Dynamic Competition in Price and Product Innovation with Network Effects and Consumers’ Adaptive Learning : A Differential Game Approach

In this paper, we formulate a differential game model to investigate firms’ competition in both price and product R&D. The significant features of our research include: (i) incorporating the factor of network effects into the framework of continuous dynamic competition; (ii) considering the consumers’ adaptive learning about the network size in the spirit of behavioral economics. Our analysis mainly suggests: (i) The network effects and consumers’ adaptive learning comprehensively have negative effects on the result of price competition but has nothing to do with the result of R&D competition under duopoly, which is not true as the number of firms increases; (ii) the incentive to acquire competitors’ state information is increasing with the intensity of network effects and the consumers’ learning speed; (iii) when we consider the competition among more than three firms under feedback information structure, the competition intensity has negative effect on the steady-state quality stock; (iv) in a market where the consumers show strong price sensitivity, the product quality is under-provided compared with the first-best optimal level regardless of the choice of solution concept