On the theme of point destruction, there’s a reasonably big literature on a variation where destruction of rewards can be undertaken by players to reduce the rewards of other players, with variations where they control who can see what cooperative acts and vary the sizes of the group. Dunbar’s number sometimes makes an appearance. I imagine you’ve heard of this, and if you haven’t hopefully this comment will add it to your arsenal of game theory. It would be awesome if it made an appearance later in your sequence :-)
The general hand-wavy upshot is that for humans (assuming you’re in a situation where large scale cooperation and positive externalities are actually possible and valuable to you) the best situation is to be in a large-ish group where people can at least see defectors after the act of defecting, and can also see other people’s punishment behavior, and can punish both outright defectors and also “punish non-punishers”. So far as I’m aware, you don’t need recourse to more recursion than that. You don’t have to get totally silly with punishing of non-punishers of non-punishers of defectors. There are elements of the literature here, here, and here, if anyone wants entry points. The first is most accessible :-)
On the theme of point destruction, there’s a reasonably big literature on a variation where destruction of rewards can be undertaken by players to reduce the rewards of other players, with variations where they control who can see what cooperative acts and vary the sizes of the group. Dunbar’s number sometimes makes an appearance. I imagine you’ve heard of this, and if you haven’t hopefully this comment will add it to your arsenal of game theory. It would be awesome if it made an appearance later in your sequence :-)
The general hand-wavy upshot is that for humans (assuming you’re in a situation where large scale cooperation and positive externalities are actually possible and valuable to you) the best situation is to be in a large-ish group where people can at least see defectors after the act of defecting, and can also see other people’s punishment behavior, and can punish both outright defectors and also “punish non-punishers”. So far as I’m aware, you don’t need recourse to more recursion than that. You don’t have to get totally silly with punishing of non-punishers of non-punishers of defectors. There are elements of the literature here, here, and here, if anyone wants entry points. The first is most accessible :-)