Do you also have a roommate who doesn't seem to do his or her share of the work? Their usual excuses are: "I am just not good with cleaning", or "I don't care about how clean the room is". If you belive them, in both cases you are left spending more hours cleaning your joint room than your roommate, and we will see why this is rational and even unavoidable unless there is some outside pressure.
Cleaning your room is not really a game, but we model it by a game. It is important to understand that this modelling has to be done with care, and you also should be cautious when drawing conclusions from your model. This is also discussed in this chapter.
This is discrete version of an example given in [Baldani/Bradfield/Turner, 18.7]. A0, A1, ... A4 are the options for Ann to work for 0,1, ... 4 hours, and B0, B1, ... B4 are the options for Beth to work for 0, 1, ... 4 hours.
Open this Excel sheet to see and change the payoff matrices for different p. The best response values highlight automatically.
If p increases, Beth works more and Ann works less. The better Beth gets at doing household matters, the more time she will have to spend with it.