Resolving chariot races need only draw on whatever that system might use for movement rules or chase/pursuit rules, modified by the GM to suit the situation.
Here are some prominent RPG systems I know of that have no rules for resolving chases/pursuits in a way that would make for a satisfying chariot race:
* AD&D (the dungeon pursuit rules just compare movement rates,; the outdoor evasion rules are not relevant to chariot races);
* B/X D&D (ditto);
* Classic Traveller (the referee would have to make up some rules based around the vehicle skill);
* Rolemaster (there are rules for resolving vehicular manoeuvres, but not in the context of a race - the GM would have to make up a system for opposed checks);
* I think RQ also has the RM problem, but I'm a bit less confident about that as it's been a while.
"Resolving" interactions with prophets or holy types rolls right into the point I'm trying to make: those interactions can occur and be roleplayed through but IMO without external pressure (which would almost invariably drift quickly into combat rules and-or GM fiat) they cannot ever be resolved in finality.
I have no idea what you mean by "resolved in finality". I mean something fairly concrete - an outcome to the present fictional situation is established, by application of the resolution mechanics, and is binding on all participants, most saliently in this context the GM.
Gygax's morale rules in his DMG assume this sort of finality, inherited from wargaming: if a unit breaks than the player controlling it can't just arbitrarily (eg in the absence of some sort of "rally" mechanic) decide that it returns to the fight.
Classic Traveller in its rules for NPC reaction rolls expressly provides for finality. From p 23 of the 1977 version:
Reactions are used by the referee and by players as a guide to the probable actions of individuals. . . . Reactions govern the reliability and quality of hirelings and employees. Generally, they would re-roll reactions in the fact of extremely bad treatment or unusually dangerous tasks
The GM can't just decide that a NPC changes his/her mind after the reaction is rolled for. Something significant in the fiction, initiated by the players (eg bad treatment, dangerous task) is required.
If nothing is binding on the GM, then nothing is
character driven via the actual mechanical processes of play as described in the OP. There is only the GM deciding what happens.
I suppose it hinges on what you mean by "mark on the gameworld".
It could be anything. In a Rolemaster campaign a PC wanted to end slavery in the Great Kingdom. Another PC in that campaign wanted to ally with Vecna to take over the government of the Great Kingdom, but also helped his sometime companion (the first-mentioned PC) at a key point in his anti-slavery and anti-chauvinist aspirations.
In a different RM campaign a PC met a sorcerer on another plane and helped rescue her. He then set out to woo and marry her. In the end he succeeded in this endeavour, the player having built up the PC's social skills sufficiently to make it possible.
In our Prince Valiant game one of the PCs started play as a squire - the son of a moderately prosperous bourgeois family - and wanted to be knighted. He achieved this by challenging a knight to a joust who was blocking the path and would relent only if defeated in a joust by a fellow knight:
The PC asked for a joust, but the proud Sir Lionheart declined to joust with a mere squire. To which the PC responded, "Fine, I'll just continue on my way then!" and tried to pass Sir Lionheart and continue along the road. This called for a Presence vs Presence check, which the PC won - and so Sir Lionheart knighted him so that he could joust and perhaps succeed where the others had failed.
That's a mark made on the gameworld, in virtue of finality of resolution.
I-as-PC might be trying to talk the party into chipping in funds toward a castle for use as a home base. Should a game mechanic be allowed to determine whether I succeed or fail?
Different systems approach this in different ways:
* In Burning Wheel, this can and normally should be resolved via a Duel of Wits;
* In MHRP/Cortex+ Heroic it can be resolved via the use of the standard resolution mechanics (this happened in our game on Sunday when the dwarf tried to dress down Gandalf but failed, and Gandalf instead mad him feel ashamed of questioning a wizard's judgement);
* In 4e D&D there is no system for player vs player social conflict, which takes this mostly out of the ambit of character-driven arcs;
* In Apocalypse World a player can't force another player to have his/her PC do something, but can make doing something difficult and/or create mechanical incentives (ie XP awards) to do something else.
In those last two games, the rules are different vs NPCs: 4e D&D has pretty robust mechanics for the players to have their PCs force their will upon NPCs; and Apocalypse World does also. Here's the AW move:
S
educe or Manipulate
When you
try to seduce or manipulate someone, tell them what you want and roll+hot. For NPCs: on a hit, they ask you to promise something first, and do it if you promise. On a 10+, whether you keep your promise is up to you, later. On a 7–9, they need some concrete assurance right now. For PCs: on a 10+, both. On a 7–9, choose 1:
• if they do it, they mark experience
• if they refuse, it’s acting under fire
What they do then is up to them.
All these differences affect the play experience.
if they say 'no', a game mechanic should never prevent me from trying again later
Once (and as best I recall only once) in our 4e game, when debate about what to do next had dragged on to a point beyond decency, I called for opposed d20 checks, I think with adds on each side reflecting CHA bonuses.
Twice in our Classic Traveller game I've called for opposed checks to settle a debate between the PCs (being played out at the table) with modifiers reflecting noble status (ie Social Standing B+) and Leadership skill.
I've got no particular aversion to applying finality of resolution in these contexts, though as I've posted above not every system provides for it. (For what it's worth, I think what I did was a much bigger hack of 4e than Traveller, which is probably why it happened once in 100-ish sessions of D&D whereas has happened twice in a dozen-ish sessions of Traveller.)