Key Points

• Amazon began blocking Meta's Muse agent from shopping on its site Sunday night, citing its conditions of use.

• Shopify's president says agent-driven orders carry the same economics as ordinary online store orders.

• The two-day rally lifted the stock's forward price-to-earnings ratio from about 52 to about 60.

• These 10 stocks could mint the next wave of millionaires ›

On Sunday night, Amazon (NASDAQ:AMZN) began blocking Muse, the two-week-old personal artificial intelligence (AI) agent from Meta Platforms, from shopping on its site. Ask Muse to buy something on Amazon now, and a message says access by "an unauthorized AI agent" violates the site's conditions of use.

One day later, Shopify (NASDAQ:SHOP) went the other way. CEO Tobi Lütke said Monday that the company is "partnering deeply with Muse to enable agentic checkout with Shop Pay on all Shopify stores."

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Shopify shares rose 7% on Monday and another 7% on Tuesday, closing at $147.74 -- up about 15% in two days.

So what does Shopify collect when an AI agent does the buying -- and is it worth a pop like this one?

Amazon's objection

Amazon says Meta never told it Muse would shop its store, that it doesn't identify itself as it browses, and that it appears to capture and store customer credentials.

"We think it's fairly straightforward," an Amazon spokesperson said, that agents buying on customers' behalf "should operate openly and respect service provider decisions about whether or not to participate."

There is money behind the principle, too. Amazon generated more than $68 billion of advertising revenue last year, a business that benefits from shoppers browsing its pages. The more trips agents handle, the less browsing there may be.

Meta says Muse "has no visibility into people's passwords or payment methods." And the agent found an audience fast, overtaking ChatGPT as the leading free iPhone app in the U.S. within 10 days of its Sept. 8 launch.

An agent's order pays Shopify like any other

When Muse completes a purchase on a Shopify store, the order checks out through Shop Pay, the company's one-tap checkout button. Shop Pay orders run on Shopify Payments, so Shopify collects its payment processing fees on each one -- just as if the shopper had tapped the button.

"[T]he agentic transactions carry the exact economics as an online store transaction," Shopify President Harley Finkelstein said on the company's August earnings call.

Merchants sold $115.6 billion of goods across the platform in the second quarter, a total the company reports as gross merchandise volume (GMV), up 32% year over year. Merchant solutions revenue (payment fees plus the other services merchants buy) climbed 37% year over year to $2.8 billion. In other words, Shopify collected about 2.4 cents of every dollar its merchants sold, up from about 2.3 cents a year earlier.

In fact, I'd argue an agent's order is worth slightly more to Shopify than the average human one. The share of platform volume running through Shopify Payments keeps stepping up: 64% in the year-ago quarter, 67% in this year's first quarter, and 68% last quarter. Every Muse checkout runs through Shop Pay by design, so agent orders arrive fully attached to the payments business from day one.

The early volume signals are encouraging, too. Shop Pay GMV grew 53% year over year last quarter, outpacing the platform, and Finkelstein said AI-driven traffic and orders to Shopify stores both tripled in the second quarter from a year earlier.

Chief financial officer Jeff Hoffmeister added a datapoint at an investor conference this month. Shoppers who begin with an AI model are about 2.5 times more likely to land directly on a product page, he said, and that produces roughly an 80% uplift in conversion.

Time to buy the stock?

To be fair, Shopify hardly needs Muse to keep growing. Not only did second-quarter operating income climb 68% from a year earlier to $488 million, but free cash flow also reached $654 million, up 55%. That's an 18% free cash flow margin, expanding from 16% a year earlier.

However, agentic shopping is still in its early innings, and nothing about the Muse partnership comes with a number attached yet. And Shopify hasn't said what agent-driven orders could add to its volume. Investors bid the stock up this week on a mechanism, not on new revenue.

But the stock's valuation already reflects plenty of optimism. At Friday's close of $128.50, the stock's forward price-to-earnings ratio (the price against next year's expected earnings) was about 52. By Tuesday's close, it was about 60.

A forward price-to-earnings ratio that high assumes years of rapid growth.

So, is the pop a reason to buy? I don't think so.

Shopify arguably got the strategy right. Welcoming the agents opens another sales channel that pays like any other order, and Amazon's block shows how seriously the e-commerce giant takes the shift. But I'd want to see agent-driven orders become a meaningful, disclosed share of the company's volume before paying this price for it.

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Daniel Sparks and his clients do not have positions in any of the stocks mentioned. The Motley Fool has positions in and recommends Amazon, Meta Platforms, and Shopify. The Motley Fool has a disclosure policy.