1. Simulating competition between two firms Paper Presented to 3 rd Irish Workshop on Simulation in Manufacturing, Services and Logistics hosted by Intel 18 th June 2007

2. (inverse) Demand p q monopoly a: reservation price b: own price effect (market response) a b = slope

3. Product differentiation duopoly d: represents the cross price effect d/b: represents the extent of product differentiation Dixit, BJE, 1979

4. Costs No fixed costs Cost is linear in quantity ie. no economies or diseconomies of scale

5. Profit

6. Cournot Nash equilibrium Game theory Strategic interdependency Cournot, 1838; Nash, 1951

11. 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 Δa i = φ i A i + ρφ j A j i =1,2, j=3 - i Π = pq – cq - A

12. reservation price quantity advertising ++ B1 advertising elasticity - + + R1 reservation price quantity advertising ++ R2 price elasticity - - + B2 price + - R3

13. φ 1 = 0.000013; φ 2 = 0 φ 1 = 0.000015; φ 2 = 0 φ 1 = φ 2 = 0 φ 1 = φ 2 = 0.000015 φ 1 = φ 2 = 0.000013 One firm advertisesBoth firms advertise Neither firm advertises

14. Both firms advertise (asymmetric) φ 1 = 0.000015; φ 2 = 0.0000149 φ 1 = 0.000013; φ 2 = 0.000012 One firm advertises with spillover φ 1 = 0.000015; φ 2 = 0; ρ = 0.1 φ 1 = 0.000015; φ 2 = 0; ρ = 0.2

15. One firm advertises with spillover φ 1 = 0.00005; φ 2 = 0; ρ = 0.5 φ 1 = 0.00005; φ 2 = 0; ρ = 0.9

16. Advertising effectiveness A B C D 00.000050.000028 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