The game theorists/economists have studied this stuff in depth under the rubric of "mechanism design" or "market design". The relevant concept is "incentive compatibility" where the agents in the system do the right thing (whatever that was intended to be/designed for) because any deviation from that costs them more than playing nice.
The Wikipedia article [0] is not yet great but does give the two classic examples of "second-price auctions and a simple majority vote between two choices". The Gibbard–Satterthwaite shows the difficulty in extending this to more choices (in that Arrow's theorem sort of way).
The best thing I've read on this stuff is Alvin Roth's "Who Gets What and Why" (2015) [1] which is worth a read in any case. Repugnant markets!
My experience tring to map game theory to people's choices in the workplace is that the action taken is typically opposite of the predicted, or optimal, 'game theoretic' action, and often with enormous benefit to that individual.
The Wikipedia article [0] is not yet great but does give the two classic examples of "second-price auctions and a simple majority vote between two choices". The Gibbard–Satterthwaite shows the difficulty in extending this to more choices (in that Arrow's theorem sort of way).
The best thing I've read on this stuff is Alvin Roth's "Who Gets What and Why" (2015) [1] which is worth a read in any case. Repugnant markets!
[0] https://en.wikipedia.org/wiki/Incentive_compatibility
[1] https://en.wikipedia.org/wiki/Alvin_E._Roth#Market_design