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Course outline I Introduction Game theory Price setting monopoly – oligopoly – Quantity setting monopoly – oligopoly – Homogeneous goods Process innovation 1 Innovation competition Product versus process innovation Drastic versus non-drastic innovation Patent race Incentives to innovate Executive summary 2 Research and development Three levels of research: – – – fundamental research applied research with project planning development of new products and their commercialization Innovation of product and process Three stages – – – invention adoption diffusion 3 Five models Patent race with respect to process innovation Process innovation leads to reduction of average cost: c c Incentives to innovate for – – – – – benevolent dictator monopolist perfect competition two symmetric firms two asymmetric firms 4 Benevolent dictator v. monopolist p p p M (c) p M ( c) c c A BD c c x incentive to innovate x MR 5 Drastic v. non-drastic innovation p p p (c ) c M Innovator enjoys blockaded monopoly, p M ( c ) c p M (c) p M (c) c p M ( c) p M ( c) c drastic innovation non-drastic innovation c c X M (c) X M c x X M (c ) X M c x 6 Exercise (drastic or non-drastic innovation) Inverse-demand function p=a-X All firms have identical unit costs c , where c a 2c Only one firm reduces its unit cost to c 2c a Infer kind of innovation 7 Perfect competition Incentives to innovate – for drastic innovation PC ,drastic M c 0 M c M c A – for non-drastic innovation c PC ,nondrastic c c D c D c dc c A PC ,nondrastic BD (compare next slide and slide „ Benevolent dictator v. monopolist”) 8 PC ,nondrastic graphically p c PC, nondrastic c X c X 9 Assumptions and notation for dyopolistic innovation competition Patent race with respect to process innovation R&D expenditure of firms 1 and 2: F1 and F2 A measure of innovation difficulty : F0 Innovation probability of firm i: Probability of no innovation: Fi wi F0 F1 F2 F0 w F0 F1 F2 10 Exercise (innovation probability) How does the innovation probability depend on F0 , F1 and F2. F1 F2 ½ F0 6F0 34F0 100F0 F0 ½ F0 F0 F0 F0 0 w1 Innovation probability of firm 1 11 Symmetric innovation competition F1 F2 1 2 Initially, none of the firms is in the market. The successful firm enters the market and receives M . 12 Equilibrium (symmetric case) Profit function of firm 1 F1 1 F1 , F2 M F1 F1 F2 F0 Reaction function of firm 1 F1R ( F2 ) M F2 F0 F2 F0 Nash equilibrium F1N , F2N , F1N F2N 1 F0 1 1 M 1 F1N F2N 0 F0 F0 2 with 24 F1N F2N M M M M 8F0 4 0 13 F2 M F0 F1R ( F2 ) Nash equilibrium F2R ( F1 ) M / 4 F0 M / 4 F0 M F0 F1 Exercise (sequential symmetric case) Consider the symmetric case with F0=0. Calculate an equilibrium in the sequential game: F1 F2 1 2 1 S. : M , F2R 4 15 Asymmetric case: one incumbent, one potential competitor F1 F2 p1 p2 1 2 Monopolist (firm 1) with average cost c , and potential competitor (firm 2) Process innovations leads to reduction of average cost: c c Profits, net of R&D expenditure M – No firm innovates 1 (c ), 2 0 – Established firm innovates 1 M (c), 2 0 – Entrant innovates (price competition) 1 0 d 1 and a2 , non - drastic innovation 2 b 2 , drastic innovation d 2 16 Profit functions (asymmetric case) Profit function of firm 1 (monopolist) F1 F2 M 1 F1 , F2 c 1d F1 F2 F0 F1 F2 F0 F0 M c F1 F1 F2 F0 Profit function of firm 2 F2 2 F1 , F2 d2 F2 F1 F2 F0 17 Incentives to innovate No firm innovates. A 2 A 1 GN 1 Entrant innovates. GN 2 Monopolist innovates. 18 Replacement effect (Arrow) The Arrow terms are defined as the profit differences a firm enjoys by innovating rather than not innovating. If the incumbent innovates, he replaces himself. If the entrant innovates, he achieves positive profits as compared to zero profits: 1A M c M c d2 0 2A a2 c c X c , non - drastic innovation b M c , drastic innovation 2 d 2 19 p p p M (c) p M (c) c p M (c) M p ( c) drastic innovation c nondrastic innovation c c x Incentive to innovate from replacement effect A 1 2 A for established firm for potential competitor x Efficiency effect (Gilbert, Newbery) The Gilbert-Newbery terms are defined as the profit differences a firm enjoys if she herself rather than her competitor innovates. The established firm’s incentive to remain a monopolist is greater then the entrant’s incentive to become a duopolist: 1GN M c 1d d2 0 GN 2 21 Gilbert-Newbery effect: 1d d2 M (c) From previous slide follows: 1d d2 M (c) 1 Drastic innovation firm 2 1d 0 and d2 M (c) Nondrastic innovation firm 2 1d 0 and 2d 2a c c X c M (c) blockade and ”=” in equation (1) deterrence and ”<” in equation (1) equation on previous slide is true 22 Replacement versus efficiency effect Replacement effect – entrant has a greater incentive to innovate A 1 A 2 Efficiency effect – established firm has a greater incentive to innovate GN 1 GN 2 23 Equilibrium (asymmetric case) Reaction function of firm 1 F1R ( F2 ) F2 F0 F0 M c M c F2 M c 1d F2 F0 F0 1A F2 1GN Reaction function of firm 2 F2R ( F1 ) F1 F0 F0 F1 d2 F1 F0 F0 2A F1 GN 2 Nash equilibrium: “forget it“ 24 Identifying the replacement effect The greater the monopoly’s profit without innovation, the less are the monopolist’s incentives to innovate: F1R c M 0 25 Special case: efficiency effect only Hypothesis: F0 = 0 i.e., it is certain that one of the two firms innovates Reaction function of firm 1 F1R ( F2 ) F2 F2 ( M c 1d ) Reaction function of firm 2 F2R ( F1 ) F1 F1 d2 c Nash equilibrium: M d d M d d M ( c ) ( c ) d d 1 2 1 2 ( c 1 ) ; 2 M d d 2 M d d 2 c 1 2 c 1 2 26 Executive summary I The higher the attainable monopoly profit, the higher the expenditures for R&D in the patentrace Nash equilibrium. The less likely successful innovation, the less all firms’ expenditures for R&D. R&D expenditures might be strategic complements or strategic substitutes. Sometimes, it may pay for the monopolist to file a patent but not to actually use it himself (sleeping patent). 27 Executive summary II Incentives to innovate for the asymmetric duopoly: If the incumbent innovates, he replaces himself. If the entrant innovates, he achieves positive profits as compared to zero profits. replacement effect The established firm’s incentive to remain a monopolist rather than becoming a duopolist is greater then the entrant’s incentive to become a duopolist. efficiency effect 28 Innovation competition with spillover effect Basic idea Simultaneous quantity competition (2nd stage) Simultaneous R&D competition (1st stage) Simultaneous R&D cooperation (1st stage) Comparison of R&D competition and R&D cooperation Executive summary 29 Basic idea It is often not possible to internalise the benefits of R&D activities perfectly: – – employee turnover analysis of patents R&D cooperation can be observed in some industries (e.g. PSA has different cooperation projects). On the product market, the firms may still compete. 30 The model Before the innovation c c1 c2 The innovation reduces costs by c1 F1 F2 c c1 to c2 F2 F1 c c2 measures the spill-over effect. Fi...R&D activity; C(Fi)...costs of R&D activity Structure F 1 F 2 x1 x2 1 2 31 Profit function Profit functions 1 F1 , F2 , x1 , x2 a bX c c1 x1 C F1 2 F1 , F2 , x1 , x2 a bX c c2 x2 C F2 assume: a c 1 and b 1 1 F1 , F2 , x1 , x2 1 c1 x1 x2 x1 C F1 1 F1 F2 x1 x2 x1 C F1 2 F1 , F2 , x1 , x2 1 c2 x1 x2 x2 C F2 1 F2 F1 x1 x2 x2 C F2 32 Cournot competition (2nd stage) Reaction functions 1 c1 x2 1 c2 x1 R R x1 x2 and x2 x1 2 2 Cournot equilibrium 1 2c1 c2 1 2 F1 2 1F2 C x1 F1 , F2 3 x2C F1 , F2 analogous 3 Reduced profit functions F1 , F2 C 1 1 2 c1 c2 2 3 C F1 C 2 1 2 c2 c1 2 3 C F2 F1 , F2 33 How Cournot outputs depend on „real“ R&D activity ci : x 0 and ci C i x Cj ci 0 R&D activity Fi : xiC 2 0 Fi 3 2 1 0, 12 Fi 3 0, 12 x Cj 34 Exercise (R&D competition on st 1 stage) Assume C Fi 12 Fi 2 i 1,2. Find the symmetric equilibrium in the R&D game. S. : F F N 1 N 2 2 2 9 2 1 2 35 Analyzing direct and indirect effects (R&D competition) I 1C F1 1 F1 , x1C F1 , x2C F1 C2 F1 2 F1 , x1C F1 , x2C F1 Influence of F1 on firm 1’s profit d 1C 1 1 dx1C 1 dx2C dF1 F1 x1 dF1 x2 dF1 direct effect 1 C F1 x1C F1 F1 =0 =0 >0 <0 x2C 2 1 0, 12 F1 3 0, 12 1 strategic 0, 2 effect 0, 12 36 Analyzing direct and indirect effects (R&D competition) II Influence of F1 on firm 2’s profit d C2 2 2 dx2C 2 dx1C F1 x2 dF1 x1 dF1 dF1 direct effect x >0 C 2 =0 =0 ? strategic effect 2 x 3 C 2 <0 1 , 0 2 4 2 x2C 3 0, 12 3 37 Exercise (R&D cooperation on st 1 stage) We assume that firms cooperate on the first stage and compete on the second. Therefore: Firms want to maximize the joint reduced profit function C F1 , F2 : 1C F1 , F2 C2 F1 , F2 . While assuming the same quadratic cost function as before, calculate the cartel solution. S. : F1K F2K 9 2211 2 38 Profit comparison of R&D competition and R&D cooperation i iK iN 0 0.5 1 39 Analytical comparison of competition v. cooperation Does R&D competition yield higher R&D activities than cooperation? In our concrete model, we find F1N F2N F1K F2K 22 21 9 21 2 9 21 2 0 , 12 1 0 , 2 40 Graphical comparison of competition v. cooperation Fi Fi K Fi N 0 0.5 1 41 Interpreting the comparison by way of external effects The influence of firm 1 on firm 2’s profit is an external effect; see slide „Analyzing direct and indirect effects (R&D competition) II“ We found K N 1 0 , neg. ext. effect F F 2 2 dx i i 2 F1 x1 dF1 0, 12 pos. ext. effect Fi K Fi N C 1 Bingo! 42 Executive summary: If spillover effects are sufficiently important, Firms want to underinvest in R&D for strategic reasons; Firms want to cooperate in order to prevent suboptimal R&D activities; Governments may allow R&D cooperation in order to enhance R&D activities. 43