Competing

Gridogram does not have a built-in mechanism to rank players. This would mean players having to set up accounts, which shouldn't be necessary for a fun casual daily game. Players can however see a graph of how their anonymous stats compare to the rest of the world:
Global stats example

Beyond that, the way players can compete is with friends, by sharing in a group chat how they did on the daily grid:
Share daily Gridogram example

This seems to work well when sharing in WhatsApp group chats, emails, and online forums. Some people compete on speed, others on accuracy — no metric is paramount. And some folk don't care much for competing, but do occasionally share their thoughts on the quote.

It's naturally possible to get an impressive result by doing the daily Gridogram on one device, and then doing the same quote again on another... But therein lies no glory.