An agent-based model of price flexing
by chain-store retailers
Ondřej Krčál, FEA MU,
MUES 2012, 15/11/2012
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Price flexing
Price flexing by chain-store retailers = third-degree price
discrimination in which individual stores set their prices
according to their local market power.
Examples:
• UK supermarket sector – Competition Commission (2000) found
this practice anti-competitive but offered no remedy
• Czech petrol stations – Shell has zero profit margin in some
regions and a PM of 4 CZK in other locations (highways)
– Office for the Protection of Competition did not find this
practice anti-competitive
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Literature review
Dobson & Waterson (2005a, 2005b, 2008)
• stylized models of a supermarket sector with two separate
markets, one monopolistic and one competitive and two retailers
• choice of both local and uniform pricing might be rational
for some parameters of the model
• also the welfare consequences of different combinations of pricing
strategies depend on parameter values.
Problem of their approach: pricing has no effect on market structure.
I propose an agent-based model where pricing strategy affects not
only prices but also number and location of stores in the market.
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Model (1/5)
Agent-based model implemented in Netlogo 4.1.3.
In each run, the model is initialized + it runs for some periods.
Initialization:
• landscape – a square of 40 × 40 patches
• 1,000 consumers who differ only in their locations. Each gets
a location with random direction and distance from the center of
a settlement. The distance ranges from 0 to h/(πu), where h
is the number of inhabitants and u population-density parameter.
• 2 chain-stores – chain 1 and 2 opens 10 stores of each with
a random location and a price pR/2, where pR is reservation price
of consumers.
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Model (2/5)
Each periods has four phases: 1) opening stores, 2) adjusting prices,
3) shopping, and 4) closing stores.
1) Opening stores – up to v stores for each chain
A new store opens only if it increases the profit of the chain –
depends on the price the new store charges:
• U – the same price as any store in its chain
• L – the lowest price charged by an incumbent store of its chain
• ˆL – the average price charged by the stores of its chain
• LL – the price of the store (of any chain) with the lowest distance
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Model (3/5)
2) Adjusting prices – each store changes its price by > 0 or by 0.
The adjustment decision depends on pricing strategy:
• uniform pricing (U) – each chain chooses the price that
maximizes its profit given the price charged by the other chain.
• local pricing (L, ˆL, or LL) – each store chooses the price that
maximizes its chain’s profit given the prices charged by all the
other stores.
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Model (4/5)
3) Shopping – each consumer chooses the store with the lowest
pit + cd2
it,
where
• pit is the price of the product,
• c > 0 is the per-patch transportation cost,
• dit is the distance to the store i.
In this store, each consumer buys
• 1 unit of the product if her reservation price pR is higher than
price + transportation cost,
• 0 units otherwise.
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Model (5/5)
4) Closing store – depends on profits of stores.
Assuming zero marginal cost, the profit of store i in period t is
πit = qitpit − F,
where
• qit are units of product sold,
• F is the quasi-fixed cost.
In period t, the chain closes store i with a probability
−πit
F
.
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Data (1/2)
Generated in Behavior Space in Netlogo for all combinations of the
following parameters/settings (1,024 runs):
• urban landscape (1 city of h = 400 and 20 villages of h = 30)
and rural landscape (30 villages of h = 30)
• population-density parameters u = 0.5 and 1
• reservation prices pR = 0.5 and 1
• numbers of new stores v = 2 and 4
• strategy profiles (U, U), (L, L), (ˆL, ˆL) and (LL, LL)
• transportation-cost parameters c = 0.01 and 0.02
• price-change parameters = 0.02 and 0.03
• quasi-fixed cost F = 5
• random seeds 1, 2, 3, and 4
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Data (2/2)
Each run of the simulation generates the following variables:
• Quantity Q = 1
100
200
t=101 ¯nt, where ¯nt is the number of
consumers who bought 1 unit of product (customer)
• Price P = 1
100
200
t=101( 1
¯nt
¯nt
j=1 pjt)
• Number of stores of chain k Mk = 1
100
200
t=101 mkt
• Revenue of chain k Rk = 1
100
200
t=101
mkt
l=1 qlktplkt
• Distance D = 1
100
200
t=101
¯nt
j=1 d∗
jt
• Consumers’ surplus CS = QpR − R − cD2
where R = R1 + R2
• Profit of chain k Πk = Rk − MkF
• Total profit Π = Π1 + Π2 = R − MF, where M = M1 + M2
• Welfare W = CS + Π = QpR − cD2
− MF
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Results (1/4)
Compare outcomes of 3 three pairs of strategies:
• (U, U) to (L, L)
• (U, U) to (ˆL, ˆL)
• (U, U) to (LL, LL).
I run a regressions for each pair of strategies and each variable of the
entire dataset (24 regressions in total) - example:
STORES NO = 19.307
(0.958)
+ 507.176
(23.652)
TRANSP COST
−3.454
(0.473)
POP DENSITY + 5.935
(0.473)
RES PRICE + 19.293
(23.652)
EPSILON
+0.325
(0.118)
ENTRANTS − 1.336
(0.237)
URBAN − 4.523
(0.237)
LOCAL
T = 512 ¯R2
= 0.677 F(7, 504) = 153.64 ˆσ = 2.676
(standard errors in parentheses)
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Results (2/4)
I run the 24 regressions also for each of the 12 partition of the data
defined by one value of the following parameters:
• TRANSP COST c = 0.01 or 0.02
• POP DENSITY u = 0.5 or 1
• RES PRICE pR = 0.5 or 1
• EPSILON = 0.02 or 0.03
• ENTRANTS v = 2 or 4
• URBAN = 0 or 1
The total number of regressions is therefore 312. The following table
presents the parameters and standard errors of LOCAL for the entire
dataset and for the partitions restricted to pR = 0.5 and 1.
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Results (3/4)
Prices for the strategy (LL, LL) for pR = 0.5 (left) and pR = 1:
• black crosses = customers with pjt ≤ 0.2
• dark gray crosses = customers with 0.2 < pjt ≤ 0.3
• light gray crosses = customers with pjt > 0.3
• dots = consumers with 0 units of product
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Results (4/4)
Change in welfare is
∆W = ∆QpR − c∆D2
− ∆MF,
where
• ∆QpR = welfare effect of quantity traded,
• −c∆D2
= welfare effect of distance to shops,
• −∆MF = effect of lower number of shops.
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Conclusion
What is the effect of local pricing on market outcomes?
The agent-based model with endogenous entry and location of stores
shows that local pricing
• reduces welfare because the effect of
quantity traded and distance to shops
outweighs the effect of lower number of
shops.
• may increase or reduce total profits and
consumers’ surplus, depending on the size
of the reservation price relative to the
equilibrium price.
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Literature
• Dobson, P. W., and Waterson, M.: Chain-Store Pricing across
Local Markets. Journal of Economics & Management Strategy,
14 (2005a), 93–119.
• Dobson, P. W., and Waterson, M.: Price Flexing and Chain-Store
Competition. Proceedings of the 32nd EARIE Annual
Conference, (2005b) available at
http://www.fep.up.pt/conferences/earie2005/cd rom/
Session%20VI/VI.J/Dobson.pdf
• Dobson, P. W., and Waterson, M.: Chain-Store Competition:
Customized vs. Uniform Pricing. (2008) available at
http://wrap.warwick.ac.uk/1375/1/WRAP Dobson twerp 840.pdf
• http://byznys.ihned.cz/c1-56929340-shell-nizkymi-cenami-v-
nekterych-regionech-porusuje-zakon-stezuji-si-pumpari
• http://ekonomika.idnes.cz/pumpari-neuspeli-se-stiznosti-na-shelld97-/eko-doprava.aspx?c=A120906
105308 eko-doprava fih
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