welcome back so we're going to apply the prisoner's dilemma example to a a an oligopoly goblin with two firms coke and pepsi obviously coconuts on the only two firms in the soft drink market they are the major competitors and we are going to do that and then at the end of this video we're going to talk about some ways the prison dilemma might be beatable and by beatable i mean where you might not end up with the not as good outcome which we will see in this one again okay so first before we get into this let's um make sense of the of the the matrix in front of us pepsi and coke the two firms competing in this oligopoly market if they both charge a high price for sodas because they're both charging the high price and they're the only options they're going to make a lot of money um if they both charge a low price they're going to receive less money which makes sense if you're if you charge a higher price you might make more money charge a lower price you're making less money doesn't say what the price is remember these numbers in here are the the payoffs that's what you end up with so they end up with more money if they both charge higher prices however if one charges a high price and the other one swoops in the low price the low price is going to win the low price is going to get all the most of the sales not all the sales doesn't get most of the sales and so therefore the low price firm will end up with more profit okay so let's take a look and take a look at this this uh matrix pepsi if pepsi chooses a high price and coke also chooses a high price they both end up with a thousand dollars if pepsi chooses a high price and uh coke undercuts some of the low price pepsi is down to only 200 bucks um whereas coke gets reaps the reward of the of undercutting pepsi meanwhile if coke goes to the high price and pepsi goes low pepsi is the one with the big reward and they both choose a low price then they both end up with less money by a lot than they would get under high price okay so let's see how this works so we'll do it the same way we did before we're going to find if there's a dominant strategy okay now if coke knows pepsi is going to charge a high price if coke knows for sure that pepsi is going to charge a high price well let's ignore pepsi's low price for a second if coke knows pepsi is going to charge a high price then peps coke is going to react with pepsi charges high price coke will charge well if coke chooses a high price they end up with a thousand dollars sorry that the a and b don't match hopefully the colors make it clear coke is red pepsi is blue just like in the real world so if coke goes high they end up with a thousand dollars if they go low they undercut pepsi and end up with the big reward of fifteen hundred dollars okay all right so let's check out what happens if pepsi is going to charge a low price so we can ignore pepsi's high price and say if pepsi is going to go low then coke can go high uh-oh end up with almost nothing 200 or a low price 400 that's not that's not as good but 400 is still more than 200 so if pepsi goes low coke responds with a low price of their own coke's dominant strategy is to charge a low price okay all right sorry i am losing there we go um okay don't clear all my drawings i just want to erase this one so now let's say what happens if pepsi thinks coke is going to go high and what you can see is since this is symmetric we're going to see the same thing if pepsi sees coke is going to go high then pepsi is going to choose a high price and a thousand undercut for the low price for 1500 1500 is better so that's what they're going to do if coke if coke is going to go low then pepsi could go high and end up with 200 the worst scenario or they can go low as well number 400 so end up with the same scenario it's symmetric if coke goes high pepsi goes low if coke goes low pepsi goes high pepsi's dominant strategy is to charge a low oh sorry i when we went through it i did it right but i just i just did it wrong if coco's low which is the one we're seeing in front of us right now pepsi also goes low right because they want to get that 400 instead of 200 so therefore pepsi's dominant strategy is to go low both go low is the nash equilibrium okay nah i cleared it all but you got the idea so we end up with this nash equilibrium here and that's the idea is that this like the prisoner's dilemma doesn't feel right it doesn't feel right that they're going to compete with one another and end up down here when they could just team up and charge a high price um and so that is that's the idea here that's why this is again a prisoner's dilemma okay so beating the prisoner's dilemma okay so i want to talk about the prisoner's dilemma really seems like okay they're gonna get stuck with these low profit profits well how can firms end up with high profits is it possible that coke and pepsi can end up with that thousand dollars each well first off colluding is illegal pepsi a green and coke agreeing to that high price is illegal but it's hard to prove firms can just see eye to eye on things and both charge high prices there's nothing illegal about pepsi charging a high price there's nothing illegal about coke simultaneously charging a high price so what would stop coke and pepsi cheating and making higher profits am i sorry i moved to the next part okay so firms could just see i die so we could just that could that could be the first thing so let's stop on that point is the first thing is if they just wink weak nudge nudge i like to give the example of like of the two um gas stations on the same off ramp um you know let's say most gas stations charge three dollars a gallon of gas but this is the only gas station in a 30 mile radius um and the gas station the shell station waltzes over with five dollars on the big sign and kind of like makes eye contact with the person across the street and puts five dollars up on the sign um that's not illegal collusion like because they looked at each other and then the chevron station across the seat also charges five dollars and they both make a killing right because they're the only gas stations in town so that's one thing but what stops the other gas station from cheating what stops the other one from seeing that wink wink nudge nudge five dollars and saying gotcha three dollars and everyone goes to his gas station and makes all the money so what so coke and pepsi have this sort of like wink week nudge nudge tacit agreement to charge the high price what stops pepsi from sneaking in with the low price right and therefore making sorry should be down here making that fifteen hundred dollars um because that's more than a thousand right letting coke go first and then sneaking underneath him um it's tricky but here's the idea first is what if this wasn't a one-time game so the idea here the way we presented this is there you go there's the profit you win the game if you make 1500 right what if it's not a one-time game what if this is daily profits so what if they're talking about making this profit daily well now think about it if we don't cheat so if we have this tacit agreement to charge a thousand dollars and we do not cheat then we could get a thousand on day one a thousand on day two and a thousand on day three and so on and so forth day four five six seven eight nine ten 100 that's enough right now let's say you're pepsi and you're thinking about cheating you're thinking i could just coke is going high if i go low i could make fifteen hundred dollars awesome congratulations you made fifteen hundred dollars is coke ever gonna charge the high price so again make 1500 on day one and now we know coke is going low so you make 400 on day two 400 on day three etc and what you quickly realize this is three thousand dollars this is twenty three hundred dollars what you quickly realize is that cheating for this one time game isn't worth it in the long run so that's one way the prisoners dilemma can be beat is acknowledging that these payoffs are not a one-time thing then cheating there's no longer incentive to go low that incentive to go low disappears and all the incentive is to go high both go high remember that's why low is the nash equilibrium is no matter what your competitor is doing there's incentive to go low in that story the incentive disappears and now the incentive is to go high the second example i want to give you is a price match guarantee maybe that's a term you've heard in advertising before price match guarantee in a lot of stores do this is where a store announces that if you bring in a competitor's price for the same item we will match the competitor's price it's like staples does this so like if you wanted to buy a i don't know copier at staples and you bring in your phone and say look on amazon it's it's less money they will charge you that low price okay um i did this once buying a couch i bought it i was gonna buy a couch from uh an ashley home actually furniture or something like that and but you got to see it in person right and so i went and saw it in person um and then before we bought it we're like okay but it's on over stock for this price um and you know you want to give the sales person opportunity to match it anyway so we they match the price we got the overstock price despite having been inside an ashley store at the time anyway that's not the points you know what a price match guarantees so what if there's a price match guarantee here what if both firms promise to match their opponent's price so what if coke matches pepsi's price what if pepsi matches coke's price okay what does that do to our matrix well think about it so let me get my pen out that means that if pepsi charges a high price and coke charges a low price then pepsi matches coke's price and now they also have a low price you see what i'm saying it's a price match guarantee so if your competitor charges a lower price than you your price will match theirs that means this sell can't happen does that make sense it can't happen right because if coke goes low and pepsi goes high no price much guarantee kicks in pepsi also goes low so this cell can't happen so the way i'm going to write this is that if coke juice is low and pepsi chooses high they end up with 400 400 anyway because the triggering of the price match guarantee makes it so um you automatically go down to the cell same thing with coke if coke goes high and pepsi goes low you might think you might think you're here but nope this triggers peps coke going to a low price so you end up here so really the payoff matrix ends up not looking like this anymore but looking like this if they both charge a high price it's a thousand dollars if either of them go low the price match guarantee kicks in and they both end up with 400 each now this is no longer the nash equilibrium the nash equilibrium of low low is gone this is the nash equilibrium high high is the nash equilibrium so is this true of the real world are price match guarantees good for consumers the evidence from economists is nope so there's a paper that i i a study i'd seen done in the tire market um you know there's a lot of tire stores you know double a tires and joe's tires and they typically sell some of them have different specials they typically sell similar tires the goodyears and the dunlops etc and so there was a there was a study done of all the tire stores in the city of chicago comparing the ones with price match guarantees to the ones without price match guarantees what they found is firms with price match guarantees charge more for their goods so you might think that the reason a a store has a price match guarantee is because they are know their prices are low and they're trying to bring you in because they have low prices and this is the way they're they're showing you but in reality what a price match guarantee is designed to do is to segment the market segment customers some customers are going to shop for convenience some customers do not screw nice prices some customers know what they want go to a store and buy it and don't think twice about it you charge a high price for them other customers are going to want to shop around for a better deal what a price match guarantee lets you do is set a high price and if there are customers out there who really want a good deal you can give them the good deal not everyone else and so price match guarantees artificially increase prices if price match guarantees were illegal prices would go down but because price match guarantees are not illegal and actually relatively common prices are inflated as a result and that's exactly what's predicted here so next time you see a price match guarantee that should be a message to you that you need to do your research and find the place for the cheaper price okay so um one more video where we're going to do a game that's not a prisoner's dilemma because not all game theory games are prisoner's dilemma