The Dish Washing Dilemma
As I begin to write this blog post, I notice that the kitchen sink behind me is filled with dirty dishes. My roommate is also seated across from me and must notice that the sink is full too. Either of us could easily fill the dishwasher in about five to ten minutes, but we both seem to play a game waiting for the other person to succumb into wanting a cleaner apartment. Since we have been living together for over a year now, I have seen the outcomes that occur. Usually, if someone has a guest coming over, they end up cleaning up. Sometimes, we mutually invite people over where we agree to do them together. However, the most interesting situation is when none of these events occur and the dishes not being done lingers on. I believe this situation can be modeled by a game theory game.
The game is quite simple. For me and my roommate, there are only two options: to clean or not to clean. There are also three outcomes. If we both do not clean, then each of our payoffs are 1. From my perspective, if I clean and he does not, my payout is 0 and his is 3. The opposite would be true if he cleans and I do not. Lastly, we if both clean then our payoffs are each two. This is similar to the prisoner’s dilemma that was discussed in class. It is also the game that is set up by the article linked below. The reasoning behind this setup is due to the assumption that resentment has some cost. More specifically, when one person cleans and the other does not that is a worse situation than just having a dirty apartment.
The Nash equilibrium, in this case, ends up being neither of us cleaning the sink and hypothetically meaning it is never cleaned. As the article mentions, this may be the equilibrium but it makes everyone worse off than if we both cooperated. It shows that rationality does not always lead to the best results. Obviously, the dishes never getting cleaned does not actually happen, so I am not satisfied with the actual setup of the game. From knowing our general personalities and observing outcomes in past games, it is clear that we actually have different tastes for cleaning. I personally am more fine with having a dirtier kitchen and my roommate tends to be a bit more of a clean freak. I believe that there is not necessarily a resentment cost for my roommate which is different than what the article postulates.
In actuality, I believe the payoffs of the game are slightly different then mentioned before. I think that when I choose not to clean and he chooses to clean, he actually gets some utility. He still likes when the apartment is cleaner even if he had to do the work. His resentment cost is not as high as mine in the opposite scenario. His payoff in this instance is actually 1.5. This changes the result of the game and leads to a Nash equilibrium of where I chose not to clean and he chooses to clean. Additionally, it does not seem that these adjusted payoffs happen immediately as the dishes are never done when the sink is filled. There seems to be a gradual shift from the original payoffs to the adjusted ones over time. It is as if we are playing this game every day, and his payoffs start to gradually change ultimately leading him to clean the dishes.
I believe this is a more accurate representation of the game we play; This is evidenced by the fact that when no guests are coming over, I rarely do the dishes. This makes me seem like an unfair roommate who does not do his share of the work. I would argue that I am simply taking advantage of being an Economics student and understanding game theory. For my sake, hopefully, my roommate does not see this blog post.
Source on the typical game of washing dishes: