholds for values of esteem and motivation for prestige) that give very different societies. Based on at least 50 simulations in each case.
	Esteem >= 6	Esteem < 6
Motivation for prestige <= 5	No elite, prestige reputation and sharing one quite high and variable. A lot of gifts.	Very few gifts, all reputation values are low
6 <= Motivation for prestige <= 9	Well separated elite, quite stable	Elite well separated often changed
Motivation for prestige = 10	Continuity between a group with no reputation to the elite	Small differentiation for an unstable elite

2.24

In the case when the esteem and the motivation are stable, the motivation is the main parameter that determines the kind of society that will appear. If the agents do not want to be prestigious, the population is homogenous in rank, although there can be a lot of gifts circulating. If the motivation increases, the elite that appears can be very stable. If the motivation is high, the mobility among agents gets really high and the elite is not stable anymore: there is continuity for the value of the rank between the elite and the group of agents that have a low prestige reputation. For these simulations, esteem does not precisely structure the distribution of gifts in the group, but is more a limiting variable. A minimum of esteem is necessary in the group to have the giving actually performed according to the agents' will, and therefore for differentiation to occur. As esteem decreases, the frequency of exchanges slow down, and 6 seems to be a significant value below which there is almost no exchange. There exists simulation outcomes with no real differentiation between agents:

• If there are not enough exchanges to have differences in reputation, it is a "low participation" society.
• If agents do not want prestige and most of the gifts are sharing gifts, one talks of a '"sharing" society.
• If all agents want to be prestigious and have an esteem that is high enough to have a lot of gifts circulate, no hierarchy ever stabilises and one gets a "challenging" society.

2.25

Conversely, one can also observe quite heterogeneous societies. For certain initial conditions one witnesses the creation of an elite of about four agents, more or less separated from the rest of the population. The agents that are in it have a much higher prestige reputation than the rest of the group. With their low ranks (high reputation is low rank), they are those who receive the main part of the prestige gifts, and thus their situation is well established and constantly reaffirmed. The elite does change, though, but the speed of change depends at the same time on the motivation and on the esteem of the whole population. The mobility of the agents between the elite and the rest of the population is what creates an intermediary group going in both direction in the order: we call it the "passage group". Stability here is what designates an order that can be observed unchanging for more than 50 steps. The time scale can vary a lot between the different simulations.

Simulations where esteem evolves

3.1

We defined esteem as the self-attributed ability of an agent to make gifts. It is linked to its integration in the group, its evolution depending on the gifts made and received. In the simulation, populations are homogenous at the beginning, and defined by the motivation of the agents and the initial value of the esteem. Different evolution of esteem can occur, creating different orders in the society.

Evolution of esteem

• If agents have a low motivation for prestige, all converge quickly to the same level of esteem, either very low or very high.
• If the esteem is less than 4 at the beginning, the esteem of all the agents falls quickly and stays at the lowest level (Figure 5),
• If the esteem is higher than 6 at the beginning, all agents quickly gain esteem (Figure 6),
• There exists one situation with a rather different result that appears only for very special initial values: initial esteem is 6 and motivation is 4. The esteem doesn't drop, never reaches 8, and oscillates for all of the agents in the same way. That phenomenon sometimes collapses where all the esteems are very low (in about one out of 20 simulations). In any case, the society is homogenous for that criterion since all agents have an analogous evolution of esteem (Figure 7).

Figure 5. Esteem of the 20 highest ranking agents when esteem is less than 4 at the beginning

Figure 6. Esteem of the 20 highest ranking agents when the esteem is higher than 6 at the beginning of the simulation

Figure 7. Esteem of the 20 highest ranking agents when the esteem is higher than 6 at the beginning of the simulation

3.2

In most situations it is not possible for the agents to differentiate themselves in terms of their esteem. The way the feed-back is defined can explain that result: if a majority of agents have a low esteem they make few gifts and a lot of agents will not get any and thus see their esteem decrease, even if it was initially high. Conversely when a lot of gifts circulate, agents always get a few, sufficient to have their esteem grow.

Table 4: value of the esteem for a motivation of 5
Initial esteem	Esteem after 200 steps in a simulation with motivation for prestige of 5
< 6	Esteem almost homogenous and less than 3 for all
= 6	Esteem oscillates for all agents between 2 and 8
> 6	Esteem almost homogenous and more than 7 for all agents

3.3

A very different situation can be found when the agents have a high motivation for prestige. Differentiation is easier: a small group has a higher esteem than the rest of the population, some attaining the maximum value.

Table 5: value of the esteem for a motivation of 8
Initial esteem	Esteem after 1000 steps in a simulation with motivation for prestige of 8
< 3	Esteem falls: almost homogenous, less than 3
3-4	Esteem increases for a small group, whereas the others have a low esteem
> 4	Esteem increases for all: almost homogenous, more than 7

3.4

The higher the motivation for prestige, the more the esteem will globally increase from a low level (which is a direct result from the feed-back definition and the way the agent chooses: any time an agent tries to make a prestige gift, if it fails, it has the opportunity to try to make a sharing gift and thus has twice the chance to succeed and hence not lose any esteem). For two special values of esteem (3 and 4) it is possible to identify a new phenomenon. All agents do not have the same esteem after a while. At the start, some agents had a higher rank, and thus had the opportunity to receive more prestige gifts in a group where a lot circulate, which enhanced their chance of keeping their esteem quite high. Their reputation stays very stable in that case and no other agent, though motivated, succeeds in getting into the elite and then receiving prestige gifts, and their esteem can drop easily when they fail to get a sharing gift: if ever their esteem increases, it decreases almost immediately (Figure 8).

Figure 8. Esteem of 20 agents with highest ranks in a simulation where motivation for prestige is high

Order in the society

3.5

If esteem reduces for all agents, the society is like one with very low esteem at the beginning. Whatever the motivation for prestige, very few gifts circulate and there is neither differentiation nor stabilisation. If agents have a high esteem and motivation for prestige is low, a lot of gifts circulate and agents' ranks vary a lot. If they have high esteem with high motivation for prestige, an elite does appear, which is usually quite stable. They are anyway more stable when there is reinforcement in the esteem than with the same average value of esteem and motivation with stable value (Figures 9 and 10,).

Figure 9. Prestige (X axis) and integration (Y axis) reputations for agents that all have a high esteem. An elite can be distinguished with 4 agents (not necessarily the same all the time).

Figure 10. Evolution of the rank of two agents that have an evolving esteem beginning at 6 in a society where motivation is 5. There is no stability.

3.6

In the only case where the esteem is not stable, the society exhibits no differentiation in prestige, as in any population with low motivation for prestige. The oscillation in ranks is the highest we have ever witnessed. Then there are a few simulations in which esteem itself is a differentiating element for the agents. Whenever it happens, it is only if the agents are tempted by prestige. The elite are more stable than for the first set of simulations: there are few big changes in status whereas there were a lot for a fixed esteem of an equivalent average. It is then very rare that more than 6 agents have enough status to become member of the elite. They are easy to identify (Figure 11 and 12). One can understand that the elite is here reinforced by the whole group of agents that are all willing to get prestige: the gifts that they make go mainly to the elite agents and thus help them to keep their esteem (Figure 13).

Figure 11. Integration reputation as a function of prestige reputation in a simulation where esteem evolves from 4 and where motivation for prestige is 8. The agents with high esteem are in pink: there are 6 of them. A very clear elite can be identified with 4 agents, and it is very stable. (The situation is the one witnessed in table 3).

Figure 12. Prestige gifts that are received by agents in 25 steps. In blue are represented the agents with high esteem, and in red are those with low esteem. The difference in number of gift received is very clear between these two groups.

Figure 13. Evolution of the rank of three agents during one simulation where esteem varies beginning at 4 with a motivation for prestige of 8. Two of the agents are among the 6 that have a high esteem (here in blue and pink): they stay in the elite forever as soon as they get in. The yellow agent (with low esteem) can get in the 10 first ranks for a while but never stays in.

Simulations where motivation evolves

4.1

In these simulations the agents can change motivation at each step, and that motivation is calculated according to the reputation of the previous time-step and the motivation change constant, which is chosen at the beginning of the simulation:

motivation for prestige / motivation for sharing = ((motivation change constant) * prestige reputation / integration reputation)

Evolution of motivation

4.2

Each simulation is characterised by two parameters: the motivation constant and the esteem of agents. Several patterns for the evolution of motivation for the agents can be identified. These patterns influence the order that appears in the society and thus the dynamic of exchanges (Table 6).

Table 6: Evolution of the motivation when the esteem is 8 (maximal value), depending on the motivation change constant
Constant	Evolution of motivation for prestige
<= 5	Motivation of all agents falls, until the average is 2 after 800 steps. Individually, the motivations can increase and decrease for a while, but eventually none is above 6 after 900th step.
6 - 7	Only 10 agents keep a high motivation for prestige. After 800 simulation steps there are only 10 candidates for prestige, but this group changes: some are replaced and all agents see their motivation oscillate. The average motivation in the group is less than 3.
>= 8	All motivations for prestige are above 6. For all agents, it is maximal and falls very occasionally. The average is very stable, slightly less than 9.

Table 7: Evolution of the motivation when the esteem is 5, depending on the motivation change constant
Constant	Evolution of motivation for prestige
<= 9	Motivation for prestige falls for all agents. It takes about 1500 steps until no agent is tempted by prestige anymore.
10 - 13	A minority always has a very high motivation, and those can be replaced every 100 steps. (The situation takes about 1500 steps to become stable. If the constant is 10, there are only 5 to 10 agents that want prestige. If it is 13, there are about 20 to 25.)
>= 14	All agents want prestige almost from the beginning. All motivations fall and go back to maximum.

4.3

If the esteem is very low, no agent is ever motivated for prestige for a long time. Even if at one step an agent might be willing to get prestige, it never lasts. It is only a sign that this agent had a very low integration reputation, but it does not influence deeply its actions in a long term. One sees that not only the value of the constant, but also the amount of esteem is very important to keep a high motivation for prestige (Figures 14 and 15).

Figure 14. Average of the motivation for prestige in simulations where constant is 9, for different values of esteem. To see the motivation stay high the esteem needs to be maximal (in yellow the esteem is 8, in blue it is 5 and in pink 2).

Figure 15. Number of agents that are motivated by prestige (having a motivation higher than 6) when the constant is 9 in a 1000 step simulation. The result is dependent on the esteem in the group: in yellow the esteem is 8, in blue it is 5 and in pink 2.

Order in the society

4.4

In these simulations with fixed esteem and evolving motivation, the stabilisation of the motivation takes a very long time and the order takes a longer time to appear than in previous simulations (in former ones, a global and stable structure could be seen after 400 steps, here it needs at least 800). If the esteem is less than 5, the society is totally fixed; without gifts and thus no differentiation ("low participation"). We shall thus be interested in cases where the esteem is more than 5, and then the order depends directly on the evolution of the motivation. If the motivation for prestige is low for all, we get a "sharing society". If a small number of agents are interested in acquiring prestige there is a small elite (about three agents, as in Figure 16), which is rather stable. The fewer agents that are tempted by prestige, the more stable the elite. If there are more than 15 , the elite is very unstable. The society is differentiated into two groups by the number of prestige gifts received. There is the elite and the rest. Some are among the 10 highest ranking agents for a long time.

Figure 16. Sharing reputation as a function of prestige reputation in a simulation where the esteem is 5 and the variable constant is 9. A minority of agents is tempted by the prestige for a long time (in pink), during which they constitute a stable elite. In blue: the agents that prefer to share.

4.5

What is quite amazing is that, contrary to the case when a minority has a much higher esteem than the rest of the group, here, there exists in no case perfectly stable elite to which the agents belong for the rest of time. Any agent that is motivated for prestige can reach the elite. If the number of agents who want prestige is high, an elite appears (Figure 17) in which agents stay for a long time (Figure 18). The order of the society is very similar to that of a society in which all the agents are motivated by prestige and have enough esteem so that they can try to get to the highest rank. Here we can notice a new situation: the minority that do not care about prestige constitute a rather small group, very distinguishable, very stable for long periods. They all have a very low reputation for prestige. On the contrary, the groups of agents that look for power are rarely stable, and their agents change all the time. It is the first time that such a group appears: the feedback on motivation can thus exclude some agents from the dynamics of getting prestige.

Figure 17. Sharing reputation as a function of prestige reputation among the agents in a simulation where they have a high esteem and their motivation varies with constant 10. The elite of 4 agents is clearly distinguishable.

Figure 18.The ranks of three agents in a simulation where motivation varies and where esteem is high. As seen before, agents can be part of the elite for a long time. What is new here is the possibility of an agent being in the lowest ranks for a long time.

Discussion

Results

5.1

The work presented here is a translation of dynamics observed in real societies in which non-merchant exchanges are important. To enable the evolution of each individual agent, two feedback loops have been defined. The first one transforms the agents' esteem that evolves according to the gifts made and received. The other is motivation for prestige that is calculated with the reputation. Some other loops can be logically deduced from the dynamics of the system:

• Agents with a high prestige reputation get more prestige gifts, which helps keeping their reputation high,
• Agents with a high esteem make gifts more easily, which keeps their esteem high,
• Agents with high reputation for prestige will be motivated by prestige and will act to increase their reputation for prestige.

5.2

What we see is that these global loops logically reinforce the dynamics, and we could believe that a lot of deadlocks would thus be created, with two main situations:

• a high stability of hierarchy, fixed because they repeat themselves,
• total randomness, in which it is impossible to identity any pattern.

5.3

But what was actually possible to detect was a great range of situations (among which some were not necessarily interesting for our concerns). The main phenomenon is that, most of the time, motivation for prestige and esteem have dynamics that go together. Both help the circulation of gifts, and then the creation of prestige reputation .

Table 8: All situations that are encountered in simulations, and conditions under which they occur (basic = fixed, variable = either esteem or motivation evolves).
	No differentiation	Two groups: an elite and others
No clear stability of agents in the elite	Basic: Motivation <= 5 / any esteem- Variable: Motivation <= 5 / Evolving esteem
Stability for some agents in the first ranks for 20 steps	Variable: Motivation >= 6 / Evolving esteem < 3 at the beginning	Basic: Motivation = 9-10 / Esteem <= 5 - Variable: Motivation >= 9/ Evolving esteem > 7
Stability of some agents in the first ranks for 20 to 200 steps	Basic: motivation = 9-10 / Esteem >= 6 - Variable: Motivation >= 6 / Evolving esteem > 5	Basic: Motivation = 7-8/ Esteem <= 5
Stability of some agents in the first ranks for 500 steps or more		Basic: fixed motivation = 6-8 / esteem >= 7 - Variable: motivation >= 6 / Evolving esteem 3-4 at the beginning

Influence of parameters

A necessary motivation for prestige

5.4

To get differences in terms of reputation for the agents, it is necessary to have agents that specifically look for prestige in the group. If the agents have the same motivation, we can indeed find a minimum value for motivation for prestige, below which there are not enough prestige gifts to get a differentiation. If agents have different motivations, a minimum of them looking for prestige is important. This is a reassuring element of our model: it proves that one main loop that was built in that system gives global results in this ostentatious society, as well as individual. It is only because prestige is a value that is shared and searched for by the agents, that it has meaning for us to try to capture its appearance.

Two implications for esteem

5.6

In the system the agents' esteem (or self-confidence) has a key role in defining their individual actions. Globally it can be noticed that few gifts circulate without a minimum level of esteem in that population, and thus no differentiation appears.The order in the society cannot be stable if the whole population wants to get some prestige and feels able to get it. That result is pretty clear when only a part of the group is tempted by prestige: when the number of such agents increases, the stability of the elite disappears. If the whole population wants prestige, there is no way to reach any stability at all.

Autonomous agents and ''social representations''

Individuals

5.7

In each society we have built, agents are defined by some attributes. The two that determine how they act can be associated with their "personality", since it is what helps them to make individuals: esteem and motivation. The latter could be seen more or less as the preferences often identified by economists. In a more social way we even identified some "function" for an agent, where its actions take a place in the others' reputation evolution in the long term. For example, when some agents cannot be part of the elite, although they want to; they make gifts that help others to stay in that elite.

Collective dynamics

5.8

In the societies we built it had been possible to identify some individual behaviours that could be related to special "personalities". But in no case has the evolution of reputation for an agent been possible without considering the whole group. If esteem evolves, it is almost impossible that one agent could have a high esteem in the long term when other agents all have low esteem: at least a few of the others must be self-confident as well. As an average value, esteem has to get to a minimum level so that exchanges occur. When only a part of the group is motivated by prestige, these agents are not necessarily those that have the highest rank. Sometimes agents that are not motivated by prestige are taken into the elite by the reception of prestige gifts emitted by others; the others' motivation can directly influence an agent's position. Hence, even if one individual agent has autonomous choices, there is no independence concerning its belonging to the elite nor to the values of its own esteem or motivation. For example, it is possible to interpret the motivation change constant as the value that the society gives to prestige compared to sharing. If the idea of getting prestigious is not very important in the group, the agents will do their best to make a lot of sharing gifts, but will not necessarily try to make prestige gifts, which is what we find in the evolution of our societies.

Describing processes

5.9

The ways that agents change their perception of themselves (esteem), of others (reputation) and their preferences (motivation) is defined quite strictly by different feedback loops. This sometimes but not always induces very predictable results. It was particularly interesting to see that in most cases the agent's rationality depends highly on its social position, although it was not directly defined in a strict way in the system. But, it can also be noticed that some very unexpected results could appear. The same processes, with slight differences in the parameters, would give very different results in the global organisation of the society. This leads us to point out an important issue: the context into which any strategy has to be described, be it learning or norm obedience, can certainly not be taken into account without the more general background, that makes all the dynamical processes possible.

A new way to represent artificial reputation

5.10

The idea of reputation is widely used in building of artificial societies where agents interact with each other. It is present in the description of individual relations in the context of strategic interactions (in the "game theory" paradigm). A prototypical example is a society where agents interact with each other and everyone has the choice of who to interact with (Lahno, 1995). The interaction being necessary for all, it can have a positive or negative outcome for the individuals: the participants can cooperate or defect in the interaction, and defection causes trouble to the other one. In the society built by Lahno, an agent remembers all its interactions and the behaviours of the ones it met. According to these past behaviours, the agent builds a representation of all the other agents: this is here considered as a reputation since the agent uses it as a base to choose whom to interact with. Thus each interaction acquires two meanings: it is important for the action that has to be performed between two agents, and it is the basis upon which the reputation of each is built in the eye of the other. When an agent defects or cooperates, it opens or closes opportunities of interactions for the future, and the strategies then take place at two different levels. In that artificial society the reputation that is built is not defined in the same way as what we call reputation in our own society. The representation that the agents have of each other is not social and is just related to individual interactions. The idea that the whole group is looking at the actions of each agent is absent. That difference is solved in a multi-agent model, where agents still perform strategic interactions, but where the memory of defection is remembered by the whole group of agents and thus creates a social punishment (Chi Wong and Sycara, 1999). In that case reputation is a direct result of individual actions: there is no interaction between the different concomitant actions in the group as we can see in our model.

5.11

In the societies described where the agents perform strategic interactions, the fact that each action influences the others' representations is only a secondary aspect. Thus, when the agent has a reputation, its options for actions do not change: it can still choose to act with someone or refuse, and choose to cooperate or defect. Actually that type of model does not allow us to capture two very important element of reputation building in societies that have been identified by sociologists and ethnologists. First there are a huge variety of behaviours that build reputation and have no other meaning in a group, and they are central in any study of reputation building (Aguilar, 1984). The second aspect is the evolution of the structure of the society due to the fact that the agents transform their own behaviour according to their situation in society (Godelier, 1996).

5.12

In our society, the act of exchange is the only way that the agents have to communicate with others. Based on the circulation of goods and the global values of the group, a common understanding is built. From that understanding, the agents acquire a status and an ability to act that is related to a hierarchical distribution of the gift. It is a strong assumption about how the agents can signal intentions to the others that we picture here: the gift has its place in a process where it delivers a message accessible to all. This is a very important result in the sense that it represents a successful representation of the ethnologists' point of view on gifts. In that exchange system, the agents do not act for their interest but to secure the group and their own reputation (Mauss, 1968). Just that wish is enough to create real dynamics: there is no such thing as an individual relation and yet the individual can define his or her own place in the group. What we get here is a complete and complex representation for the agent (which includes a representation of all the others and a personal representation allowing its actions), without basing it on a sophisticated individual cognition. The coherence of the evolution of reputation and of actions is kept, although only the structure of the exchange is what constrains the understanding. The societal element is predominant in the actions of the agents, but they still have completely individual choices, which is a good representation of the sociologist's point of view on society.

Notes

¹ In a paper in which he discusses different motivations for giving, Van de Ven Jeroen (2000) explores different cases when gifts are not given back.

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