Anna and Ben’s kitchen problem

AGATA KOMENDANT BRODOWSKA: Before we start analysing global problems, let’s look at what happens when people share a good, but on a smaller scale. Here’s Anna. And here’s Ben. They share a kitchen.

It’s not so easy to keep the kitchen clean, right? Let’s think why. Anna and Ben both would like the kitchen to be clean. But let’s face it– they don’t like cleaning that much. So why doesn’t Ben clean more often? Let’s look at the situation from his point of view.

Both Anna and Ben can either clean or not clean. The best option for Ben is when he doesn’t clean and Anna does. The kitchen is still clean, and Ben can enjoy his free time. The worst option for Ben is when it’s the other way around. Ben does all the cleaning, and Anna doesn’t. The kitchen is clean. But Ben is really frustrated. You have probably already come up with the third possibility– when both Anna and Ben clean. For Ben, this option is almost as good as when only Anna cleans. Because the kitchen is clean, and they can share the work. This leaves us with the fourth scenario– when nobody cleans up. The kitchen is very dirty, but Ben avoids the frustration.

So this option is better for him than cleaning by himself. Let’s look at all the possibilities we’ve discussed so far. We can rank them from the best to the worst according to Ben’s preferences. This is the best scenario. This is the second best scenario. This scenario is yet worse, and this scenario is the worst one. So let’s assign some numbers to those results. The more points, the better the result– 1 for the worst one and 4 to the best one. And now, let’s look at those scenarios from Anna’s perspective– again, 1 for the worst one and 4 for the best one. We can organise those four scenarios in a simple table.

So what will happen? Let’s look at the situation from Ben’s point of view. What if Anna cleans? He gets free points if he cleans and four points if he doesn’t. So his best response to Anna’s behaviour is not to clean.

What if Anna doesn’t clean? He gets one point of he cleans and two points if he doesn’t clean. His best response is not to clean. Again, no matter what Anna does, the best choice for Ben is not to clean.

But wait– Anna situation is a mirror image of Ben’s. No matter what Ben does, her best response is also not to clean.

How do you think they will end up?