Market dominance breeds complacency, arrogance, and reduced innovation. If Apple wants to thrive, it will need to make major changes to its corporate culture.

By Gerard J. Tellis

FORTUNE -- In the last few years, Apple (AAPL) has grown into a dominant player in several related markets: ultra-light laptops, tablets, smartphones, apps, and digital music. That dominance has led to massive cash reserves and a super-high market cap. Such success is not a cause for comfort or gloating. Rather, success is a curse.

I come to this conclusion after conducting extensive research into the history of innovation, covering the origin and growth of 66 markets, the rise of about 90 radical innovations, and a survey of 770 firms across 17 nations. Success, and especially market dominance, breeds complacency, arrogance, and reduced innovation. Companies such as Sony (SNE) in mobile music, Hewlett Packard (HPQ) in personal computers, BlackBerry (BBRY) in smartphones, General Motors (GM) in automobiles, and Kodak in analog photography were at the top of their respective markets, when their decline began. What caused the fall?

Critics often fault the rise of external technologies when discussing a company's demise. But that is a superficial cause. In all the above-mentioned cases and many others, the revolutionary innovations that catapulted upstart firms were also available deep within the bowels of these dominant companies. But those innovations were put on hold, ignored, or belittled. What caused firms to overlook such radical innovations? A risk-averse culture, that's what. Such a culture stems from a firm's dominance and its success with its current stable of products. My coauthors and I have called this the "incumbent's curse."

MORE: The mystery company importing Americana to the Mideast

In Apple's case, the curse is particularly poignant because the tech giant seemed to rely heavily on a top-down model of innovation. Its former CEO, Steve Jobs, took a strong interest in the management of innovations. He not only directed the broad markets that the firm should enter but also reviewed and directed day-to-day progress on some of the radical innovations that propelled Apple into leadership within at least six different markets.

It has worked for Apple, for now. But my research suggests that a bottom-up approach to idea development and innovation is richer, more stable, and more robust in the long term. Innovation is fraught with failures. The innovator makes many missteps before finally hitting a sweet spot. And it is very difficult for one person to get it all right, all of the time. Steve Jobs himself was associated with many failures (e.g., Lisa, Macintosh, Rokr, Newton), some of which led to initial ejection from Apple.

It is better to rely on the "wisdom of the crowd," within and outside an organization. With this approach, a firm can encourage innovation throughout the organization and encourage employees to compete to introduce new ideas.

This kind of approach also opens the door for asymmetric incentives, which involve strong rewards for success with weak penalties for failure. It's akin to what Google tells it employees, Go ahead and experiment with innovations. If you succeed, you will be rewarded, if you fail, it's on me. Learn and move on.

MORE: Inside Fisher-Price's toymaker lab

Many employees throughout an organization have valuable ideas. The firm needs to empower and encourage them through competitions at all stages of the process: idea fairs, funding contests, prototype races, competing divisions, or market tests. Employees and outsiders can serve as judges. This is a form of crowdsourcing for improving a company.

Apple's biggest enemy today is not Google (GOOG), Samsung, Microsoft (MSFT), or Amazon (AMZN). Apple's biggest enemy is Apple. Can it overcome the incumbent's curse that has come from its success and reconstruct its corporate culture?

Gerard J. Tellis is a professor, Neely Chair of American Enterprise, and director of the Center for Global Innovation at the USC Marshall School of Business. He is the author of Unrelenting Innovation: How to Build a Culture for Market Dominance (February 2013, Jossey-Bass), part of the Warren-Bennis Leadership Series.