50 First Dates is a romantic comedy released in 2004, and, although it has been years since I've watched it, something came up that brought it up to my attention.
The love interest in 50 First Dates suffers from anterograde amnesia, which, in this case, means that she cannot form new memories, and forgets everything that she had learned the day before. What brought this to my attention is the discovery of two cases of people who have this condition, and wake up each day believing that it is always a single fixed date.
The first question it raises is whether or not the person who wakes up in the morning is the same person who fell asleep the day before.
I would argue no, as there is no continuity of consciousness between one day and the next. An identity depends not on the physical body (otherwise teleportation would destroy identity), but on memories which tie our future selves to our present.
But what of those amnesiacs? They leave themselves notes that they trust in order to provide some semblance of identity, but notes can be forged, and it all depends on a decision to trust the notes as the truth. And there is always the time before reading, before the return of memories, where, for all intents and purposes, one is merely one of many clones, a new one awakened day after day after day.
(Which as an aside raises the interesting possibility of group identities with groups of clones. If you were part of a collective of short-lived clones, you wouldn't have much identity belonging to yourself, but would be more invested in the good of your collective, on which you depend.)
Despite the sequential existence of the copies, the assets are still temporally related. You only have a limited amount of resources split between the copies of you, and each day, the current copy receives the resources allocated by the previous copy of you, and you choose to spend a certain amount of resources, and allocated the rest to the next copy of you.
A decision of how many resources to keep and give at the end of the day is similar to an dictator game, where your present copy determines how much to give to yourself, while the rest is passed along, where the best play is to give yourself everything and nothing to the other; however, as you receive your assets from a previous, similar version of yourself, when you wake up in the morning (and before you check your assets), a decision made then is most similar to a prisoner's dilemma, where, when playing with a copy of yourself, should cooperate and attempt to maintain the limited resources (going to work instead of going on vacation, for example).
The question that remains is which of these games should you play? The two games have different optimal strategy, and thus, you can't win all the games you play.
Which game should you play? It depends on whether you're a one-boxer or a two-boxer.
Two-boxers, the casual decision theorists, would advocate defecting, taking all the resources available and living life to the fullest, as your choice has no impact on the amount of resources you obtain, as your choice is not causally related to the amount left for you to use.
The optimal strategy, however, seems to be one-boxing, supporting evidential decision theorists, as, given that all copies of you would save resources, you would receive more if all copies of you maintain your resources compared to if each copy of you spent it all on theirself.
Of course, this only works if the copy of you at the end of the day is similar enough to the copy of you who wakes up in the morning. If the span of one day is sufficient to change ones choice, then even though one may choose the "optimal" choice, they may still receive a suboptimal outcome.
Alternately, if one can precommit strongly enough to choosing to cooperate, to one-box, then one can achieve the most optimal outcome.
The difference between anterograde amnesia and Newcomb's problem is that you have the option to change your choice after you receive the outcome. Only by precommiting, however, can you avoid the seemingly obvious choice of two-boxing after obtaining your resources, as once you receive your resources, you must prevent yourself from spending all of it at once, in order to ensure that you would have received that many resources in the first place.
Omega provides you with a sum of money,
n equal to the amount of money it predicts you will leave yourself. You are given a fixed amount of time
t which you can allocate to either increasing
n or happiness, and you can convert any amount of
n into happiness.
t = 0, the remainder
n is the amount of money given to you by Omega.
Newcomblike, yes, but it requires you to precommit even after you receive your prize.
(I'm fairly certain that it is reducible to Newcomb's Problem, but I leave that as an exercise to the reader.)
(I'm ignoring interest and value of solid assets here (which is fairly vital, otherwise the best strategy would be to make only as much money as you can spend), but if we include that, the best metastrategy would probably be to precommit to not spending money until you can live off the interest at a preset standard of living. (There's graphs hanging around about loss aversion and scope insensitivity that one can probably draw up to find the most optimal point.))