Do you have any suggestions on how to convey this through game mechanics or story techniques?
Before I begin let me say three things:
- I do love to talk about quantum mechanics, that does not mean I'm good at it. My understanding is that of a layman. I love to eat tasty pastries too but can't bake for crap.
- While my answer is somewhat similar to Simon Gill's it has some base differences that may merit separating them.
- I will be focusing on the story techniques with just a bit for mechanics.
I will assume the following things:
- The PC's are hooked up to a quantum computer and have no knowledge that this is a simulation.
- They are not the only people hooked up the computer. Every NPC's is another person too, just not one that the computer is "interested" in.
- While the computer is exceptionally powerful, it is doing something that requires all of that power. In effect resources are limited and the computer must use some form of algorithm to manage resources.
- The computer is some form of AI, limited or not, it has an "interest" in some of its charges. That is, I think, grounds for it being self aware.
What is a Timeline?
In the normal course of life (simulated or otherwise) all possibilities appear to collapse into a single waveform flow of events. Some of these events lead directly to and impact other events, hence they influence the probability waveform of these later events by making some possibilities more probable than others. The participants in these events have recall of the events. This, more then anything else, gives the timeline a form. What happened is a function of what is remembered nearly as much as what really happened.
Concurrent Multiple Simulated Timelines - Say what?
The world the players live in is a simulation running on a powerful quantum computer. That computer can simulate quite a few parallel branches of the multiverse, but not all of them, so it collapses those that are not significant to the objectives of the simulation.
I will refer to the source of one or more uncollapsed timelines as an "Open Event".
At some point the computer wants to investigate multiple timelines by keeping parallel branches alive. When this happens an Open Event is marked and the fork in the simulation is created spawning two or more parallel timelines. In creating and maintaining these timelines the computer has to invest resources. First are the computational resources required to branch the simulated reality. Second is the memory management of the subjects connected to the simulation. Both of these areas would have an initial cost as well as a running cost as more resources are allocated to feed the on going process.
While it is very tempting for me to get into the hows and whys of this resource management algorithm; it's a trap. Ultimately, that level of detail is not important to the exercise. In keeping this more general all that needs to be said is an event could be classified on a scale by how many people it directly effects and how many events it directly sets in motion. The higher it goes on the scale the more resources it uses and the more memory management is required. Of these two things, I think memory management would force a collapse of timelines more often then a lack of resources. More on that later.
If you want to bring this to the in character level memory management of the PC's is a good place to start. It is an excellent opportunity for adding a game play element. What if the PC remembers the Open Event with some ambiguity, such as they recall each outcome of the Open Event because each of them happened. As more stuff happens in each line they recall the events. This could lead to insanity. Once (If) they figure out what is happening then I see a motivation to make the timeline collapse in favor of the parallel they feel is most desirable. Once the timeline collapses would they lose the memories? Not necessarily but they should know that line ended.
In relation to NPC's it could function differently, I think the computer would be motivated to preserve the integrity the the simulation in respect to those minds experiencing it. While it may justify limited breaks in this for the PC's, NPC's would be a different matter. Having a few people realize reality is not real is one thing, having a few million with the same idea could undermine the purpose of the simulation, rendering it useless.
In light of that line of reasoning, it seems a parallel line may be "forced" to collapse well before computer resources become problematic due to the need to preserve reality integrity for the masses. In some special cases an NPC may get the same treatment as a PC. This could be a vehicle used to create a "Lex Luthor" type and have a main NPC work against the PC's because they want a different timeline to "win".
Pulling it all together
At the end of the day a GM can do what they want with their game. That is the nature of it. So if you want to play fast and loose with this then that is how you should go.
While I could go on and do this complex thing about assigning points to aspects of the Open Event and bookkeeping a number called a Tangent Resource Pool (TReP), I'm not. The more I think about that the more work it would be for the GM and it gets crazy fast. I'll just say that if you want to you could have a thing called TReP (trip) and give it a value to represent "mana" for maintaining parallel timelines. Use up all the points and one or more timelines collapse to free up TReP points.
Alternately, you could simplify things and have one major Open Event and say two or three minor ones running at any given time. That simplifies things greatly and lets you concentrate on story and your PC's.
While I would lean toward designing the TReP (I have a propensity for overkill) I would end up using something more like my second option.
Are there any games out there that already implement (something similar to) this premise?
Yes, with what I have state one could work in elements of WoD Mage the Ascension (editions 1 and 2 being what I know) looking at the paradox mechanics for inspiration in regards to memory management and forcing timeline collapse.
Also, check out The Wheel of Time books. There is an RPG based on that as well but I only played it once so I can't say if that will help you at all. The books, however, deal with the concept of Ta'veren extensively. That could be an excellent aid in storytelling shifts in probability. People "feel" the weave of the reality shift around a powerful Ta'veren.