Re-posting of an article first posted in May 2007.
Okay, here's a game sketch. This idea is supposed to be a game that could live on a Web site somewhere, support a large number of players, but be fun to participate in even if you are brand new, or only connect occasionally, or if there are few or no other players. Kind of like Wikipedia - except that my idea would actually know it's a game, unlike Wikipedia which thinks it's an encyclopedia. I'm posting this here to make it harder for anyone to patent.
You start with some kind of complicated, interesting simulation that evolves over time. For example, it could be a simulation of British noble families during the Middle Ages. The nobles own property, they reproduce, they get richer or poorer, they die and leave their propety to their descendents, and so on. This simulation is deterministic, but pseudorandom: that means that from any given state the simulator can compute all future states, but it's hard to predict the future states as an outside observer who doesn't know all of the current state. Also, the accuracy of your predictions declines over time, so that a small change today tends to gradually have larger and larger effects.
All the history of the simulation is posted on the Web, and it gets run forward at some rate relative to real time, with all the new history posted as it happens.
You, the player, are a time traveller. You have some opportunities to make small changes in the past of the simulation. If you do, the simulator will pick up from the point where you make the change, run forward with your change added, and that becomes the new history of the simulation.
For instance, suppose that Lord Bob has a large estate, which will pass to his heirs according to the rule called "male primogeniture," and his only child is Lady Alice, who in turn dies giving birth to Lord Dave. Lord Dave stands to inherit Lord Bob's estate. But then Lord Bob's first wife dies and he marries Lady Carol, and she gives birth to Lord Fauntleroy. Lord Dave suddenly loses his inheritance; his new uncle Fauntleroy, being a direct male-line descendant of Lord Bob, takes precedence over Lord Dave, who stands in his deceased mother's place in the succession, after all those related through sons of Lord Bob, such as Lord Fauntleroy.
Lord Dave wouldn't go so far as to actually murder the child, but... Many years ago, when Lady Carol's now-deceased father, Lord Herbert, was a boy, he was thrown from a horse and nearly died. "What if Lord Herbert's injuries had been a little more serious?" thinks Lord Dave. "He's dead now anyway, so nobody today is in a position to care, but if Lord Herbert had died on that earlier occasion, he'd never have fathered that whore Lady Carol, and she would never have gotten her hooks into Grandpa, and I'd still be in a position to inherit the fortune..."
Imagine that a mysterious figure visits Lord Dave one day and offers, for a price, to make a small change in history.
As a player, you get to be the mysterious figure. Looking at the current state of the world, at any given moment there will be a bunch of assignments you can accept. Some of them will be easy, with a clear way of accomplishing them - such as "Lord Dave wants to inherit his grandfather's wealth." It seems like all you need to do to make that happen is kill somebody who is an ancestor of Lord Fauntleroy and not of Lord Dave, before they get a chance to breed. Others will be harder, possibly much harder. I envision a list of job postings, with different characters offering different prices for different services. Goals count, not how they're accomplished.
If you accept a job, you get the chance to make a small adjustment in the past. I imagine a list of opportunities for those, too, and you'd have to choose which one(s) to use. Adjustments in the recent past come for free, but for earlier ones, you will have to enter a single-use code. If your attempt is successful in achieving whatever result you were aiming for, you're rewarded with a code that you can use in making other time jumps.
It's possible to handwave the code thing by talking about time machines that allow travel into the past, but only a limited amount of time before the first invention of the time machine (argument: the present day is apparently not overrun with time travellers, so maybe right now is before that limit). If you make a small jump successfully, you have the opportunity to plant the knowledge of time travel at an earlier date, which will allow other jumps to even earlier dates. Or something. In a medieval frame of reference, you can talk about the time travel being accomplished through actions with the spirits in the style of John Dee (he was Renaissance, not Medieval, but whatever) and there being secret words needed to command the spirits, passed down through families or something, and so on. The explanation doesn't need to really hang together because that's not the point.
So the simulator has an initial state and a list of exceptions. It runs forward from the initial state to the first exception, implements that exception (which could be something like "but this character, who survives under the pure simulation rules, dies after all!"), and continues running. This is a pseudorandom, but deterministic, process - so if you do it again with the same initial state and list of exceptions, you get the same result. Exceptions that aren't applicable when their time comes, are ignored (maybe even flagged and removed). Time travellers get to add to the list of exceptions; when they do, the whole mess can be recomputed from scratch, or just the part from the new exception onwards. The history up to the present time gets posted on the Web for players to examine when deciding when to play their exceptions.
Although players do not directly correspond to characters in the game, you can see this as something like an RPG with a sort of p-kill; but instead of killing other players, you're causing them to have never been born in the first place by killing their ancestors.
There would probably have to be some limits in place to prevent, for instance, people from jumping before the original simulation start date, or to prevent them from murdering all of the last couple generations so that the game comes grinding to a halt. These kinds of things wouldn't be hard to enforce, though. The list of opportunities to change history just wouldn't include opportunities to kill characters at times when the population is considered too low - and low population might also make characters more fertile, so as to keep the population generally stable as the death rate due to time traveller interference fluctuates.
It needn't be limited to inheritance among nobility, either - any kind of complicated and interesting system that can be simulated over time would be a candidate for this treatment. The general outline is: players have goals in terms of the current state of the system, to accomplish them they have the chance to make changes in the past, and the bigger the goals they are able to accomplish, the farther back into the past they're allowed to reach.