A game theoretic model of intraself cooperation
Erstwhile, I published Don't torture your innie. Here are some more thoughts on this on this extending or generalizing this framework more formally using a game theoretic model of intraself cooperation:
There’s also something about your happy self or healthy self: if you only allow yourself to not work and be productive whenever you feel sick or depressed, you’ll rebel and develop hypochondria in the limit.
Or another way to bribe the productive self is with stimulants: the deal is that the morning self is allowed be high in exchange for work.
I guess ultimately you can view yourselves cooperating in a not entirely unadverserial way: you need to trade with yourself. You need to give your morning selves or your happy selves, or your productive selves a deal. And in order to establish cooperation and not have any of your selves defect, in game theory the only way to do so is playing iterated trust games.
In a trust game you give your game partner an initially small amount because you don't know they react - say $1. If the partner doesn't cooperate and defects in this trust game, they return nothing. And if they know that the game will be over after one round, and you have no way to retaliate that's indeed the most sensible strategy. However, if you have an infinite number of rounds (or don't know when the game ends or how many rounds there are), then it makes sense to cooperate. In many games we play there are gains from trade: In the stag hunt game we get a bonus for cooperating because that's often good because it allows specialization and division of labor. Together we can hunt a stag rather than two rabbits. So in the trust game that is also a stag hunt game, if your partner cooperates they can give say $2 dollars back so you get a return on your initial investment. Then in the next round you've got some info on your partner: You know the guy cooperated in the last round where you weren't going all in and only gave them a dollar. You might up the ante and give them $2 this round and if they give you $4 back, you might up the ante again. Lots of social relationships are like that (e.g. the long term customer who gets credit, credits scores generally, friendships, etc.).
Now: we can apply this to your multiple selves as well: In order to cooperate with your selves you need to not defect. The evening self and sick self needs to not totally pig out and eat everything in sight only for the health / morning self to pick up the slack the next day and eat salad and work. There needs to be fair division of labor.
In that sense loving yourself is not procrasting on stuff because that's similar to swiping your friends credit card with no intention of paying it back. Often, because we're bad at delaying gratification, this simply boils down to being better at delaying gratification (e.g. saving for retirement, dieting etc.). But even this should be done in moderation: if you always postpone the fun for the sake of some later self, you will burn out. Such an IFS model of burn out makes sense to me. I think moderation, mixing things up and 'keeping things short' and sweet, and concrete take aways from this model.