@Quincy
We are in a highly competitive tourist destination, with lots of choices available, and have studied this quite a bit. Despite the substantial competition, we do have the benefit of high demand, so perhaps it's a bit different than some others.
Nonetheless, our observation is that lowering prices to compete can actually be detrimental in some circumstances. It's not quite that simple.
First, there are different demographics of guests. For example, there's those who are more interested in the price than the quality. This probably constitutes the largest segment of the market. They shop entirely on the basis of price, or perceived value. If it appears to be a bargain, then it's attractive. They'll book it.
Then there's the type who are less concerned about price, and more interested in what they believe will best suit them, or provide the most comfort. They'll shop on that basis, do more research, and then secondarily, consider price. Generally speaking, these tend to exhibit more desirable guest characteristics.
So, who are you targeting? Consider that.
But wait, there's another metric. In our case, there's demand. Lots of it. So we tend to look at the competition in the same class of accommodation, and price a bit higher. This tends to lengthen the booking lead time until the lower priced competition is booked up. Then you and a handful of others are the "only game in town", so to speak. You just have to be patient.
And then there's ratings. Many will downplay the importance of that, but when it comes to price competition, your ratings can be the difference between someone choosing a less expensive place with lower ratings and your place, with glowing reviews.
Also, styling makes a difference. The photos tell people a lot. And they're more likely to choose something they find more appealing even if the price is a bit higher. And this tends to attract the latter demographic, which is generally a more desirable type of guest.
Also, if the price is too good to be true, then it probably is. Smart shoppers know this.
So, be careful about engaging in price wars, as it can come back to bite. Create a unique and desirable space, make your listing stand out in the photos, consistently achieve good reviews, be patient, and price competition will be far less of a problem. The lesser of your worries, really.