The overall fascination with the idea of online sales doesn’t really seem to apply to the art market despite repeated fixation from several quarters. Part of the problem would seem to be the ham-handed attempt to apply the lessons of physical retail to art sales where payment has rarely been a pain point.
Today we have two different takes that reinforce the impression that the distinction between retail and online is irrelevant to the art market (which isn’t to say that art trading is immune to the overall effects of the mobile and internet revolutions.)
In Sotheby’s earnings report this morning, the firm emphasized its growth in online bidding:

Year to date, online sales at Sotheby’s have already exceeded $119 million, a 23% increase compared to 2015, which is particularly meaningful given the decline in sales volume overall.

In truth, that number is only 5% of Sotheby’s total sales. It may represent a larger portion of the “middle market” sales where Sotheby’s earns a higher commission and would yield more margin from lower selling costs but the absolute numbers are still a tiny fraction of Sotheby’s actual revenue. That may explain why Sotheby’s release takes pains to illustrate other benefits to the firm:

One in three bidders at Sotheby’s bids online. Online bidding has emerged as the most popular method of participation for new clients – with 44% of all new bidders coming through our online channels.

Most powerful is the fact that 40% of all online buyers are new to Sotheby’s – so it is not just about existing clients choosing an online path to engage with us – this is about adding new clients.

Artnet News also explored this issue in an article casting about for a response to Instagram’s testing direct purchase buttons on the platform. The reporter did not find many dealers who thought the sales platform would progress from a marketing channel to a direct sales channel:

“The ways Instagram has changed the art world are actually underestimated,” says Lauren Marinaro, director/partner at New York gallery Feuer/Mesler. “In the case of the Loie Hollowell show we have on right now, almost every person coming in, including big-time collectors, says they’ve seen a lot of it on Instagram. That’s the first thing they say.”

Hollowell didn’t think buttons would have a material effect on sales, an opinion shared by one of her more aggressively online peers:
“I don’t think click-for-purchase Instagram tags are applicable to art in particular,” said collector/dealer/advisor Stefan Simchowitz in an email. “The complexity of the art transaction and lack of simplicity will only make it possible for art-related products like prints and posters,”