It'll make you feel like Cormac McCarthy.
This is a pretty common writing prompt. You might have even done it before. If so, or if you just want to make it a bit more challenging, try this: introduce a third person. Using only dialogue, write a conversation among three people in such a way that the reader knows exactly who said which lines.
The purpose of this exercise is to get you to think about (and then act on) creating unique voices for characters. The goal is to develop a character voice that is so recognizable that readers know a particular character is speaking even without the usual speech markers.
You have a number of tools to use to create a character's voice: word choice, the use of space fillers, speech impediments, consistent speech errors (think Mrs. Malaprop), and even accents (though I should warn you against overusing eye dialect). So give it a shot. And have some fun with it.