Abstractly, it seems like you just can’t enforce such a rule at all, but it seems to me that often people are able to be honest in the face of punishment, so not all hope is lost.
I think people being honest in the face of punishment is due to the repeated/indefinite nature of the game (i.e., people trying, perhaps not consciously, to build up a reputation for being honest and avoiding a reputation of lying).
But this leaves open the question of how in practice to estimate this probability, calculate the appropriate punishment level, and how much effort to put into detection of rule violations when nobody has confessed to a violation.
Solving the game theory for any realistic game is computationally infeasible, plus humans don’t satisfy the assumptions that game theory makes anyway, so I think “calculate” is out in most cases and probably the best you can do is learning/optimizing a policy through some sort of trial-and-error process. But beware that whatever policy you learn probably won’t be robust to distributional shifts. It might be best to use cheap technical solutions where possible (e.g., buy a hidden camera for your room) and just not think about it too much otherwise (i.e., let your System 1 do the best job that it can). If you’re faced with a really high stakes situation, maybe seek the advice of people who either have a lot of intellectual firepower and can try to solve/approximate the specific game for you (like RAND was doing for the US government), or has built up good social intuitions from extensive experience and can give you advice based on their intuitions.
I think people being honest in the face of punishment is due to the repeated/indefinite nature of the game (i.e., people trying, perhaps not consciously, to build up a reputation for being honest and avoiding a reputation of lying).
Solving the game theory for any realistic game is computationally infeasible, plus humans don’t satisfy the assumptions that game theory makes anyway, so I think “calculate” is out in most cases and probably the best you can do is learning/optimizing a policy through some sort of trial-and-error process. But beware that whatever policy you learn probably won’t be robust to distributional shifts. It might be best to use cheap technical solutions where possible (e.g., buy a hidden camera for your room) and just not think about it too much otherwise (i.e., let your System 1 do the best job that it can). If you’re faced with a really high stakes situation, maybe seek the advice of people who either have a lot of intellectual firepower and can try to solve/approximate the specific game for you (like RAND was doing for the US government), or has built up good social intuitions from extensive experience and can give you advice based on their intuitions.