1 PATENT RACING-THE GAME THEORETIC APPrOaCh Assume two firms a and b who want to decide whether they should attempt to produce a new product with marginal cost c. The demand for the good is P=a-bQ and as for the r&d effort, the costs of sett a research lab are K and the probability that the lab will successfully the product is p If both firms successfully develop the product they will be a Cournot duopoly 4g, PC=93,9f=92=3), while if only one of the two develops the new product she will be rewarded with monopoly profits (M=(a2,PM=盟,QM=2B) The expected profit net of setup costs if only A establishes an R&d lab while b does not is E(B I R&DA=0, R&DB>0)=E(A I R&DA >0, R&DB=O) 1+(1-p)0-K=pM-K If both establish R&D labs, then E(TB I R&Da>0, R&Db >0)=E(TA R&da>0, R&zDB>0)= =p(1-p 4+n2(a 96--K=pMa p-K 9 No R&d r&d No R&d0,0 I R&d pM-K, 0 pM(1-p)-K,pM(1-p)-K 1.1 Possible Nash equilibrium outcomes 1. Neither firm establishes an R&D lab if pM <K. a(R&D, no R&D)>(no R&D, no R&D)(if pM>K)and if 2. Only one firm establishes an R&d division in equilibrium b(R&D, no R&d)>(r&D, R&D) 0>pM(1-8)-K→K>pM(1-8) ining a and b gives M>K>PM(1-P) 3. Both firms will R&D in Nash equilibrium if pM(1-6p)> K. In this case b prefers to r&d irrespective of whether A r&zDs or not and the same applies for A. Hence the(r&D, R&D) is a dominant strategies equilibrium 1