[Thread] What are some of your favourite learnings from Game Theory?
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:
- Both deny then, both can't use Grapevine for 2 days.
- 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.
- 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.
- 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.
Lovely revision of game theory :)
Brought back college economics lectures, but just done much better!
Why’d you pick Biryani and Potato specifically, do you feel they are more likely to steal?
Remember being in strategy class just a month ago when game theory was being taught(at one of the iims) .. Right before the class began the prof asked how would you rate/describe yourself, the students had to choose between three options collaborative/team playe,competitive and lone warriors. Most say 95 percent of the people raised hands for collaborative because duh the safest/coolest option to pick from to portray yourself as teamplyaer. But then he introduced the game theory where the matrix was like between the two students, if each pick on the other they get a- grade but if you pick on other and the other supports you they get c grade and you get a grade surprisingly most people stepped on each other's toe and choose to get a for themsalves than to choose a-grade for both which would have been an ideal outcome for both but yeah then he went on saying "there's a difference between saying and doing" as most people choose to maximise for themsalves. Was a good learning
@Sabre Wow now that is something isn’t it. Player motivations reflect in the type of reward as well, punitive vs positive.