[MUSIC] The guiding philosophy in game theory is this, you will pick your strategy by asking what makes most sense. Assuming that your rival is analyzing your strategy and acting in his or her own best interests. As to why game theory is important in business, here's two very good reasons? First, many different possible gains articulated by the theory help capture the essence and complexity of aligopoly conduct. This is because with mutual interdependence recognized between firms, oligopoly conduct becomes a game of strategy, such as poker, chess, or bridge. And the best way to play your hand in a poker game often depends on the way rivals play theirs. Second, game theory shares a very bright light on the importance of collusion in driving socially undesirable economic outcomes. In this way, the insights of game theory thereby help to underscore why such collusion is often made illegal in a given economic system. To show you what I mean, let's look at the prisoner's dilemma, a well know game that demonstrates the difficulty of cooperative behavior in certain circumstances. Suppose then, there are two suspects in a bank robbery, Bonnie and Clyde, are arrested and interrogated in separate rooms. And each of the prisoners is offered the following options. Option one, if one prisoner confesses and the other does not, the one that confesses will go free, and the other will be given a 20 year sentence. Option two, if both confess each will receive a 5-year sentence. Finally, if neither Bonnie nor Clyde confess, each will be only given a six-month sentence on a minor charge. So here's my question to you, which strategy would you choose if you were Bonnie or Clyde sitting alone in an interrogation room unable to talk to your accomplice? Take a minute now to pause the presentation and think this through. What would you do? Confess and maybe go free but also risk a 5-year sentence, or not confess and perhaps wind up in the slammer for 20 years if your accomplice betrays you. [MUSIC] Well, this is certainly a tough one. But if you don't trust your partner, and your partner does not trust you, the most likely outcome will almost certainly be choice b. And that's what makes the prisoner's dilemma so very interesting. Because you can see that it is pretty clear that if both prisoners could talk to one another after they were arrested, they could easily collusively agree not to confess. And both would wind up serving only six months rather than five years. However, in the absence of collusion and trust, there is great pressure on each prisoner to confess, because each knows if he or she does not confess and the accomplice does, the result would be a very long sentence. [MUSIC] So what the heck does this have to do with economics? I thought you'd never ask. [MUSIC] In fact, the prisoner's dilemma has its simplest application to oligopoly when the oligopoly is a duopoly. In this key definition, a duopoly is an industry that consists of only two firms. In the real world, this form of oligopoly, the duopoly, might emerge in an industry when the minimum efficient skill of production is about half that of total industry sales. And that's what we will assume in this set of figures that depicts a duopoly in packaging material. In particular, in the left hand figure, we have drawn the average total cost and marginal cost curves for one of the firms. Note that the minimum efficient scale occurs at point A where the ATC is at a minimum and production is 4,000 tons. Assuming that both firms in the duopoly have identical cost structures, we can them draw supply demand and several possible equilibria in the packaging materials market. So here is your first question. Suppose that just like in the prisoners dilemma, that two firms are unable to communicate with one another. And therefore are unable to collude in any way either explicitly or tersely. What is the likely strategic pricing decision to be? How much will each produce? And what will be their total economic profits? Please pause the presentation now to think this important question through, really try to nail the answer here. [MUSIC] Well, the correct choice is a. Did you get it right? Here's the underlying logic. In the absence of collusion, the two duopolists are likely to behave like perfect competitors. In this case, the market price will be $500 per ton, output will be 8,000 tons or twice that of the minimum efficient scale of production. And economic profits would be zero. Here's your next question, suppose on the other hand the two duopolists are able to fully collude and each keeps the bargain that they strike. What now is the likely market price, output, and profit? And which of the two oligopoly models we discussed does this outcome most resemble? Again, let's pause the presentation and get this one right. [MUSIC] Here, the correct choice is b. Did you get it right? Here's the logic. If the two duopolists can collude, they will indeed act together, just like a monopolist, and jointly maximize their profits. In this case, the price will be higher at $600, and output will be lower at 3,000 tons per firm. And, of course, profits will be higher and equal $75,000. [MUSIC] Okay, so far so good, but now here's where things really get interesting and strategic. [MUSIC] So here's the next scenario. Sure, the two colluding duopolists shook hands on their deal, but one of the two is a no-good, backstabbing varmint who decides to cheat on the agreement. In particular, this cheating duopolist refuses to limit its share of production to 3,000 tons as promised and, instead, produces 4,000 tons, a situation depicted in this set of figures. So, what do you think happens now to the market price and output? And, what do you think happens to the level of profits? And, more importantly, the distribution of profits across the two duopolists? Let's figure that out now as you pause the presentation and jot down your answers. [MUSIC] Well, the correct choice here is a. Did you get this right? In this case, industry output increases to 7,000 tons and the price falls to $550 per ton. Moreover, the price will stay at $550 per ton so long as as the non-cheating duopolist firm does not increase production. As for the profits of each firm, this is where things get even more interesting. So please note in this figure that the non-cheating firm receives $550 per ton. However, because that firm does not produce at its minimum efficient scale, it actually incurs costs of $575 per ton. And this leads to an actual loss of $75,000 for the non-cheating duopolist as indicated by this blue shaded rectangle. In contrast, the cheating firm is able to produce at its minimum efficient scale when costs are $500 per ton. And its profit is the brown shaded area in the figure or $200,000. Now please pause the presentation to study this graph carefully to make sure you understand everything going on here. It's a complicated graph, so taking a few minutes with it will help you cement your understanding. [MUSIC] So what have we shown with this example of duopoly? Well, the example has clearly demonstrated the often huge incentives to cheat that exist when colluding oligopolist try to fix prices and output. In this case, the successful cheater actually more than doubled for profits from $75,000 to $200,000. Now here is how game theory can be helpful in sorting out all of the strategic implications of such situations. [MUSIC] In fact, it is precisely to provide insight into the kind of strategic situations firms face that the tools of game theory were developed for economics. One such tool and our next key concept is the so-called payoff matrix, as illustrated in this figure. In this matrix, each box shows the payoff from a pair of decisions listed in the columns and rows. Note that the blue triangles show firm's A profit, while the yellow triangle show firm's B profits. So from this payoff matrix, you can see the four possible outcomes of this duopoly game. The upper left hand box indicates a successful collusion. Both firms makes $75,000 by a combination of fixing prices and restricting output. In contrast, the lower right hand box indicates a deal in which both firms actually cheat on the other. The result here is zero profits which is to also say zero economic profits just as what occurred in the case of perfect competition. As with the lower left and upper right hand boxes, these are the cheating outcomes. If one firm cheats and the other doesn't, the cheater literally makes out like a bandit while the non-cheater suffers a heavy loss. So here's the question, if you were on the management strategy team for your firm and you gain this situation for your chief executive officer. And you know that your firm won't be able to detect cheating by the other firm. What would be your recommendation to your boss as to what to do in this very serious game? And more importantly, what do you think the final outcome of this game will be? Please pause the presentation now to think this through. And if you can get the answer right, you will have figured out something that a genius named John Nash from Princeton University actually won a Nobel Prize for. [MUSIC] Of course, this duopoly game is simply the prisoner's dilemma applied to business. Here's the likely answer. As a management strategist, you will surely recommend as the optimal decision, that your firm cheat on the deal. You will do this not necessarily because you lack ethics, but rather because you are almost certain that the other firm will cheat you. And by the way, if the other firm doesn't cheat your firm will reap a generous profit anyway. So cheating is you optimal profit maximizing strategy. But check this out. Your counterpart management strategist at the other firm is likely to make the exact same recommendation. So the likely outcome of this duopoly game is that just as both prisoners wound up confessing in the prisoner's dilemma, both firms will cheat in this business dilemma. And the happy result, at least for consumers and society, is that the market will deliver the competitive market equilibrium in the lower right-hand box. In fact, in game theory, this is called a Nash equilibrium, named after the aforementioned Princeton professor. In this key concept, a Nash equilibrium describes a situation in which no player can improve his or her payoff given the other player's strategy. Let me repeat that, a Nash equilibrium describes a situation in which no player can improve his or her payoff given the other player's strategy. This key concept of the Nash equilibrium is important because it often describes a non cooperative equilibrium. Here, in the absence of successful collusion each party will choose that strategy which is best for itself and without regard for the welfare of society or any other party. At least in this case, the Nash equilibrium nonetheless delivers a win from both consumers and society. [MUSIC] Okay, at this point, we have completed all of our lessons on market structure, market conduct and market performance. And you've gotten at least a glimpse and taste of how firms operate in a strategic context. And in the process, maybe you, yourself have learned to think a bit more strategically in both your personal and professional lives. In the next set of lessons, we are going to move on to the topic of how factor prices like wages and interest rates are set in the market place for a factor inputs like labor and capital. So when you are ready, please forge ahead to the next lesson. In the meantime, please remember that economics is not something to be memorized, but rather something to conceptualize. So as you study it, think about it, too. Your job, and your business, just might depend on it. From the University of California, Irvine, I'm Peter Nevarro. Will see you next time. [MUSIC]