(AMZN -0.29%) has changed the game for retail.

The online retailer started by disrupting the book industry, putting Borders, one of two major chains, out of business, and leaving only Barnes & Noble to fend for itself. Now, Amazon has, of course, moved well beyond books and media content into pretty much everything else. You can buy a TV or loose tea on Amazon as easily as you can buy pajamas or stuffed llamas.

That has been bad news for brick-and-mortar retailers, which have struggled to compete with the online leader, specifically when it comes to price. This problem is not limited to physical stores either, as a new study shows that the most loyal Amazon customers, the ones who pay $99 to join its Prime service, generally do not look anywhere else before making a purchase.

Amazon has an expanding base of incredibly loyal customers who trust the online retailer enough to not bother looking anywhere else. If this research from Millward Brown holds true in the long term, the digital and physical retail worlds are going to be littered with a lot more Borders.

Prime is $99 a year, but Amazon offers a free month-long trial. Source: Screenshot

What the research says
Amazon Prime members are likely to do their shopping on Amazon without checking other sites or visiting a physical store, reported Internet Retailer on the Millward Brown research.

The report found that the loyalty of Prime members is much stronger that of customers who do not pay for the service, which offers free two-day shipping and other perks:

Less than 1% of Prime members are likely to consider other [popular] online retailers during the same session. Take, for example: A non-Prime member is eight times more likely than a Prime member to cross-shop between Amazon and Target in the same session. For retailers not named Amazon, this means fewer chances to influence the growing Amazon Prime segment and heightened pressure to get the experience and value perception right.

For any company that is not Amazon, this is a very troubling trend, especially when you consider how popular Prime is becoming. An estimate earlier this year from investment firm Macquarie said that half of U.S. households could be members of Amazon Prime by 2020, according to Internet Retailer. Macquarie estimated that 20% to 25% of U.S. households (roughly 40 million) already include a Prime member. The research firm also said that in the fourth quarter of 2014, 10 million consumers signed up for Prime.

That is a huge chunk of the U.S. population likely to buy from Amazon without even looking at other stores.

More bad news for retailers
Not only do Prime members show loyalty to Amazon -- they also make a purchase much more often than any other online shoppers.

Prime members have a stunning conversion rate of 63% per shopping session, according to Millward Brown. That is "nearly five times the conversion rate of non-Prime members," Internet Retailer reported. "It's also far higher than the typical 3% to 4% conversion rate of U.S. e-retail sites in general."

What can competitors do?
Amazon has built a powerful retail model with Prime. Because a customer has already paid for free, two-day shipping, he or she has an incentive to shop more on the site to make that purchase a better value. Add in the perception (and often reality) that Amazon has good prices, and customers have little reason to comparison shop.

Why drive to a retail store or even visit another website when Amazon offers one-click purchases, free shipping, and typically competitive prices, if not the best prices? Even if a competitor was a little bit cheaper, is it really worth leaving the house or entering your credit card info for another retailer?

To compete, physical and digital retailers have to take a page out of the Amazon playbook to find ways to tie consumers to their brand. That is easier said than done, but loyalty programs, subscription services, and other long-term relationship builders are the place to start.

Amazon has forged a strong relationship with its Prime members, and it has continuously enhanced that relationship. Since the program launched in 2005, annual membership fees have gone up only once, from $79 to $99, and the retailer has added impressive video and music services to the program. The company has continued to enhance the offering, which not only keeps customers loyal but also draws new ones in.

If the rest of the retail world hopes to compete, it has to find ways to offer similar value and to attract customers to their stores and their sites.