So, welcome everyone to this video lecture. And we're going to be talking about a phenomenon that we call the Bertrand Paradox. And we'll split that in two. First, we'll look at the theoretical model in this video. And then we'll look at relaxing some of the assumptions and trying to find ways of getting out of the Bertrand trap, or Bertrand Paradox in the next video. But, so what is the Bertrand model in the first place. We typically assume that there are two companies and for a particular example let's just take the example of two ice cream sellers on a beach. There is price competition and it's easy in that case to think about two sellers of ice cream just setting the prices for this ice cream. They both sell identical products, so it's the same type of ice cream that both of these sellers are stocking. The game is played a single time, so there's one day on which both players, both ice cream manufacturers or sellers are on the beach. And they try to sell their ice cream so it's price setting but it's just once. You'll have market transparency, so consumers know both prices, so everyone knows the prices that both firms will set. And there's infinite price elasticity, which means that no matter what the price difference is, the seller with the lower price will get all the consumers, okay? There also, finally, there are no capacity constraints. Which means that each of the sellers can produce or can stock or can replenish endless amounts of ice cream. So, if we just take these assumptions. Two companies, price competition, identical products played once with full market transparency, with infinite price elasticity, and there are no capacity constraints, then we can think of analyzing this game pretty much as a game as we did in the five lectures previously. So, each seller can set a low price or a high price. So, that's if we have competition between these two players that just have two possible options. And, if we just take the simplest assumption here, we've got seller A and seller B, and they can set either high prices or low prices. What we find is that if both firms charge the same prices, then they both share the market equally. And if one of them charges the low price they get market share of 100. Okay? So, in that very simple game we basically get a Nash equilibrium where both firms both sellers set low prices. Now, prices though, are not typically a discreet thing. They're not a binary thing. You can either charge high prices or low prices. You often have continuous prices, meaning that you can charge the price of $1 or $1.01 and $.02 and so on. So, it's almost a continuous price that we can set, so each seller sets any price. Now, what's interesting here is that we find a unique Nash equilibrium where both players charge prices equal to cost if there are no fixed costs. So, they charge prices equal to cost. And profits are zero. And that's very weird, isn't it? Because in reality we see firms making profits. In this model, we see firms making zero profit and charging very aggressive prices, charging prices equal to their marginal cost. And so this phenomenon, this paradox that in real life we seem to see positive profits and in this model we don't, is what we call the Bertrand paradox. And we'll look at this Bertrand paradox in more detail in the next video. So, thanks very much and stay tuned.