Marco Janssen and Wander Jager (1999)
Journal of Artificial Societies and Social Simulation vol. 2, no. 2, <http://jasss.soc.surrey.ac.uk/2/2/2.html>
To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary
Received: 2-Feb-99 Accepted: 10-Mar-99 Published: 14-Apr-99
|Figure 1: Share of product 1 for 3 possible runs of the very simple model|
(1) Si = Shi*D
The share of the demand is adjusted by changed in indicated shares (IndShi):
(2) dShi/dt = (IndSh-Sh)/ta
This indicated share is determined by a multinomial logit function of the prices of the products. This logit function weights the relative prices (Pi) where parameter mu indicates the sensitivity of the consumers to price differences.
(3) IndShi = EXP(-mu*Pi)/(EXP(-mu*P1)+EXP(-mu*P2))
Prices depend on fixed and variable costs, and a learning factor:
(4) Pi = LFi*(FCi + Si*VCi)/Si
The learning factor (LF) decreases by cumulative production of the product according to the principle of learning-by-doing (Arrow, 1962). The more a product has been produces, the lower the cost price per unit. The parameter gamma determines the cost reduction per doubling of cumulative production.
(5) LFi = (CLi / CLI-in)-log10(gamma)/log10(2)
(6) dCLi/dt= Si
(1'a) S1 = MIN(Sh1*D+ N(0,sigma),D)
(1'b) S2 = D - S1
|Figure 2. Two possible developments of the market given two identical products (ta=2, gamma=0.9, sigma=0.5, FC=10 and VC=10). A lower sensitivity for the demand for price differences (mu=0.5) was used in the upper figure than in the lower figure (mu=0.65).|
|Figure 3: The Moore neighborhood template. The red cells are neighbours of the cell in the middle of the lattice.|
|Figure 4: The red cells are the neighbors of the cell in the left lower corner of the lattice.|
|Figure 5: A torus, a 2-dimensional cellular automatum with the edges pasted (Hegselman and Flache, 1998).|
|Figure 6: Schematic overview of the behavioural processes of the agents in relation to changes in their environment.|
LNS1 = 1-SxNij/8 if xij=0 else LNS1 = SxNij/8
LNS2 = b 0ij if xij=0 else LNS2 = b1ij
LNS3 = B/P0 if xij=0 else LNS3= B/P1
C=C-1*(1-m)+l0*#(xij=0) + l1 *(#xij =1)
Individual sensitivity to pollution (a ij) determines the individual level of satisfaction for the need subsistence and is related to the concentration level.
LNS4 = 1-exp(- aij/C)
LNSij = LNS1gamma1ij * LNS2gamma2ij LNS3gamma3ij * LNS41-gamma1ij-gamma2ij-gamma3ij
In fact, the way the different needs are implemented cause four different feedbacks: (1) the need for identity related to the local (neighbourhood) characteristics, (2) the need for personal taste is related to individual preferences, (3) the need for leisure related individual abilities to macro information (product prices), and (4) the subsistence need may lead to a product related feedback, while pollution is caused by consumption of specific products.
Uncij=S k abs(LNSkij -LNS-1kij)
Max (LNS(xij=0), LNS(xij=1))
LNS = LNS1gamma1ij * LNS2gamma2ij LNS3gamma3ij * LNS41-gamma1ij-gamma2ij-gamma3ij
LNS1 = 1-(S xNij)/8 if xij=0 else LNS1 = (SxNij)/8
LNS2 = b 0ij if xij=0 else LNS2 = b1ij
LNS3 = B/P0 if xij=0 else LNS3= B/P1
LNS4 = 1-exp(- aij/ (C-1*(1-m)+l 0)) if xij=0 else LNS4 = 1-exp(- aij/ (C-1*(1-m)+l1))
xij = 0 if
#[(xNij =0) and (Bij * (1-Btol) £ Bneighbours £ Bij * (1+Btol))]
#[(xNij =1) and (Bij * (1-Btol) £ Bneighbours £ Bij * (1+Btol)) ]
else xij = 1.
xij = x-1ij
xij = 0 if #(xNij=0) > #(xNij=1) else xij = 1.
|Figure 7: Spatial pattern in the lattice of consumption of product 0 (red) and 1 (blue), for 3 points in time (t=0, t=10 and t=100).|
|Figure 8: Types of cognitive processes for the population of 900 consumats (red = delibertaing; yellow = social comparison; green = repetition; blue = imitation)|
|Figure 9: Distribution of share of product 1 in time step 100. If this share is equal to 0 or 1 a macro-level lock-in has occurred.|
|Table 1: Statistics for the experiment of 1000 model runs: the average values of the model parameters and the standard deviation (in brackets).|
|Gamma1||0.251 (0.142)||0.290 (0.147)|
|Gamma2||0.253 (0.142)||0.020 (0.018)|
|Gamma3||0.250 (0.146)||0.424 (0.164)|
|Gamma4||0.245 (0.141)||0.266 (0.166)|
|LNSMIN||0.499 (0.291)||0.594 (0.272)|
|UncMAX||0.493 (0.291)||0.680 (0.214)|
|Btol||0.499 (0.285)||0.434 (0.241)|
|Figure 10: Distribution of the average different types of products consumed by the neighbors in time step 100. If this average is 1, a macro-level lock-in has occurred. If this average is 2, the consumption is randomly distributed over the lattice. A low average suggests spatial patterns.|
|Table 2: Statistics based on the results of 1000 model runs (t-values are in brackets)|
|Figure 11: The average share of product 2 for a whole range of time steps|
|Figure 12: Distribution of share of product 1 in time step 100. If this share is equal to 0 or 1 a macro-level lock-in has occurred|
|Figure 13: Distribution of the average different types of products consumed by the neighbors in time step 100. If this average is 1, a macro-level lock-in has occurred. If this average is 2, the consumption is randomly distributed over the lattice. A low average suggests spatial patterns|
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