In game theory, coordination games reflects the benefits of everyone settling on the same rules. Settling on the same rules can avoid a conflict and destructive competition. For example, some rules may be arbitrary, such as on which side of the road we’ll all drive. It doesn’t much matter whether a country’s vehicles drive along the right or left side of the street. As long as everyone is in the same lane, we overwhelmingly benefit from our coordination. The matrix below describes the game.
The above game reflects that whether we agree to drive on the left or on the right is trivial and that the important detail is that we agree on what the rule is. Rules like this are arbitrary. No amount of cost benefit analysis changes the answer. Other coordination rules are seemingly arbitrary, but do have different welfare implications. For example, according to English common law, a farmer was entitled to prohibit a herdsman’s flock from trampling his crops even if the farmland had no fence. Herdsmen were responsible for corralling their flocks or paying damages if they grazed on the farm. With lots of nearby farms, total welfare was higher with a rule of cultivation rights rather than grazing rights.
But the property rights could have been assigned to the herdsman instead. The law could have said that the sheep were free to graze with impunity and that the onus was on the farmer to build fences in order to keep the sheep at bay. In a world where there are a lot of farmers who are very nearby to one another, a small flock of sheep can do a lot of damage. And so, the cost-benefit analysis prescribes that herdsmen bear the cost of restricting the flock rather than the farmer. The matrix that describes this circumstance is below.
The above matrix reflects that agreeing on any rule is better than no rule at all. And, the rule that is selected has societal welfare implications. Choosing the ‘wrong’ rule means that we could get stuck in a rut of lower payoffs because coordinating a change in the rules is hard.
Another way in which the specific rule can be important is by whether it instantiates or works contrary to pre-existing incentives. Before compulsory schooling laws were passed, US states already had very high school attendance rates. Most parents sent their kids to school because it was a good investment. The ages at which children should be required to attend is largely, though not entirely, arbitrary. And wouldn’t you know it, most states applied their compulsory schooling legislation to the age groups for which the vast majority of children were already attending school. Enforcing a law against the natural incentives of human capital investment would have been more costly. The particular ages of compulsory schooling had different welfare implications due to the differing costs of enforcement.
Remember ‘Hey Arnold!’? It’s a show about a boy who lives in a boarding house that’s owned by his grandparents. There was an episode in which Mr. Hyunh repeatedly throws a fit because he has to clean out the clothes dryer lint trap of other people’s lint before he dries his own clothes. I understand the moral indignation of doing something which seems to be someone else’s job. After all, it wasn’t Mr. Hyunh’s lint – why should he have to empty the trap? Moral preferences aside, what should the rule be? Empty the lint trap before you start your laundry? Or empty it afterward?
It seems like an arbitrary matter. Either way, you’re emptying lint, right? If everyone follows the rule then we’ll all be on the same page. Absolutely. The logic is sound. But the logic includes an assumption that isn’t applicable to reality. The ‘if’ is a big if. People do not have the same incentive to comply with both versions of the rule and that makes the rules different. Whereas a perfectly enforced rule will have no welfare implication, the rules differ by ease of enforcement.
Here’s how. You run your clothes in the dryer. Once finished, you place in your clothes in the basket and you’re on your way. You just left the lint in the trap for the next person to worry about. If you think about others a great deal, then maybe you were pro-social and emptied the lint trap. But, if you have your own concerns at the front of your mind, then failing to empty the lint trap has no effect on the rest of your day. You have no incentive to comply with the rule.
On the other hand, if you don’t empty the lint trap prior to starting the dryer, then your clothes may require longer to dry. If the dryer is a common dryer, that may mean more quarters – an explicitly pecuniary cost. Of course, a lint trap that is too full could also start a fire and damage your clothes or worse.
Therefore, the natural incentive lies with the rule of emptying the lint trap prior to dryer use. The fact that the lint is from someone else’s clothes is immaterial to the economic incentives, the ease of rule compliance, and therefore, to a uniform distribution of costs. The rule has welfare implications.
Way back when, bathtub faucets had this tab that you’d pull up on in order to divert the water to the shower head. As technology progressed, we began installing lever systems instead. There are 1 or 2 levers or dials that control hot and cold water and an additional lever that controls whether the water exits the bath faucet or the showerhead. This technology introduces a coordination problem. If the last user didn’t turn the lever to bath-mode, and neither do you, then you can be in for an abrupt awakening as initially cold water shoots out of the shower head and on to you. Yikes!
Who should ensure that that bath-mode is selected? The person who showered? Or the person who is about to shower? It’s the same as the dryer lint example. If you neglect to select bath-mode when you exit the shower, then your day proceeds unaffected. But if you don’t ensure bath-mode at the start, then you get a face full of cold water. Should bath-mode be the default according to standards of propriety such that the bather should return the default after use? I have no idea and I don’t care. I do know that enforcement between the two rules differs such that less coordination occurs in one case and more coordination occurs in the other.
Rules aren’t always about right and wrong. Some rules are arbitrary if they’re perfectly and equally enforceable. When enforcement costs differ, we should try to adopt rules that result in greater compliance, all other things held constant. Be the change that you want to see in society. Let the drier lint lie. Just get out of the shower and enjoy your days. Leave the lint and levers to those who have reason to worry about them.