TWO kids I know—let’s call them Jeff and Mimi–wanted a cat, so they begged their reluctant parents for months. Eventually the parents gave in, but they forced the kids into an agreement: “The cat box will need to be cleaned every day. We expect you to alternate days. If you miss your day, we’ll take fifty cents out of your allowance and give it to your sister/brother. If you like, you can think of the fifty-cent transfer as a ‘fine’ that we pay to your sister/brother for your failure to hold up your end of the agreement.” The kids agreed and Corbin the cat was purchased (or, rather, obtained from the Humane Society). The litter box-cleaning arrangement went well for three whole days, but compliance started to wane on day four. Hostilities began to simmer. Jeff became reluctant to clean the litter box on “his” days because of Mimi’s failures to keep up her end of the bargain, and vice versa.

“Recriminations” began to pile up.

After two weeks, the agreement was declared dead. The parents became the chief cleaners of the litter box. The father continues to wonder whether he should have read more game theory before even entertaining the idea of getting a cat.

Cooperative agreements like these tend to be dicey propositions: What’s Mimi supposed to do if Jeff fails to clean the box on his appointed day? Should he view it as a sign that Jeff no longer intends to honor the agreement (in which case she should stop honoring it herself, notwithstanding the $.50 fine that Jeff had to pay to her), or should she view it as a one-off aberration (in which case she might want to continue honoring the agreement)? It’s not clear, and that lack of clarity can make problems for the stability of such agreements.

Luis Martinez-Vaquero and his colleagues addressed this issue in a recent article that caught my eye. The paper is complex, but it’s full of interesting results (some quite counter-intuitive) about when strategic agents should be expected to make commitments, honor commitments, retaliate when those commitments are broken, and so forth. I suggest you give it a read if you are at all interested in these issues. But what really grabbed my interest was the authors’ exploration of the idea that the key to getting such agreements to “work” (by which I mean, “become evolutionarily stable*”) was to build in an apology-forgiveness system that causes agreement-violators to pay an additional cost (over and above the fine specified in the agreement itself) after a failure to cooperate, which might cause the defected-against partner to persist in the agreement despite the fact that it has been violated.

The researchers’ results enabled them to be surprisingly precise about the conditions under which highly cooperative strategies that used apologies and forgiveness in this way would evolve*: The costs of cooperating (cleaning the litter box) must be lower than the cost of the apology (the amount of money the deal-breaker voluntarily passes to his/her sibling), which in turn must be lower than the fine for non-compliance that is specified within the agreement itself (fifty cents). When those conditions are in place, you can get the evolution of actors who like to make agreements, accept agreements, honor agreements, and forgive breaches of agreements so that cooperation can be maintained even when those agreements are occasionally violated due to cello lessons that run late, or unscheduled trips to the emergency room, or geometry exams that simply must be studied for.

I’ve written here and there (and here) about the value of apologies and compensation in promoting forgiveness, but the results of Martinez-Vaquero and colleagues suggest (to me, anyway) that forgiveness-inducing gestures such as apologies and offers of compensation can come to possess a sort of fractal quality: People often overcome defections in their cooperative relationships through costly apologies, which promote forgiveness. Throughout the history of Western Civilization, various Leviathans have capitalized on the conflict-minimizing, cooperation-preserving power of costly apologies by institutionalizing these sorts of innovations within contracts and other commitment devices that specify fines and other sanctions if one party or the other fails to perform. But after the fine has been paid for failure to perform, what’s to keep the parties motivated to continue on with their agreement? Martinez-Vaquero et al.’s paper suggests that a little “apology payment” added on top of the fine might just do the trick. Apologies within apologies.

By the way, Jeff and Mimi’s parents are reviewing the terms of the old agreement later this week. Perhaps it can be made to work after all.

Reference:

Martinez-Vaquero, L. A., Han, T. A., Pereira, L. M., & Lennaerts, T. (2015). Apology and forgiveness evolve to resolve failures in cooperative agreements. Scientific Reports, 5: 10639.  doi:10.1038/srep10639.

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*By which I mean “come to characterize the behavior of individuals in the population via a cultural learning mechanism that causes individuals to adopt the strategies of their most successful neighbors.”