Raking Leaves versus Retaining Your Coat

Altruistic Elder with Free-Riding Younger?

Every autumn, whether in Bloomington or Seoul, the kids go out and play in the fallen leaves. The air is clear and brisk with an aroma of freshly decaying detritus, conditions are ideal. Larger piles obviously yield the greater joy as riskier dives are attempted. However, larger piles require more non-jumping effort of raking, resulting in an optimization problem only elementary children can fully appreciate. The dilemma arises when one child rakes up the leaves and the free-riding sibling jumps in, destroying the efforts and future benefits of his toils. The frustrated child then refuses to rake any further, resulting in a sad looking layer of leaves with even sadder faces staring at it.

When the kids are young, I find myself doing most of the raking (usually for the private objective of ridding my yard of grass rotting waste). Recently, I noticed my eldest taking on a majority of the leaf raking into piles. This has two conclusions. First, the older you are, the more efficient (less costly) you are at raking. And second, the older you are, your payoff from jumping in the leaves is lower than the payoff you get from watching your younger offspring enjoying themselves (or avoiding the sight of their sad little faces).

In other words, the solution to the Prisoner's Dilemma game (where both don't rake, but would be better if they both did rake) is to have the game repeated over time with players that have different time horizons, hence the chance for pairing young and old, otherwise known as overlapping generations. This is highlighted in the economics and biology literature explaining altruism (why cooperate if you know you will be cheated?) In a way, this describes how older generations need to be more altruistic to allow the younger generation greater chances to survive or succeed.

I am reminded of Thomas Hardy's description of the decision to take off one's coat or not at a dance in his book "Under the Greenwood Tree".

"Before we begin...'twould be a right and proper plan for every martel man in the dance to pull off his jacket, considering the heat...If I strip by myself and not necessary, 'tis rather pot-housey...but if we stout chaps strip one and all, 'tis the native manners"
"'Strip we will!' said the three other heavy men who were in the dance; and their coats were accordingly taken off...Dick, fearing to lose ground in Fancy's good opinion, retained his coat like the rest of the thinner men..."

Sometimes, we should just rake the leaves because we have already had our turn.