# Game Theory in Microeconomics

By Aidan Hackett. Edited by Arjun Chandrasekar.

Overview

Game theory is, according to Investopedia, “a theoretical framework for conceiving social situations among competing players”. Basically, what this means is analysing what one person should do, assuming they are rational and acting in their own self-interest, contingent upon what other people are going to do.

Before its formal study, game theory was used all throughout history in most interactions. Politics, war, business, evolutionary biology even, all use game theory to optimise outcomes for the individual. An example of this is in war when any deaths caused by an enemy sniper would be retaliated by killing one of the enemies. This causes a pseudo-truce between the two sides, as each value one of their soldiers alive than an enemy soldier dead.

The field of game theory was pioneered by John Von Neumann, a Hungarian born, American mathematician, and Oskar Morgenstern, a German born, American economist, who were both working at Princeton at the time. The field was significantly forwarded by John Forbes Nash Jr., an Princeton based, American mathematician, who had his life story and work popularised in the movie “A Beautiful Mind:, were he was portrayed by Russell Crowe.

Prisoner’s Dilemma

Nash is known most notably for his work on the Nash Equilibrium, a concept that won him the Nobel Price in Economics in 1994. This concept is best illustrated by the prisoner’s dilemma. In this game, two prisoners are caught and held separately so that they cannot collaborate. It is also assumed that they have no reason to trust one another or be looking out for anyone but themselves. If they both don’t talk, they each get 1 year, but if one talks and the other doesn’t, the one who talks gets no time, while the other gets 5 years. If they both confess, they both get 3 years. This is represented in a payoff matrix.

It might seem intuitive to assume that both prisoners would remain silent – it is the best outcome for both. But note one very important thing. If suspect A thinks suspect B is going to remain silent, suspect A can get off with no prison time by confessing. This would cause suspect B to go to prison for 5 years, but both are just looking out for themself and themselves alone – no honour among thieves after all. If we assume that suspect B also notices this, we are now at a point were both prisoners will spend 3 years in prison. This is the Nash equilibrium. While it is not the best outcome, it is the only place were neither suspect can change what they are saying and receive a lighter sentence.

Dominant Strategies

A dominant strategy is the strategy that a player should take regardless of what any other players do – it is the best in every situation. Looking at the last example with the two suspects, we could say that blaming is the dominant strategy because you are always better of blaming, regardless of what the other suspect does (0 years better than 1 year, 3 years better than 5 years).

The difference between a dominant strategy and Nash equilibrium is knowledge. In a Nash equilibrium situation, the dominant strategy of every other player is known by all of the players. In a dominant strategy situation, you only know your own immediate dominant strategy.

Real World Applications

Now that we know the theory, let’s look at some real world applications.

In general, there are four types of market. Perfectly competitive (low barrier to entry, anyone can do it, like drop shipping, selling generic items online and farming), monopolistic competition (low barriers to entry and many producers, but products are not exactly the same, like clothes retailers, shoes manufacturers and fast food restaurants), oligopoly (high barrier to entry, a few companies control most of the market share, think phone and laptop manufacturers), and monopoly (one company dominates the market almost completely, Google is a great example).

Game theory is best used and described in markets that are an oligopoly. In these markets, there is usually only a handful of large players, and any other companies are small and on the periphery. A great example of this is the smartphone market, where the two main choices are Apple and Samsung, with other brands such as Huawei, BlackBerry, Google, etc. only holding a very small market share. Consider what would happen if Apple increased the price of all of their phones to \$5,000. While some people would buy them, a lot of people would go to Samsung. Apple does not want this, so they keep their prices at about the same levels as Samsung keeps their top range phones.

So, if price really isn’t an option for differentiation, what do companies do? They participate in what is known as non-price competition. This means they advertise how good and different their product is. They put in new novelties, release new colours, have convenient store locations, position their brand well, etc. They try and convince a buyer to go with their product, even if it may cost them a little more than their competitor. This is the same with every company that has a slightly different product to their competitors, be it multi-national conglomerates to the coffee shop on the street corner.

Cartels

A syndicate or a cartel is formed when two or more companies enter into an agreement to fix prices for their very similar products. This happened with light bulbs in the early 20th century and was the cause of light bulbs lasting shorter and shorter as years went on, right up until LED was invented.

If companies making toasters entered an agreement to sell their toasters for \$100 when the price they should really be selling them at is \$35, this would be a cartel. But why would this cartel actually keep to their prices. Using game theory, we can see that any rational company would undercut his competitors, and sell their toasters for \$99. But every other company would think this too, and charge \$98, then \$97, \$96, so on, until the equilibrium price of \$35 was reached. Because each business is looking out for themselves, it has actually worked out best for the consumers.

Outside of cartels, the competition that can be studied through the lens of game theory has been a great good for consumers, delivering them new products at cheaper prices, because companies, looking out for themselves, their margins, and their shareholders, have been undercutting competitors prices and improving their products and services.

Conclusion

Game theory is a useful tool for analysing transaction in the microeconomy. By individually studying what each actor should do, we can discover dominant strategies that a company should take in every situation, Nash equilibriums if actors have perfect knowledge, and then make a decision about what should be done. Competition in product and prices has also lead to more goods at acceptable prices for consumers in the markets where companies operate.