Alison Heppenstall, Andrew Evans and Mark Birkin (2006)
Using Hybrid Agent-Based Systems to Model Spatially-Influenced Retail Markets
Journal of Artificial Societies and Social Simulation
vol. 9, no. 3
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Received: 23-May-2005 Accepted: 20-May-2006 Published: 30-Jun-2006
|Figure 1. Map showing the location and spatial variability of retail petrol prices within West Yorkshire. Urban areas are indicated by station density and by name|
|Figure 2. Intra-urban price variation for two typical cities|
|Table 1: List of agent characteristics|
|Autonomous||React to other petrol agents on basis of individual and local information.|
|Heterogeneous||Stations can have individual rule sets, price and profit levels.|
|Communicative and Cooperative||Pricing and location information shared between agents for competition.|
|Pro-active||Monitor their own profit/price levels and take action to maintain or maximise their profit.|
|Reactive||Decision making on pricing rules and updating of prices based on information supplied to them.|
|Figure 3. Flowchart illustrating the operation of rules within the petrol agent during one iteration. For the values of parameters like "maximum price change allowed, see Appendix 2|
Smij is the amount of fuel m sold by garage j to ward i.The stochastic term in the calculation of the weighted distribution of sales allows for the representation of imperfect knowledge and non-rational behaviour in customers and for the addition of a random perturbation to the model. For the purposes of this paper ε is taken as being normally distributed with a mean of 0.0 pence and a standard deviation of 0.05 pence.
δmj is 1 where garage j sells fuel m and 0 otherwise.
dij is the distance between ward i and garage j.
pmjis the price of fuel m at garage j.
Hi is the number of households within the ward i.
Fm is the amount of fuel of type m required per car per day.
ε is a stochastic term.
|Figure 4. A section of the weighted graph network|
|Figure 5. Distribution of consumer density before (a) and after (b) application of the networking|
|Table 2: Comparison of the Hybrid and Network models running the models in deterministic and stochastic mode. The model was run ten times in stochastic mode to generate the ranges. The first and second rows are the mean and standard deviation of the errors between the real and predicted data|
|Business as usual||Deterministic||Stochastic||Deterministic||Stochastic|
|Mean||0.160||0.138||0.137 — 0.143||0.152||0.149 — 0.155|
|SD||0.976||1.007||1.004 — 1.012||1.037||1.036 — 1.044|
|RMSE||0.987||1.018||1.012 — 1.019||1.046||1.044 — 1.054|
|MAE||0.773||0.783||0.781 — 0.788||0.806||0.805 — 0.814|
|Figure 6. Price distributions for the various models ten days after runs started with all stations initialised at 71p: (a) Hybrid-model and (b) Network-model. Data from day ten of the real data set (c) is included for comparison|
|Table 3: Aggregated results of running the model with a random price drop and increase of 1p and 3p at random stations. Each experiment was run ten times. The first and second rows are the mean and standard deviation of the errors between the real and predicted data|
|Test||Price Drop||Price Increase|
|Mean||0.160||0.183 — 0.196||0.199 — 0.777||0.177 — 0.203||0.179 — 0.200|
|SD||0.976||1.018 — 1.043||1.031 — 1.590||1.012 — 1.038||1.027 — 1.058|
|RMSE||0.987||1.033 — 1.058||1.048 — 1.767||1.026 — 1.056||1.042 — 1.078|
|MAE||0.773||0.788 — 0.803||0.798 — 1.271||0.786 — 0.801||0.786 — 0.810|
|Figure 7. Spatial diffusion of prices over time for a price drop of 5 pence. All stations are initialised with real prices from day zero (July 27 th)|
|Figure 8. Location of stations examined in the experiments|
|Figure 9. Change in (a) price and (b) profit over time for the selected stations in the real data diffusion experiment with a price drop of 5 pence|
|Figure 10. Mean price (a) and profit (b) plotted against time for simulations of the "rockets and feathers" effect using the West Yorkshire data|
|Figure 11. Map showing the profitability of stations in Leeds using the Network-model with data from 1999. Also shown for comparison are the status (open or closed) of the stations in 2004|
|Table A1: Parameters|
|B||Coefficient controlling the impact of distance.|
|λ||Coefficient controlling the impact of price.|
|fixedCosts (£)||The amount the petrol station has to pay per day to keep running.|
|costToProduce (p)||The amount per litre that it costs the station to produce and sell the petrol.|
|changeInProfit (p)||The level of profit under which the station will not change its strategy.|
|Overprice (p)||The amount by which petrol stations can be more expensive than their neighbours without becoming uncompetitive and being forced to cut their price.|
|Undercut (p)||The amount by which petrol stations can undercut competitors, e.g. 1p, 2p.|
|Neighbourhood (km)||The distance that the petrol stations will treat as their neighbourhood e.g. 2km, 3km.|
|Table A2: Experiment parameter values|
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