A game model of competition for market share between a new good producer and a remanufacturer

We analyze the hitherto unstudied duopolistic interaction between a new good producer and a remanufacturer who compete for a dominant share of the market for a particular product. Each firm i spends d_i ≥ 0 on product development to sway consumers and this expenditure increases the likelihood that firm i captures a dominant market share. The revenue to each firm from obtaining a dominant market share is r>0. Our analysis of this interaction leads to five results. First, given the two product development expenditures (d_1,d_2), we specify the expected profit for each firm i. Second, we describe the function that characterizes each firm’s best response function. Third, we compute the unique Nash equilibrium. Fourth, we show what happens to this Nash equilibrium when the revenue r increases. Finally, we study what happens to the Nash equilibrium when the remanufacturer’s revenue from capturing a dominant market share is still r but the new good producer’s revenue is θ r, where θ >1.