Consider a society, consisting of two classes of autonomous agents. One class is the small and medium-sized enterprise’ and the other is the big
enterprise’. The numbers of SME agents and BE agents are nS and nB, respectively. Subscripts “si”
and “bj” represent the i-th SME and the j-th BE, respectively.
In this model, the transaction between SME and BE is focused on only one kind of products, for sim-plicity. SME supply the products and BE demand them for the construction of other products like big machines. The transaction process is described in the following section.
3.2 Transaction between SME and BE
Fig. 2 shows outlines of SME and BE behaviors.
Each SME agent decides the extent of implemen-tation of environmental management at every time.
In this model, the extent of implementation of envi-ronmental management is called “envienvi-ronmental management level (EM Level)”.
Each BE agent also decides “greening condition level (GC Level)” every time. The “greening condi-tion level” means the minimum environmental man-agement level that SME must satisfy as the condition of business. Any BE trades only SME with not less than its own greening condition level.
At time t, the environmental management level of si SME agent and the greening condition level of bj BE agent are Esi(t) and Ebj(t), respectively. Both
levels are zero or positive integer not exceeding E^.
That is, 0 < Esi(t), Ebj(t) < E^. Every agent of SME and BE adjusts and decides his level with his own adjusting level rules, described next section.
Each SME agent searches BE whose greening con-dition level he satisfies. When he finds plural BE, he chooses one BE with his own rule set concerning BE selection. Each SME decides bid price with his own rules.
Each BE selects SME as subcontractors according to the selecting SME rule. Each BE refers bid prices of SME who tendered. Every BE agent selects SME with the lowest bid price among the tendered SME.
This process of selecting SME by BE is a model of the electronic bidding which has been spreading in recent years. In the interview-based survey of Zaima (2005c), some directors of SME actually said that only the company tendered by a lower price than they assumed could acquire work because the order became electronic tender. At time t, the bid price of si SME agent and the selected price of bj BE agent are Psi(t)and Pbj(t), respectively.
In the transaction, there are cases in which SME can’t find BE to satisfy the level or in which SME is not selected as a subcontractor because his bid price is too high. There also exist cases in which BE can’t find any entered SME because his level is too high for SME to enter.
3.3 Rule Sets for Decision Making
As described above, each BE agent has one rule set concerning the adjustment of greening condition levels. And each SME agent has three rule sets con-cerning the adjustment of environmental manage-ment levels, selection of BE, and decision of bid price.
3.3.1 Rule Set of Adjusting Levels
Rules of adjusting levels are based on the social norm factor of Hirose (1995) scheme, as shown in Fig. 1.
In our model, other agents’ action of social norm factor is represented as the average value of action variables of agents. It is assumed that every SME agent knows the average value of environmental management levels of the entire SME agents and that every BE agent knows the average value of greening condition levels of the entire BE agents. At time t, these average values are ES,avr(t) and EB,avr(t), respectively.
Each agent recognizes the difference between his level and the mean value of the same class as about
“It is very large”, “ large”, “almost the same”, “ small”, and “ very small” according to the value of the expression (1).
(1)
The relation between the ranges of and the recognitions of category is shown as Table 1.
There are three ways to adjust levels. They are “to raise one level”, “to keep the same level” and “to lower one level”. The change values of levels are 1, 0, and -1, respectively.
One rule of adjusting levels is composed of “the conditional part”, “the action part”, and “the evalua-tion value” as shown in Fig. 3. The condievalua-tional part is a category that shows the level of the value of the
expression (1), and the action part is an action value.
Each agent recognizes the category of ∆ and the condition he faces. Among plural rules with the same condition, each agent selects one rule accord-ing to the roulette selection based on the evaluation values of rules. The evaluation value of each rule is defined as a mean value of profits acquired using its rule.
Each agent sets his change value of levels accord-ing to the selected rule. We describe change values of each agent at time t as Lsi(t)and Lbj(t),
respec-tively. And the levels are adjusted as following (2).
(2)
3.3.2 Rule Set of Deciding Bid Prices
The subcontractor is informed of the assessed price to be decided to trade after the decision mak-ing of the parent company (Zaima (2005c)).
Considering such a fact, in this model it is assumed that every SME agent knows the average value of bid prices of the entire SME agents as the assessed price of parent company. At time t, the average value of bid prices is described as PS,avr(t).
∆1 ∆2
Each SME agent recognizes the difference between his level and the mean value of SME as about “It is very large”, “ large”, “almost the same”, “ small”, and “ very small” according to the value of the expression (3). The relation between the ranges of ∆and the recognitions of category is the same as rule sets of adjusting levels for simplicity, shown in Table 1
(3) One rule of deciding bid prices is also composed of “the conditional part”, “the action part”, and “the evaluation value” as shown in Fig. 4. The
condition-al part is a category that shows the level of the vcondition-alue of the expression (3), and the action part is an index value of margin. The index value of margin is a posi-tive integer from 0 to 9. Fig. 4 shows one example of rules of deciding bid prices.
Each SME agent recognizes the category of ∆and the condition he faces. Among plural rules with the same condition, each SME agent selects one rule according to the roulette selection based on the eval-uation values of rules. The evaleval-uation value of each rule is defined as a mean value of profits acquired using its rule.
Each SME agent sets his index value of margin according to the selected rule. The index value of si SME agent at time t is Msi(t). And the bid price of si SME agent is defined as the following (4).
(4) Here, the parameter cvis the variable cost of pro-duction. This parameter is positive real number.
3.3.3 Rule Set for Selecting BE
As described above, each SME agent searches BE whose greening condition level he satisfies. When he finds plural BE, for simplicity, it is assumed that SME agent chooses one BE with his own rule con-cerning BE selection. In order to simplify the model,
the process of selecting BE is as follows.
One rule of selecting BE is simple and is com-posed of each BE name and the corresponding eval-uation value as shown in Fig. 5. Among BE candi-dates satisfied its greening condition level, each SME agent selects one BE according to the roulette selection based on the evaluation values. The evalu-ation value of each rule is defined as a mean value of profits acquired using its rule.
3.4 Profit Function of BE
Any BE agent has the capital restriction to pur-chase the products. The capital for the procurement of the products is described as cBand is positive real number and constant.
The total volume that bj BE agent purchases is Qbj(t)and it is defined by the following expression.
(5) Here, the parameter e0 is a positive real number and it means a unit cost of environmental audit for greening SME. We assume that the auditing cost becomes larger as the greening condition level is high.
When the number of SME which bid the lowest price is not zero, the number is represented as sbj(t) and the volume of each SME, qbj(t), is calculated as the following (6).
(6) We define the profit function of bj BE agent at time t, Rbj(t), as follows.
, if transaction is done and
, if transaction is not done. (7)
3.5 Profit Function of SME
The profit function of si SME agent is defined by the expression (8).
, if transaction is done and
,
if transaction is not done. (8) Here Qsi(t) is the volume of supply informed by the BE. The parameter cE is positive real number and means the price of environmental equipments.
In our model, any SME agents should pay costs to introduce environmental equipments when he
improves environmental management level. And any SME agent can sell the environmental equipments and acquire capital by sales when he lowers environ-mental management level.
The parameter e1is a positive real number and means a unit cost of implementation of environmen-tal management. We assume that the implementa-tion cost becomes larger as the management level is high. The unit cost of the parameter e1is assumed to be much smaller than the equipment cost of the parameter cE.
3.6 Fitness Function of Learning between Agents of Each Class
At every time, each agent makes decision on his transaction using his own rule sets and does rein-forcement learning of rules. Each agent refers each other among agents of his class, learns more prof-itable rule sets and revises his rule sets to new ones.
That is, our model involves double loop learning.
The fitness functions of si SME agent and bj BE agent are aggregated profits of z terns written by the following (9).
(9) The parameter z is the learning cycle between agents. Agents learn rule sets each other according to the roulette selection based on the fitness values.
In the simulations, the number of double loop learn-ing is w.
3.7 Values of Parameters
The basic values of parameters used in the simulations are shown in Table 2.