How to loop a video on a WP site?

I have been consistently challenged by a client to make a video loop on a website, whenever a person visits the site. My initial response to them is that, I don't think that's possible especially with more website viewers using mobile devices. With the influx of mobile device users, this would mean upon visiting the site, their data plan would be used drastically each time they visit the site. Is this correct on my assumption?

If not, how do I make a video loop indefinitely.