Thanks for these thoughts. Yes this is broadly the direction I am headed, and planning to explore further in future posts. I agree that both repeated (IPD-style) interactions and kin-interactions are ways of developing the evolutionary prisoner’s dilemma so as to ‘integrate Moloch and the Goddess into a single model’ as I put it at the end of my post. Another approach is to introduce spatial structure.
There are a number of different specific models to explore here, and I prefer to look at the simplest and clearest versions. Your presentation is very dense, and I think introduces some complications that are not necessary to make the point. For example I’m not sure why you introduce the assumption about two descendants and their pc±ϵ probabilities to cooperate. You can just construct the model using a variant of Hamilton’s rule where r is the probability of interacting with kin rather than a random member of the population, this will result in cooperation growing if r is high enough relative to the payoffs.
Thank you for the detailed critique! The second model ensures that the probability to interact with kin varies over time. While the more recent mutations don’t have kin to interact with, older ones either die out or create an entire group of descendants, and the group itself interacts with itself and few neighbors. The bigger the group is, the smaller is r and the harder it is for defection to spread further.
Thanks for these thoughts. Yes this is broadly the direction I am headed, and planning to explore further in future posts. I agree that both repeated (IPD-style) interactions and kin-interactions are ways of developing the evolutionary prisoner’s dilemma so as to ‘integrate Moloch and the Goddess into a single model’ as I put it at the end of my post. Another approach is to introduce spatial structure.
There are a number of different specific models to explore here, and I prefer to look at the simplest and clearest versions. Your presentation is very dense, and I think introduces some complications that are not necessary to make the point. For example I’m not sure why you introduce the assumption about two descendants and their pc±ϵ probabilities to cooperate. You can just construct the model using a variant of Hamilton’s rule where r is the probability of interacting with kin rather than a random member of the population, this will result in cooperation growing if r is high enough relative to the payoffs.
Thank you for the detailed critique! The second model ensures that the probability to interact with kin varies over time. While the more recent mutations don’t have kin to interact with, older ones either die out or create an entire group of descendants, and the group itself interacts with itself and few neighbors. The bigger the group is, the smaller is r and the harder it is for defection to spread further.