First of all, you don’t know if there are other advertisers for that keyword or not. You may not see them for a variety of reasons, some of them I’ve pointed out earlier. There may be seasonal effects that others know about and why you didn’t see ads. Their budget for the day may already be depleted. They may show ads only on certain days or only during certain times of the day. Some may simply not be advertising for that keyword at this moment. Some may not be advertising in your area, doing so only in certain countries for example or even a specific city. If I advertise only in New York, you will not see my ad if you are in Miami.
So never assume you are the only advertiser for that keyword, no matter what you see when searching for it on Google.
Even if that were so, as seen in the Quality Score sections above, Google will not give you a perfect ten just because you may be the only advertiser at this moment. There is historical data they take into account. You also may not have good keyword relevancy which will drop your QS.