Competition is a prerequisite for Innovation. Competition motivates the leader to out innovate and stay ahead in the game. It makes the companies doing the catch-up to think outside the box to beat the leaders. A business lacking competition often stagnates because there is no need to innovate.
There are several examples where competition has led to innovation and lack of competition has led to stagnation in the same industry. The best one that comes to mind is the web browser industry. In mid 90s, the browser industry had fierce competition between Netscape, Microsoft and a few other players. Between 1995 and 2001, both Netscape and Microsoft came out with six versions of their browsers out-innovating each other over and over again with new releases every few months. Eventually Netscape became less relevant and IE captured about 90% of the market. For the next five years starting 2001, there was literally no innovation in the web browser industry till new browsers like Mozilla, Firefox and later Chrome started becoming relevant. It took Microsoft five years to come up with IE7 in 2006. And since then, competition has fueled innovation for the three big players coming out with new features in the browser every few months.
The same dynamics is visible in many spaces, be it video games, cell phones, hybrid cars or social media. There are always lot of other factors in play like macro-economic conditions, state of the broader industry etc., but competition is the driver when it comes to innovation.