Price and product innovation competition with network effects and consumers’ adaptive learning: A differential game approach

Abstract

For many high-tech and Internet related products, the utility of consumers depends partly on the scale of user groups, which is called network effects. In this paper, we formulate a differential game model to investigate the joint price and product innovation competition in a market exhibiting network effects. In the spirit of behavior economics, the consumers’ adaptive learning about network size is considered. The unique steady-state equilibrium is analytically characterized under both committed and feedback information structures. Our analysis mainly shows that (i) the network effects have negative influence on the result of price competition but have nothing to do with the result of product innovation competition under the premise of low market density; (ii) the marginal impact of network effects on the steady-state price is decreasing with the consumers’ learning speed; (iii) in the long-run, the product price converges to the level either higher or lower than the stationary price, depending on the strength of network effects; (iv) in a market where the consumers are extremely sensitive to the product price, the quality provision is insufficient compared with the first-best optimal level regardless of the choice of solution concept. The dynamic evolution patterns of the price and product innovation competition are illustrated by numerical experiments.