Agent-Based Modeling on Technological Innovation As an Evolutionary Process

Agent-Based Modeling On Technology Innovation

Analysis for Fashion Emergence by Agent-based Simulation

Fujii Shintaro*1, Wang Zhontuo*2, Nakamori Yoshiteru*1

*1: School of Knowledge Science, Japan Advanced Institute of Science and Technology

1-1Asahidai, Tatsunokuchi, Ishikawa 923-1292, Japan

*2: Institute of Systems Engineering, Dalian University of Technology

116024 Dalian China

*Corresponding to:

ABSTRACT

Latane insists consolidation in Dynamic Social Impact Theory (DSIT) which shows a majority increases in number as time. But fashion or innovations hasa reverse process that a minority increases in number as times.

This paper analyzes mechanism that the small fluctuation spreads to the whole system by taking notice of the behaviors of consumers.

Our agent-based simulation assumes two types of agents by two tendencies i.e., Pioneer and Follower.Pioneers have lower thresholds than Followers. Agents behave according to two kinds of information, i.e., local information and global information, which lead to the influences. When there are the small number of Followers and initial adopters, a minority can expand. The behavior of agents shows an unexpected order. When there are enough Pioneers, critical mass is created where the number of adopters expands explosively once it exceeds. The work of global information is to decrease the necessary number of Pioneers to expand and makes Pioneers spread a phenomenon to Followers.

KEYWORDS: agent-based simulation, emergence, modeling, interaction

1. Introduction

We are often said to be so weak for a pressure from groups that we tend to conform to a majority in a group(Asch S., 1951). However, the real society is not uniform. Latane insists Dynamic Social Impact Theory (DSIT) where he shows the following features: though a majority increases in number as time, a minority never disappears in spite of decreasing in number (LatanéB., 1997). The system keeps diversity because a minority survives by clustering locally. Ishiguro et al. introduce global information (Ishiguro I. et al., 2000). In their model, global information behaves as the generalized other. This fifth agent brings two paradoxical changes to DSIT results. One is that it prompts the consolidation by increasing a majority. Another is, meanwhile, global information may keep the system from uniforming. When the initial number of minority is larger, the clusters increase in number though the average size becomes small.

But if a majority always increased in number, any changes wouldn’t happen in our society. It has developed by accepting something new. Fashion or innovation has a reverse process that a minority increases in number as times.

Fashion emerges as follows: at first, a few people adopt a new style. When it comes to majority through the interaction among individuals, it becomes fashion. It can be said that fashion is a process of social diffusion by which a new style is adopted by some group(s) of consumers interacting with each other (Solomon M R., 1996, Kawamoto M., 1981). Fashion is not only peculiar to clothes. It includes a prevailing or preferred manner of dress, adornment, behavior, word, thought or way of life at a given time (Solomon M R., 1996). Here we define the word “fashion” as something with prevailing processes of a minority. All of these have the mechanism that a small fluctuation spreads over the whole system in common. Our goal is to determine how it occurs and what brings it.

We apply the agent-based simulation constructing a virtual society consists of agents. Our basic concept is based on the complex system: the activities in micro levels build a macro level, and also the upper level determines the behaviors in the lower levels. Here, agent is micro level; it receives information as inputs and decides its attitude as an output. The set of outputs emerges a phenomenon on a system. A macro level represents a system. Fashion is a phenomenon emerged in a society by the result of the agents’ behaviors. Imagine a whirlpool, it is a phenomenon emerged on the sea by the result of the behavior of each water molecule. Therefore we build this model taking notice of agents’ behaviors bring a phenomenon and interaction between two levels, then analyze how fashion emerges through observing the macro level. Since our concern is located on fashion emergence, this paper doesn’t deal with its end.

Agents behave according to two kinds of information i.e. global and local information. Information stands for the number of adopters. It becomes influence. The more adopters increase in number, the stronger influence to agents is. Agents have unique thresholds to influences. When influences exceed their thresholds, agents change their behavior. This paper presents three models. The first model is the global interaction model, which shows global information. The second one is the local interaction model based on local information. Last, both models are integrated.

1. Global interaction Model

The first model is “Everyone knows everything” model because all agents get identical information about the whole environment they live in i.e. the total number of adopters in the environment. This is global information. It becomes global influence forcing each agent to behaves based on. When global influence exceeds the agents’ thresholds, the influenced agents become adopters and when it falls below their thresholds, they stop adopting. Here, agents interact with the system that determines the agents’ behaviors, and agents’ behaviors change it, which is fed back to agents again. When there are 30% adopters in the system, agents receive influence 30. Assume an agent with threshold 30. This means if more than 30% of agents become adopters, then it follows other adopters. And when the rate falls below 30%, it gives up adopting.

Graph 1 illustrates the distribution of thresholds and the accumulation rate. In the line A, 1% agents have the thresholds lower than 10, 4% agents have between 10 and 20 so that 5% agents have the thresholds lower than 20 in accumulation. This means, when there are 20% initial adopters, the adopters’ rate at the next step becomes 5%. It has decreased in number by step and eventually faded away (arrow S). Whenever the rate of initial adopters is less than Q, the line A disappears. However, if it is over Q, the reverse process is observed. Adopters’ rate always reaches to 100%. The point divides whether expanding or not is called the critical mass.

Graph 1: Global Interaction Model

Consider another case. For the rate of agents with lower thresholds, the line B is more than the line A. There are 25% agents with thresholds less than 20. For thresholds under 50, the line A has 35% agents comparing B having 61%. The line B has two critical masses. One is P. When the rate of initial adopters is lower than P, adopters disappear too. But if over P, it necessarily results in R (arrow T). In contrast, if over R, it always converges on R. R is another critical mass. The expanding process can happen easily in B rather than A.

From these results, fashion emergence depends on the number of initial adopters and critical mass. Fashion can happen much easily under the condition that more agents are “sensitive” to influence. The positive feedback works in the expanding process like arrow T, and the process decreasing in number is the negative feedback like arrow S. This simulation reveals that the positive feedback and what agents are sensitive are necessary for a small fluctuation to expand.

1. Local Interaction Model

The second model has agents got information from neighbors, in other words, agents have the finite sight range. This is “each one knows neighbors” model. The basic concept is same as the previous model; agents adopt when influence exceeds their thresholds. Here, information comes from neighbors. The number of adopters around an agent is local information for the agent and it becomes local influence to the agent. Thresholds give agents tendencies i.e. Pioneer and Follower(Simmel G., 1971). Pioneers are agents who are so sensitive to influence that their thresholds are lower than Followers. In short, Pioneers tend to adopt rather than Followers.

The simulation is experimented as the following: 100 agents are distributed on the 10 by 10 lattice without overlapping at random. Any movements of agents are not considered. This paper applies Neumann neighborhood, which means that each agent checks four directions neighbors (up, down, left, and right) with the exception that marginal agents do two or three. The important thing is that even if adopters are majority in the system, they are minority for an agent when the agent has only an adopter in its neighbors, and vice versa. Adopters have one influence on neighbors. When the accumulated local influence (LI) exceeds the threshold, the agent changes its attitude. The adopting rule is:

Pioneer:

at+1(i, j) = {1 | if LIt (i, j)=1, 0 | if LIt (i, j)=0 || LIt (i, j) >2}[1]

Follower:

at+1(i, j) = {1 | if LIt (i, j) > 2, 0 | if LIt (i, j) <2 }[2]

at: attitude at the step t, i, j : position, 0: reject, 1: adopt

LI: the number of adopters around the agent

If LIt (i, j)=2, then at+1(i, j) will not change in the both tendencies.

Giving to the number of initial adopters and Pioneers, agents begin interactions one another. They decide their attitudes, adopting or not, once in a step. One round consists of 30 steps. The average number of last five steps provides the number of final adopters in the round. Since agents are distributed at random, each round has the different results under the same condition, which has the same number of initial adopters, Pioneers. 1000 rounds simulating gives the maximum, minimum and average number of adopters under the same condition. The average number of final adopters is used for analysis.

The simulation results point out two cases that initial adopters expand. One is the case with the large number of Followers and initial adopters. Another is one with the small number of Followers and initial adopters.

Graph 2: Change of the number of final adopters

(Initial adopter: 3, Pioneer: 35, k=0)

Graph 2 illustrates the average number of final adopters increasing initial adopters 0 to 100 when the number of Pioneers is 0, 13, 29 and 100. If the number of Pioneers is between 13 and 29, final adopters always decrease in number in average. When there are 30 Pioneers or more, initial adopters can expand when they are a minority. Contrary to this, when there are less than 12 Pioneers, initial adopters can expand as long as they are majority. In this case, seen from another viewpoint, the majority is those who are not adopters. Therefore a minority is expanded in a system with many Pioneers, and reduced in a system with few Pioneers. The latter case seems to explain DSIT. As for the maximum number of final adopters, it seldom changes after the certain number of initial adopters. This implies the number of Pioneers determines the maximum capacity of system.

Table 1 shows the distribution of final adopters beginning at 3 initial adopters. As Pioneers increase in number, the average becomes larger. 3 initial adopters expand to 20.7 in average when there are 60 Pioneers. However provided 20 Pioneers, they are reduced to 0.9. The more pioneers are, the wider the distribution is, for example, final adopters are distributed between 0 and 11.0(51.0), 65(40.3)% concentrates ~10(~40) in the case of 20(60) Pioneers. Considering a state of final adopters as an equilibrium point, the system with many Pioneers has lots of equilibriums.

Table 1: Distribution of final adopters (%)

1. Integrated Model

The last model integrates two previous models. Agents behave based on two kinds of influence: global and local influence. Akuto insists people recognize something by impersonal information and evaluate it by personal information (Hiroshi A., 1992). We apply his model for this model. Agents make decision based on local information same as the second model, and we add global information there as changing their adopting rule. Global influence GI is denoted by the below formula:

GI = kNi[3]

(k, i is constant, i < 1, N is the number of adopters)

Global influence is updated for every step. GI becomes larger with adopters increasing in number, but the increasing rate per adopter becomes smaller. Agents have two thresholds to each influence. The distribution of thresholds to global influence follows the normal distribution; the number of agents with the lower or higher threshold becomes smaller (Rogers E M., 1962). In this model, Pioneers are the agents with the lower threshold to global influence. When there are 30 Pioneers, they are the agents to 30th with lower thresholds. Influenced agents by global information can adopt at lower local influence. When GI exceeds thresholds, the adopting rules of influenced agents are:

Pioneer:

at+1(i, j) = {1 | if LIt (i, j)<2, 0 | if LIt (i, j)>2}[4]

If LI=2, then Pioneers keep current attitude

Follower:

at+1(i, j) = {1 | if LIt (i, j) ≧2, 0 | if LIt (i, j) <2 } [5]

In Graph 3, the case A has 35 Pioneers and global influence (k=10). B is the case with 70 Pioneers and no global influence. Both of them have the same number of final adopters in average when there are 3 initial adopters. The average Followers’ rate of adopters at the step 30 is 44.5 and 5% for each. The maximum number of adopters in the case A is 72, which consist of 83.3% Followers. In the case B,it is 57, which consist of 24.5% Followers. Though the number of Pioneers at the step 8 is 29, it is 13 at the step 30. In the case A, global influence promotes to spread fashion by making Pioneers convey it to Followers, which causes Pioneers to stop adopting because of too many adopters around them.

Graph 3: Followers’ rate at each step

Global influence works to reduce the necessary number of Pioneers for expanding. From the difference of the maximum and average number in the case A and B, global influence enlarges the distribution. Graph 4 shows the effect of global influence to initial adopters and Pioneers. The right graph fixes the number of Pioneers to 35 and then changes the number of initial adopters and global influence. It implies that (1) global influence is more effective in the smaller number of initial adopters, (2) it has the effective strength and (3) the effective strength seems to be particular to the number of Pioneers. In this case, it is quite effective when mass effect k is between 6 and 12. Since this range is in common with four lines, it seems to depend on the number of Pioneers.

Graph 4: Influence of global information

The number of initial adopters is fixed to 3 in the left graph. The effective strength is shown as well, but it differs in one another. It appears earlier as Pioneers increases in number. However, global information doesn’t work well in the system with too many or a few Pioneers. Especially with 100 Pioneers, negative effects are observed.

1. Critical Mass

The behavior of agents brings about an unexpected order spontaneously. When there are enough Pioneers, a critical mass is found. At the above Table 1, the number of final adopters flies to 37.8 from 20.2 when there are 80 Pioneers. This indicates that the number of adopters expands explosively once it exceeds a critical mass. Graph 5 shows 1000 results in ascending order under different global influences. The case with 40 Pioneers doesn’t have such point when there is no global influence k=0, but it creates the critical mass by increasing global influence. Unless there are no Pioneers, however strong global influence is, it doesn’t appear. It is considered global influence doesn’t create a critical mass but promote Pioneers to create it.

Graph 5:Distribution of final adopters

And this graph implies global information makes the capacity of system larger. The maximum number of final adopters is larger as global information becomes stronger. Generally speaking, global influence amplifies the function of Pioneers.

1. Conclusion

Simulations reveal the condition that a small fluctuation can spread over to the system in common. It happens in the system with more agents with lower thresholds (Pioneers). They are sensitive to influence. They adopt something at the earlier step and convey it to others. They form the critical mass through the correlation. It is characteristic of fashion emergence. Once the number of adopters exceeds the point, the positive feedback works strongly and it brings the explosive expanding. Another work of Pioneers is to determine the capacity of system. As initial adopters increase in number, the number of final adopters approaches there. Global information amplifies their works. It reduces the necessary Pioneers’ number to expand, helps to form the critical mass and increases the capacity. It also prompts to spread to Followers from Pioneers.

As a conclusion, we suggest fashion emerge in an “unstable” environment. A stable environment means a robust system that has such a strong pressure to remove a small fluctuation that a minority decreases in number as shown in DSIT. On the other hand, an unstable society is so fragile to a small fluctuation that it cannot keep the homogeneity.

The system with global information forms fashion consists of many Followers meanwhile the system without it forms fashion consists of many Pioneers. The former fashion is considered more robust than the latter. If categorizes fashion by the holding period, the latter case is fad which is called “collective fool” because it expands and disappears relatively quickly.

Pioneers make a system unstable and global influence amplifies it. The system with more Pioneers and with stronger global information is sensitive to a small fluctuation. They enlarge the distribution of final adopters. The state of Final adopters represent the equilibriums of system. Fashion is considered as one of the result among possible equilibriums. It also proves the instability in that the system with lots of equilibriums means a small difference can result quite large under the same condition. Brian Arthur states competitions between technologies may have multiple potential outcomes. It may happen that a technology that by chance gains as early lead in adoption may eventually dominate potential adopters (Arthur W B., 1986). Fashion is common to his theory.

Ikeuchi classifies social types into “dynamic” and “static” (HAJIME I., 1968). The dynamic society prompts to prevail meanwhile the static one inhibits fashion. The dynamic society is characterized by increase of the speed, range and frequency of communication and transport, fluidity of power constructers and so on. Intuitively, the dynamic society seems to include many Pioneers. On the other hand, the static society like a conservative one consists of many Followers. He continues, “a dynamic society is an opened one idealized by change, progress, development and expansion comparing that static society idealized the status quo”. Dynamic society is sensitive for change and “unstable” in that it doesn’t hope the status quo.