I would say the Nash Equilibrium for me.
Essentially, It is a stable state of a system where no participant can gain by a change of strategy as long as all the other participants remain unchanged.
Imagine if @BiryaniEnthu and @potatomato are captured by Grapevine. They are taken into two different rooms and given an option to confess or deny that they stole Grapes.
The rules are as follows:
1. Both deny then, both can't use Grapevine for 2 days.
2. If @BiryaniEnthu confesses and @potatomato doesn't then, @BiryaniEnthu can't use Grapevine for 1 day but @potatomato can't use it for 10 days.
3. If @potatomato confesses and @BiryaniEnthu doesn't then, @potatomato can't use Grapevine for 1 day but @BiryaniEnthu can't use it for 10 days.
4. If both confess then, both can't use Grapevine for 3 days.
So, what is the optimal strategy?
Let's plot this as a matrix
where b = BiryaniEnthu and p = potatomato
p confess p deny
b confess [[ 3\3 , 1\10 ],
b deny [[ 10\1 , 2\2 ]]
For @BiryaniEnthu, if p confesses then, best option is to confess else they will get punished for 10 days.
For @BiryaniEnthu, if p denies then, best option is to confess because they will get punished for 1 day only.
Same applies for @potatomato, their best option is to confess too because of symmetry in the matrix.
But did you notice one thing? When both confess, both will get 3 days punishment, which is the Nash Equilibrium state which is extremely stable as it covers downside risk.
However, the global maxima for both was when both will deny it, so that both get 2 day punishment but this is an unstable state because it relies on the assumption that the other person will deny, especially when the other person knows that confessing will lead to a better outcome.
Hence, there is a tension between individual rationality and group rationality. The Nash Equilibrium represents a situation where, despite the possibility of a better global outcome, the self-interest of each player leads them to a less optimal, but stable, outcome.
