4.21 Nash Equilibrium AP Micro

alright guys welcome back in this video we're gonna be looking at trying to find a Nash equilibrium so how do we do that in the previous video we talked about how to find the big firm has a dominant strategy so remember dominance ad you're talking about what is that firms best action regardless of the actions of the other player the other firm so in that case if they have a dominant strategy then that's easy enough to find the Nash equilibrium however does not necessarily require that a player has a dominant strategy so we're gonna go through and see how to find whether there's a Nash equilibrium so let's start by defining Nash equilibrium Nash equilibrium is when both players are both firms in this case find themselves in a position where as a result of the actions of the other players neither player has an incentive to change their decision so in this case we're going to have the decision of regarding low output or a high level of output if we find ourselves in Nash equilibrium that means based on the actions of the other players neither Pope nor Pepsi has any incentive to change their current action and so we find ourselves in what's known as a Nash equilibrium so let's go ahead and walk through this to see if we can find one so again I like to start always with the left with the horizontal axis that's just a personal preference it does not matter which one you do but we're going to start by searching for a dominant strategy that's gonna be our first thing that we do so remember when we're reading this from left to right the left numbers those represent be the dollar amount or in this case the profit that we gain by Pepsi since they're on our horizontal axis so just as a reminder I'll put the letter P there I'll put it kind of small but Pepsi Pepsi Pepsi and Pepsi so that's those are the four options at what Pepsi can earn and that'll be the same for Coke those are since it's a vertical it's on the right side so these are four options for coke alright again just as a reminder to keep in mind now the question is we want to think about when we're considering Pepsi regardless of what Coke does does Pepsi have a dominant strategy so we're looking for dominant strategies for Pepsi first so what that means is we want to find out if Pepsi does low output right regardless of if coke does high or low output is there something that's gonna make Pepsi better off okay and then the same thing when it's high output regardless of what coke does is there something that will make Pepsi better off so when we start this we're looking at if Coke does low output okay coca-cola decides to the loop to do low output Pepsi has two options they can either do low output as well or they can do high output so there are two options when Coke does low output as Pepsi can either do low and earn 200 or they can do high output and they can earn 160 which one is better well the larger numbers can be better so Pepsi in this case is better off making the low output if coca-cola does law but because $200 is greater than 160 dollars alright now we want to see well what happens if coke does high output because remember Pepsi at this point doesn't know what Coke is doing but we have that interdependence so if Coke does high output does Pepsi I'm a dhama strategy or is there something there better always doing so let's see if Coke does high-output Pepsi can either earn 110 dollars by doing low output or they can earn ninety dollars but also doing a high output like Coke so we again compare these and 110 is greater than 90 which means that Pepsi is better off in this case also do the low level of output what we notice here is that this means that when Coke does low output Pepsi's better off doing low output when Coke does high output Pepsi is better off still doing low output this means that Pepsi has a dominant strategy and Pepsi's dominant strategy is to do low output alright so we have a winner for Pepsi they are going to do low output they are better off either way regardless of what coke does remember that's what dominant strategy is it's when that is your best action regardless of what the other player does Pepsi's better off either way doing the low output when coke does low it's 200 to 160 with coke those high it's 110 to 90 but either way Pepsi's better off with low level of output alright so we know what Pepsi is gonna do now we want to find does coca-cola in this same game have a dominant strategy alright so now we're gonna look at where you compare the numbers on the right hand side because that's our values for coca-cola so when we look at well if Pepsi does a low level of output what's better for Coke well if Coke also does a little level of output they earn 110 dollars I'm gonna use the color blue for Coke just to change it up a little bit coke will earn 110 or if they do a high level output they would earn 150 150 is greater than 110 so that's all you have to do so that means that Coke in this case if Pepsi is doing low level output coke is better off doing a high level of output alright simple enough now we come down to what if Pepsi does a high level of output all right well coke has the option they can either Garn 125 by doing the low output or they can earn $90 by doing the high output clearly they're gonna pick a larger number so that's 125 now here's the thing does coca-cola have a dominant strategy and we notice the answer is going to be no coca-cola does not have a dominant strategy because when Pepsi does low level of output coke is better off doing a high level of output on the other hand when Pepsi does a high level of output coke is better off doing a low level of output so there is not a single choice that Coke can make that will always be correct they do not have a dominant strategy again dominant strategy something that is always right regardless of the the other player clearly coke does not have that because one time they should do how out put and the other version they should do a low output so in this case only Pepsi has a dominant strategy do we however have a Nash equilibrium Nash equilibrium is when we look at based on the actions of the other players is there something that would make it so that nobody would want to change and the answer to this question is yes we have a Nash equilibrium and the reason for that is because we know what Pepsi is going to do don't we since Pepsi has a dominant strategy we know that that firm will do their dominant strategy which is to do a low level of output which means that for all intents and purposes coke does not need to worry about what if Pepsi does a high level of output because that is not going to be Pepsi's decision Pepsi has the dominant strategy of low output so all coke needs to do is determine alright if Pepsi does low level of output what are we better off doing low output or high output we already said it's high output so what this means for us is that we have a Nash equilibrium I wish I had a black mark right now so I want to put a well which one do I care about the least I guess we'll go with red this quadrant represents with that that's bad now this represents our Nash equilibrium Coke is going to do a high level of output Pepsi we already said put a double check there they are going to do a low level of output again Pepsi's dominant strategy low level of output because coke knows that then they just have to figure out what's better for us in response to a Pepsi's doing 150 is greater than 110 so they are going to do a high level of output and this will be our Nash equilibrium alright till next time this has been on the money production

Channel: Carey LaManna

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Keywords: LaMoney, LaMoney1313, AP, Advanced Placement, AP Micro, AP Econ, AP Microeconomics, Micro, Microeconomics, Economics, ACDC, Krugman, Mankiw, McConnell, Gwartney, Game Theory, Nash Equilibrium

Id: 7M-3CII2ZJ8

Length: 8min 7sec (487 seconds)

Published: Wed Nov 15 2017