Simulating competition between two firms

Paper Presented

to

3rd Irish Workshop on Simulation in Manufacturing, Services and Logistics

hosted by

Intel

18th June 2007

(inverse) Demandp

q

ii bqap monopoly

a: reservation price

b: own price effect (market response)

a

b = slope

Product differentiation

jii dqbqap duopoly

iji 3;2,1

d: represents the cross price effectd/b: represents the extent of product differentiation

Dixit, BJE, 1979

Costs

iii qcqC )(

No fixed costsCost is linear in quantity

ie. no economies or diseconomies of scale

Profit

iiii qcp )(

iii qpR

iii CR

Cournot Nash equilibrium

224

2)2(

db

dcbcdbaq ji

i

222

2222

)4(

)2)2())(4()2()2((

db

dcbcdbadbcdbcdbcdbab jiijii

iji 3;2,1

Game theoryStrategic interdependency

Cournot, 1838; Nash, 1951

Total_variable_cost

Total_cost

Gross_income

Revenue

Demand_reservation_price

cross_price_effect

units_demandedown_price_effect

fixed_production_cost

Unit_variable_cost

managerial_Incentive_factor

Unit_price

Price_elasticity_of_demand

Gross_income

CapitalDepreciation

Net_operating_income_or_EBIT

Earnings_before_tax

Net_income

Interest

Accumulated_loss

Tax

DividendRetained_earnings

Capital

Accumulated_loss

Retained_loss

Accumulated_profit_NPV

Retained_profit_NPV

Retained_profit

Depreciation_rate

Interest_rate

discount_rate

Advertising

Dividend_retention

Tax_rate

units_demandedRevenue

cross_price_effect

Unit_price

Price_elasticity_of_demand

cross_price_effect

Demand_reservation_price

own_price_effect

Advertising_weighting_factor_1

Advertising_weighting_factor

Cross_advertising_impact_on_cross_price_effect

AdvertisingAdvertising_elasticity_of_demand

advertising_rate

advertising_interaction_factor

advertising_effect_on_reservation_price

Own_advertising_impact_on_cross_price_effect

Advertising• Selection of amount of advertising

– Dorfman-Steiner

• Impact of advertising– Shifts demand function to the right

• ie. changes intercept of inverse demand function

– Tilts demand function • ie. changes slope of inverse demand function

– Freidman

• Cost of advertising– Reduces profit

i

Aii

iRA

2,1i

Δai = φiAi + ρφjAj

i =1,2, j=3 - i

Π = pq – cq - A

reservation price

quantity

advertising

+ +

B1advertisingelasticity

-

+

+

R1

reservation price

quantity

advertising

+ +

R2

priceelasticity

-

-

+

B2

price

+-

R3

Time

Retained_earnings

11

22

0 50 100

275,000

276,000

277,000

278,000

279,000

280,000

1 2 1 2 1 2

Time

Retained_earnings

11

22

0 10 20 30

250,000

300,000

350,000

400,000

450,000

1 212

1

2

1

2

Time

Retained_earnings

11

22

0 10 20 30 40 50 60

276,000

278,000

280,000

282,000

284,000

1 2

1

2

1

2

1

2

1

2

1

2

1

2

φ1 = 0.000013; φ2 = 0

φ1 = 0.000015; φ2 = 0

φ1 = φ2 = 0

Time

Retained_earnings

11

22

0 10 20 30 40 50 60

277,000

278,000

279,000

280,000

281,000

282,000

283,000

1

2

12

1 21 2 1 2 1 2 1

φ1 = φ2 = 0.000015

Time

Retained_earnings

11

22

0 10 20 30

300,000

330,000

1 21 2

1 2

12

φ1 = φ2 = 0.000013

One firm advertises Both firms advertise

Neither firm advertises

Time

Retained_earnings

11

22

0 10 20 30 40

300,000

350,000

400,000

450,000

500,000

1 2 1 21 2

1 2

1

2

Both firms advertise (asymmetric)

φ1 = 0.000015; φ2 = 0.0000149

φ1 = 0.000013; φ2 = 0.000012

Time

Retained_earnings

11

22

0 10 20 30

278,000

280,000

282,000

284,000

1

2

1

2

1

2

1

2

Time

Retained_earnings

11

22

0 10 20 30 40 50

270,000

280,000

290,000

300,000

310,000

320,000

1 2

1

2

1

2

1

2

1

2

1

2

One firm advertises with spillover

φ1 = 0.000015; φ2 = 0; ρ = 0.1

TimeRetained_earnings

11

22

0 10 20 30 40 50

280,000

285,000

290,000

12

1

2

1

2

1

2

1

2

1

2

φ1 = 0.000015; φ2 = 0; ρ = 0.2

One firm advertises with spillover

Time

Retained_earnings

11

22

0 1 2 3 4

280,000

300,000

320,000

340,000

360,000

1 2 1 21 2

12

1

2

φ1 = 0.00005; φ2 = 0; ρ = 0.5

Time

Retained_earnings

11

22

0 1 2 3 4 5

300,000

350,000

400,000

1 2 1 2 12 1

2 12

1

2

φ1 = 0.00005; φ2 = 0; ρ = 0.9

Advertising effectiveness

A B

C

D

0 0.000050.000028

0.25

0

1.0

0.000013

0.82

Advertising interaction

• A: both firms tend to a terminal Cournot equilibrium

• B: both firms grow exponentially

• C: non-advertiser driven out of the market

• D: non-advertiser outperforms the advertiser