Sure! Here's a simple game implemented as a single HTML file using JavaScript. Since you mentioned pictograms, I'll use emojis as visual representations for the game elements. This game is designed for smartphone operation.
This game will display a pictogram (emoji) representing the active player on the screen. Each time the screen is tapped, it will switch to the next player in the sequence. The game will continue until someone leaves the game by pressing any key.
You can modify the `players` array to include different pictograms if needed.