Is there a game theory for doing the dishes in a shared living situation? It occurred to me this morning (when I was intentionally not tidying up my flatmate's dishes) that doing the dishes in a shared living situation, such as at an office, or living with housemates, might be subject to a kind of game theory. 
The idea being, that there's a conflict between doing the dishes yourself and immediately producing value for yourself, and the others, but at the sametime enabling the lazy housemate, and decreasing the likelyhood that they'll do the dishes in the future. 
Are there any studies or research or theories around this?

This is called "chore division". It's in some sense dual to the better known topic of "fair division" (dividing a cake, an inheritance, the contents of a treasure chest etc.). You can find out more via web search.
