How to find Nash Equilibrium in a 2X2 payoff matrix

if this videos gonna go over strategies to figure out where the Nash equilibrium is if you're given a payout matrix so first what I'm going to do is set up your standard payout matrix just so you can remember what it looks like I'm gonna call this guy a column player and then this guy on the side we will call row player I know I know confusing we'll have the two choices they can make so here I'm gonna go with high and low and then here I will also have high and low and then we will get our payoff matrix so when I talk about finding the Nash equilibrium this is sort of the setup we have so I'm gonna fill this out real quick I'm gonna make this guy blue and I'll have his payoffs be and then we can make the Rope layer red and I will have her payoffs be here so this probably looks familiar based on some of the homework assignments or textbooks that you've been given so you look at this and you're like okay all right I have this information here I have two players that each have two choices they have Associated payouts higher is better now where is Nash equilibrium what's gonna happen okay so first what we have to do is figure out what the dominant strategy is and the dominant strategy means that regardless of what the other person chooses to do you will choose the same thing so you may be asking okay that's great dominant-strategy we'll figure that out but first where did these values come from in case you're curious what I'm going to assume here is that we have a ten dollar market share and then they have high or low advertising amounts they can choose to do so if they choose to advertise the high amount it costs four dollars if they choose to advertise the low amount it costs two dollars and I assume that if they choose the same advertising amount that they split the market share however if one of them does the high amount and the other does the low amount then the high advertiser wins the total market share so you can see column player blue if they advertise high they get $10 minus 4 for a payout of six our row player red gets a market share of $0 but they still have to pay two dollars in advertising so they get a negative two if they both do high they split the market share five five they each pay four dollars resulting in one in one so if you're curious where those values came from that's why but now let's look at the dominant strategy and first let's focus on blue or the column player so we're looking at blue and they can choose either to advertise a high amount or advertise low amount and so what we want to do to see if there's a dominant strategy or not is assume the road player chooses high advertising okay so if the row player chooses high advertising the column player has a choice between a payout of 1 or negative 2 which are they gonna choose well they're gonna choose 1 obviously because they've now that rather make $1 then lose $2 now assume that the row player is going to choose a low amount of advertising they have a choice between making $6 high advertising or $3 low advertising so again they choose to do high advertising and they get the $6 payout so this is a clear example of a dominant strategy regardless of what the rope layer does it's in the column players best interest to choose a high amount of advertising now let's consider the rope layer imagine the column player decides to do high advertising okay so the rope layer in this instance can either do high advertising or low advertising did they want one or negative two well obviously they'll choose one now imagine the column player does low advertising do they want six or three well obviously they want six so we can see here that high is also a dominant strategy for the row player so what ends up happening in this case is we see that this cell right here if one cell results in both dominant strategy outcomes it is a Nash equilibrium so in this case what we needed to do was figure out okay what is the dominant strategy for each player in this case both dominant strategies resulted in them choosing the high advertising amount and if both of them choose the high advertising amount regardless of what the other player does that will be the Nash equilibrium now there are some caveats there may not be a Nash equilibrium imagine I changed some of these values around and the dominant strategy for the column player was low then what would happen in this situation is that the Nash equilibrium would change potentially based on what the values were and what the ROE player ended up deciding to do so in order for this strategy to make sense or in order for there to be at Nash equilibrium regardless both of the players have to have a dominant strategy and that dominant strategy has to result in them both getting that stable sell

Channel: Free Econ Help

Views: 51,484

Rating: 4.6363635 out of 5

Keywords: nash, equilibrium, game theory, oligopoly, payoff matrix, microeconomics

Id: KV3VURTcW8g

Length: 7min 29sec (449 seconds)

Published: Wed Jun 27 2018