Nash Equilibriums – Chess and the Instability of Cartels

One of the neatest developments in economics is the formulation of game theory. Even though its strategies and recommendations have been known to people throughout history, game theory puts these strategies on a theoretical structure. One of the situations thrown up by game theory is a Nash equilibrium.

Assume that there are competing players in a situation (call it a game). Each player has to choose which strategy to adopt. The outcome of that strategy is going to depend on what other people choose. In such a situation, a Nash equilibrium is formed when each player knows what strategies the other player is going to adopt and will gain nothing by changing his/her choice.

Let us take an example of chess. If you watch a Grandmaster play chess against someone who is well beneath him or her in playing stature, you will probably be surprised that the Grandmaster will take longer to beat the novice than an expert would take, although the expert is still much superior to the novice but far inferior to the Grandmaster.

Grandmaster Chess

Grandmaster Chess. Photo by Kryten. Taken from Everystockphoto.com

The reason for this is that when you try and finish off an opponent quickly, you leave gaps in your own defenses. These gaps are not easy to spot, but Grandmasters are in a position to take advantage of them. Therefore, it is in the interests of anyone who is playing a Grandmaster to take their time and not rush. So if there are two Grandmasters playing each other, each knows that the other will adopt the strategy of non-rush and will therefore play non-rush themselves. Because of this, Grandmasters are in the habit of taking their time, securing their defenses, and playing slowly.

However, when the expert plays the novice, he has no problems about tearing the poor novice apart because he knows that the novice can’t take advantage of the weaknesses that he leaves behind while attacking. If the expert were to play the Grandmaster, however, he would be a fool to rush into the attack.

In the case of the two Grandmasters, the Nash equilibrium consists of both players choosing the strategy of non-rush because they know that their opponent will do the same. It would be foolish to attack a Grandmaster hastily because they would be building their own defenses, and if you don’t do the same, you will be left in an untenable position. Therefore, the strategies of two Grandmasters playing each other are stable. Each will not change their own strategy if the other continues to maintain theirs.

In a cartel, a group of players who control the supply of a certain product get together and agree to keep the price of that particular product high. There are two strategies here – high prices and not so high prices. It’s easy to see why all the cartel members benefit in the long run if each follows the strategy of high prices. However, it is unstable because it is not a Nash equilibrium.

This is because of the fact that if one of the cartel members changes their strategy to not so high prices, that person will get all the customers who will no longer buy from the other players since they are following the high prices strategy. This will lead to a dramatic gain of business for the player who changes his strategy to not so high prices. Naturally, this situation can’t last. The moment the other players find out that one of them has changed their strategy, it is no longer in their best interests to adhere to the strategy of high prices. Thus, they change their strategy to not so high prices as well, and the cartel breaks.

OPEC Headquarters in Vienna

OPEC Headquarters in Vienna

Cartels are so unstable precisely because of the threat of betrayal. And the more people that make up the cartel, the more unstable it becomes since there are more chances of any one person changing their strategy.

Cartels like OPEC have stood the test of time because, firstly, there are not too many players. And secondly, they all recognize that they’re here for the long term and that if one of them breaks the cartel by adopting not so high prices, then all others will follow suit, and they will be back to square one with lower prices.

Indeed, the only real reason for any cartel to stay together is if they are in the long run together and realize that united they stand and divided they fall.

Editor’s note: Last year a German watch magazine did an interview with John Nash. Read more about it at Amateur Economist. Thanks to Chris Meisenzahl for the link!

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