The oil price war is actually just a return to equilibrium

The 'war against coronavirus' may be just getting under way, but it wasn't the only war in the news in the past couple of weeks. Saudi Arabia and Russia have fired the first shots in an oil price war. The New Zealand Herald reported:

Expect to see petrol prices fall sharply in coming days after fears of a global price war sparked an historic collapse in crude oil barrel prices this morning

Oil prices plunged as much as 30 per cent as markets opened this morning - the biggest one day fall since the start of the first Iraq war in 1991.

Brent crude is currently down about 20 per cent.

But this follows falls of 10 per cent at the weekend on fears that Russia and Saudia [sic] Arabia will launch a full-scale price war.

Saudi Arabia slashed the price of its crude and upped production after Opec and Russia failed to agree on a supply response to coronavirus.

The industry had hoped that major players would agree on production cuts to mitigate the impact on global demand.

But talks in Vienna failed late on Saturday (NZT).

Global crude oil production is an example of an oligopoly - a market where there are many buyers, but few sellers. When there are few sellers, it is in the sellers' best interests to work together as a cartel. A cartel essentially acts like a monopoly seller - it is able to use market power to extract greater economic rent from the market (in the form of higher profits, arising from higher prices), than the countries would be able to extract if they were competing with each other.

This is another example of game theory in action. Let's say that there are two players - Saudi Arabia and Russia. Each player has two strategies - high production (which leads to lower prices and lower profits for oil producers), or low production (which leads to higher prices and higher profits). If one country has high production and the other low production, the high production country benefits more. However, if both countries have high production, both are worse off. These outcomes and payoffs are illustrated in the diagram below (the payoff numbers represent profits, but are just made up to illustrate this example).

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If Russia chooses high production, Saudi Arabia's best response is to choose high production (since 4 is a better payoff than 2) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Russia chooses low production, Saudi Arabia's best response is to choose high production (since 10 is a better payoff than 8);
3. If Saudi Arabia chooses high production, Russia's best response is to choose high production (since 3 is a better payoff than 1); and
4. If Saudi Arabia chooses low production, Russia's best response is to choose high production (since 6 is a better payoff than 4).

Note that Russia's best response is always to choose high production. This is their dominant strategy. Likewise, Saudi Arabia's best response is always to choose high production, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both countries choose high production.

Notice that both countries would be unambiguously better off if they chose low production. However, both will choose high production, which makes them both worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off).

That's not the end of this story though, because the simple example above assumes that this is a non-repeated game. A non-repeated game is played once only, after which the two players go their separate ways, never to interact again. Most games in the real world are not like that - they are repeated games. In a repeated game, the outcome may differ from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome.

And that is what happens when a cartel forms. If Saudi Arabia and Russia work together and both agree to choose low production, both countries benefit. That is what they were doing, up until a couple of weeks ago. The problem here is that both countries choosing low production is not an equilibrium. Each country individually realises that it can benefit by choosing high production (knowing that the other country is choosing low production), thereby cheating on the agreement. If both countries cheat, then the agreement breaks down and we end up at the Nash equilibrium (which appears to be what has happened). So essentially, the current oil 'price war' is simply a return to the equilibrium in this game.

However, it probably won't last. After a little while at the Nash equilibrium, it is likely that both countries will realise their folly, and work towards a new cartel agreement based on low production. And the cycle will begin all over again. Essentially, this has been the story of OPEC since soon after its formation - agreement by all (or most) parties, followed by selective cheating, followed by a breakdown in the agreement, followed by a new agreement.

So, make the most of low petrol prices. The coronavirus pandemic may keep them low for a while yet (due to low demand), but eventually Saudi Arabia and Russia will get their act together, and we'll be back to a world of higher oil prices (and consequently higher petrol prices).

[Updated 15/04/2020: To correct the positions of ticks and crosses in the payoff table]