hi guys welcome back so let's look at the details of nash equilibrium so a strategy profile s so don't forget what strategy profile is right it's a vector which basically tells us what strategy player 1 player 2 all the way to player and will play so a strategy profile is a nash equilibrium if and on if each player's strategy is the best response to his or her opponent's strategy and that's true for each player that's it all right so the idea is very simple every player is best responding his opponent that is alternatively i'm just
opening up this condition basically uh strategy profile s is nash equilibrium if and on if uh the payoff of a player i when he plays si and his opponents are played as sub minus i is greater than or equal to his payoff when he plays something else keeping his opponent's strategies fixed for every s i prime in s i right so therefore s i is the best response to s minus i and this should be true for each player i that's it that's the definition of nash equilibrium so it's it's it's it's actually very simple
uh concept uh but the confusion usually arises when you apply this concept to uh different game forms so uh there are a few remarks that i would like to make one of them nash equilibrium nash equilibrium is a stability concept all right well yes it is true that we use nash equilibrium as a solution concept but in fact it's a stability concept what does that mean that means uh once the game is is finished meaning everybody selected his or her strategies and then they learn what you know uh you know strategy they played after the
game none of the players would regret his or her choice none of the players will say should i should have played this if i knew you would play blah blah then i would actually play some you see what i mean so it's in a sense uh i mean it's not the second sort of i i mean the same thing nash equilibrium nash equilibrium is a what i call regret free code in code i mean i'm using this regret notion loosely speaking regret free outcome i mean nobody will regret from his or her choice that's that's
the idea okay uh i mean once the game is played and everything is realized you know no player will say should i i should have played something else all right um so every every player is going to say well i mean i did my best right given given what you guys have played i my my choice is actually the best i could do all right so in that sense the nash equilibrium the idea of nash equilibrium is selecting uh probably more than one strategy profiles that is regret free uh so that's uh so in that
sense it's stable nobody would like to uh nobody would like to change his or her outcome uh or change his or her selection of strategy once the game is realized you may say look i mean you know this is a static game right players are choosing their actions simultaneously and without knowing the other's choices and so why are we using this kind of solution concept which actually cares about uh you know whether the players are going to regret once the game is over well that's the well my answer would be to this question well that's
the best solution concept we have um all right so if you come up with a better alternative well i i believe the entire uh field of economics will appreciate your invention but trust me that's kind of the best solution concept that we have at least for so far and in fact nash equilibrium is a very nice property for many other reasons i don't know if we are going to have time to talk about you know what nice properties nash equilibrium has but yeah this is exactly why we use nash equilibrium not because it's it's it's
the perfect solution we know it's not the perfect and to be honest we don't know if there is a perfect or the perfect solution but it's one of the you know nicest solution concepts that we have all right so another idea of stability concept is due to the fact that it's it's um it's looking at a strategy profile where nobody wants to deviate right again it's like uh i am best responding what you're doing uh again and most of the times students confuse this like look i mean this is a game where when i pick
my strategy i don't know my opponent's strategy right s minus i so how would i best respond something that i don't know um well as i said this is exactly why i use this idea of nash equilibrium is worried about once the game is over and the outcome is realized and so nobody is going to regret nobody is going to say should i should have played something else all right alternatively you can you can think nash equilibrium is selecting strategy profiles where one each player [Music] is best responding his or her beliefs about what the
uh you know what the other guys are gonna do and then second uh each player each player's belief is is is true what do i mean by this i mean the following so if s or let's denote it as i s minus i if s is a snash equilibrium that means player i and this is by the way true for every player i so player i is going to believe that his opponents are going to play s minus i and therefore sr is going to be best response to this belief and that the second of
all you know each player's belief about his opponent are going to be correct they're not going to believe something else they're going to believe exactly what their opponents play so this is i mean i don't know if i can uh explain it correctly but uh this this is a very strong assumption right i mean we are you know two guys are playing a game and i i i believe something about what you're gonna do and then i best respond this well that's pretty intuitive that's sort of the definition of rationalizability in a sense so it's
a rational behavior to do you know best response my belief but then the second condition what i believe is actually what you will play all right so my belief is going to be correct uh so that's that's way too strong um and so uh i mean you can you can interpret the nash equilibrium concept in this fashion uh where it makes a very strong assumption about the players beliefs are in fact true or you can you can just you know admit the fact that nash equilibrium concept is actually worried about once the game is realized
and the outcomes are sort of observed by everybody and nobody is going to regret from it and say i should have picked something else all right everybody is going to be sort of happy with his or her choice and say well given that what you played uh there was no way i mean i mean i i basically selected my best strategy
