The paper analyzes how the structure of social networks affects innovation diffusion and competition under different information regimes. Diffusion is modeled as the result of idiosyncratic adoption thresholds, local network effects and information diffusion (broadcasting and demonstration effect from previous adopters). A high social cohesion decreases the probability of one innovation cornering the market. Nonetheless, with imperfect information, in small-world networks the higher speed of diffusion produced by the low average distance increases this probability. A low social cohesion also increases the probability of falling into traps of under-adoption. However, such probability is significantly lower with imperfect information, because such regime is characterized by higher levels of market concentrations and this reduces the frictions due to the coexistence of non-compatible product innovations.