Sunday, April 30th 2017

Article by: Shrey Srivastava

Microeconomics has many captivating branches within it, but the newest and most exciting one has to be game theory. In fact, just two years ago in 2014, the Nobel Memorial Prize in Economic Sciences went to the game theorist Jean Tirole. This is indicative of just how far game theory has come in such a short time, since John von Neumann set the building blocks for game theory not even a century ago, in 1944. Nowadays, it is an essential part of microeconomics, which helps one understand how firms operate in a variety of different situations. But what exactly is it?

Nowadays, it is an essential part of microeconomics, which helps one understand how firms operate in a variety of different situations. But what exactly is it? Game theory is the study of strategic decision-making; of mathematical and economic models of both conflict and cooperation between intelligent rational decision-makers. In the case of microeconomics, the “intelligent rational decision-makers” more often than not are individual firms themselves, who have to make a decision whether to collude with other firms in an oligopoly or not.

But before we get onto that, let’s look at why game theory is so important. This is because, like much of microeconomics, it is vitally important in the real world and is used there today. For example, the former Greek Finance Minister, Yanis Varoufakis, used game theory in his negotiations with the European Union, and game theory is widely used in the OPEC cartel, something I’ll touch upon later. One of the most famous examples in game theory, first of all, is the Prisoner’s Dilemma.

This dilemma is what much of game theory is based upon and expounds on: the idea that firms, or people, will not trust each other even if it seems like the rational choice at the time. Originally, as the name suggests, the dilemma gave the example of two prisoners, however, to make this more relatable, I will give the example of two firms operating in an oligopoly (a state of limited competition, in which a market is shared by a small number of producers or sellers.)

In turn, this does mean that the firms in that oligopoly have the power to control the supply of their goods, thus controlling the price, and creating a sellers’ market. Let’s take Pepsi and Coca-Cola, two competing companies in an obvious oligopoly. If both collude to set the price for a can of drink to, say, a high £2 (people can’t just buy from elsewhere

In turn, this does mean that the firms in that oligopoly have the power to control the supply of their goods, thus controlling the price, and creating a sellers’ market. Let’s take Pepsi and Coca-Cola, two competing companies in an obvious oligopoly. If both collude to set the price for a can of drink to, say, a high £2 (people can’t just buy from elsewhere as, remember, we’re operating in an oligopoly), then both will take home an annual profit of £50 million. In this situation, one would think that they would both win. But, as the Buddha once said, “there is no torrent like greed.” If Coca-Cola continues to set the price of a can to £2, but Pepsi sets the price of a can to £1, Coca-Cola will make a measly profit of only £20 million, while Pepsi will take home a massive £80 million. The reverse happens if Coca-Cola sets the cost of a can to £1, while Pepsi keeps their cost stable at £2. Now, the final option is that both Pepsi and Coca-Cola set the cost of a can of drink to £1. Now, both will only take home an annual profit of £20 million. This situation, where both firms in an oligopoly set a low price, is called a Nash equilibrium (a stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged.) Through this example, we can already see the real world applications of game theory for firms operating in an oligopoly. However, there’s one problem in all of these cases: the consumer is losing.

An idealist would say that, in the long run, there’s very little chance of the consumer being wronged, over such a long period of time. Fortunately for us, they’re right. This has one, simple reason: there’s always the chance that another producer will swoop in and take your market share. In addition to this, a high price means that the opportunity cost of buying an elastic good (a good that is sensitive to changes in price or income) such as a can of drink will increase, resulting in a decrease in total consumption and demand for the goods.

Intuitively, we can see that this results in a decrease in profit for the producers of the goods; we don’t get our Cokes, they don’t get our money.

Therefore, cartels have to lower the high price, which they previously set, or otherwise risk getting priced out of the market. In the 1970s, this very same thing occurred with the oil price. When the price of a barrel of crude oil reached $34, countries including the USA and Russia entered the market, taking advantage of the cheap cost of production.

What this did was increase the supply and therefore decrease the price of oil, which was exactly what OPEC didn’t want, as many of their Middle Eastern constituents (for example, Saudi Arabia) had an oil-based economy, rather than a consumer-based one. If you want an idea of the effect that low oil prices have on Middle Eastern countries, there’s no better place to look than the Gulf nations right now, with the price of crude plummeting by the day.

So, we’ve seen that cartels aren’t exactly durable organizations, due to the ever-present incentive to quietly deceive the other firms operating within an oligopoly. However, there is a way to make these cartels more durable, and it’s known as a trigger or punishment strategy. In a research paper entitled “A Non-cooperative Equilibrium for Supergames”, published by James W. Friedman in 1971, Friedman postulated that the very reason that some collusion occurs here is because of the aforementioned punishment strategy. In essence, this theory can be boiled down to the statement that a cartel will bear the current price level because the punishment strategy is so large that the benefits of colluding are greater than the benefits of Machiavellian deceit.

There are a plethora of factors that affect the so-called “collusive equilibrium”, the first of which being market transparency. If a market is more transparent, the likelihood of an individual firm deceiving the others decreases significantly, as it is easy to detect changes in their price or output. Therefore, the likelihood of collusion increases.

The difference in firms’ cost of production also plays an important role in the likelihood of collusion. If one firm has a greatly different cost structure than the other firms operating within the oligopoly, then they have a great incentive to lower their cost of production, thereby forcing other firms out of the market. Among others, these are the two most important costs affecting the collusive equilibrium in an oligopoly; needless to say, there are far, far more, some of which have not even discovered yet.

As microeconomic game theory marches into its brightest era yet, it is fair to say that far more aspects of this infant science are yet to be discovered. Iota by iota, game theory is capturing the imagination of many an armchair economist, and for good reason.

This science, only really discovered in 1944, is the key to unlocking many of the microeconomic secrets which economists the world over continue to ponder on. And the most exciting thing is: it’s only going to get more and more interesting. I, for one, just can’t wait for the rise of game theory in microeconomics.

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