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Nash Equilibrium and the Real World

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Prof. John Nash, one of the intellectual parents behind game theory died with his wife in a car accident on the night of 23rd May 2015. Tragically, his death occurred after returning from Norway where he received the Abel Prize, the equivalent of the Nobel Prize in mathematics (fun fact: there is no Nobel Prize for mathematics). He also has a Nobel Prize in Economics. It was for his work in game theory that won him this award, specifically in defining what is now called a ‘Nash Equilibrium’.

Game theory existed before John Nash, but the only equivalent equilibrium concept was the MinMax theorem formulated by John von Neumann (another fun fact: apparently he inspired the mad scientist character in the movie Dr Strangelove). Unlike the MinMax concept, the Nash Equilibrium was a broader solution concept that could be applied outside of zero sum games. For me, what inspired me to study game theory was that it could help explain why we live in an imperfect world. Without the Nash Equilibrium, game theory and economics wouldn’t have the power it has today. We would all believe that somehow we can’t do better than competitive markets. Well, game theory and specifically using the Nash Equilibrium concept allows us to look at the choices that face people, firms, politicians and see whether or not we could have done better. In this article, I want to examine some specific cases that we can all observe. But first, what is the Nash Equilibrium?

What is the Nash Equibrium?

A Nash Equilibrium is essentially what the economist Samuel Bowles called “a situation in which everybody is doing the best they can, given what everybody else is doing”. That is, it is the outcome where strategic actors adopt the best strategy given their best guess of what the other actors would do.

A classic example is the Prisoner’s Dilemma game. Two criminal lowlifes have been brought into the cop shop for the same crime and have been put into different interview rooms. They have broadly two strategies, 1) sing like a bird (i.e. confess and stitch up their mate) or 2) say nothing. Now, the best outcome is if both of them say nothing, that way the police have no evidence against either of them. But neither of these crims know what the other would do which prevents them achieving the optimal outcome. At the back of their minds lurks the possibility that their erstwhile mate spills the beans to cop a lighter sentence. But this throws that crim under the bus and he gets put away for a long time, by the time he comes out his son will just be entering prison for the first time. So, with the uncertainty, which undoubtedly the cops are playing up, it looks like the lowlife might be better off ratting on their mate, even though they will still do time. At least they will get to see their son before they are old enough to make the same mistake as their dad. So, in the end, while it would be best if they both shut up and lawyered up, their inability to cooperate prevents them working towards the optimal solution.

In this case, the Nash Equilibrium is for both crims to confess. Clearly, this is sub-optimal for them. Also, the concept of the Nash Equilibrium helps narrow down the number of possible outcomes, and therefore strategies that would be played. In a world of bewildering complexity, whispers, fake smiles and cloak and dagger, the Nash Equilibrium can help poor innocents such as myself to understand this world.

Commodity Busts

Why are commodity booms and busts so common? Commodities are relatively responsive to prices. In turn, prices are driven by supply and demand. When prices are high, this indicates that demand is higher than supply. This encourages commodity producers to increase supply. This can be problematic in the case of commodity industries where there are long lead times on output expansion such as iron ore. All the commodity producers see the prices and want to get a piece of the action so they increase their supply. Even though they know that if everyone increases production than prices fall. In the case of iron ore, the new production capacity has come on line. Unfortunately for the industry, a lot of that new capacity is with the lowest-cost producers BHP Billiton and Rio Tinto who are able to absorb the lower prices while the highest cost producers are struggling to break even.

Clearly, the industry would be better off forming a cartel to set prices. The Organisation of the Petroleum Exporting Countries (OPEC) is the most famous example of a commodity cartel. Oil prices have been set by the cartel with the threat that Saudi Arabia would flood the market if anyone ‘defected’ and produced more than their quotas. This is a ‘credible threat’ because Saudi Arabia has a large amount of excess capacity that could be deployed to quickly flood the market. In most other commodities, this is not possible. For example, in the case of iron ore, cartels are illegal in one of world’s largest producing countries (Australia) which would make it difficult to form a stable collusive agreement.

Clearly, the Nash Equilibrium is to ramp up production when prices are high, despite the threat of a commodity price crash. As the old saying goes, ‘make hay while the sun shines’. You won’t know when the weather will be so benign.

Road Congestion

As I argued in a previous post, more roads will not reduce road congestion. This is because more roads ‘induces demand’. Eventually, the new road capacity is filled and we are back to the situation of congested roads. Unfortunately, this phenomenon is a global one.

It is a Nash Equilibrium for commuters to choose to drive because initially it is faster. But because everyone is thinking the same, more people will start driving to work which leads to congested roads. So the increased supply has increased the gains for driving versus other modes of commuting. Clearly, a better solution would be less traffic but this is only possible through government regulation such as congestion pricing and investing in alternatives.

Dysfunctional Democracies

Why are democracies so dysfunctional? How did they manage to get anything done in the past when there were great statesmen like Winston Churchill? The institution, adversarial nature and processes of Parliamentary democracies are essentially unchanged. Elections used to be fought on ideas and policies, now much of the work in government is to develop announcements that can determine the ‘optics’ and ‘atmospherics’ of the government’s ‘narratives’.

It appears to be a Nash Equilibrium strategy for political parties to adopt the strategy that will win votes. Maybe today that means less detail such as outcomes and more focus on what will grab the voters’ attention. After all, political parties have to compete with Netflix, football, celebrity scandal, My Kitchen Rules and Game of Thrones to get voters’ attention today. So a political strategy that will generate most voter interest may be mutually exclusive to policy that maximises social, economic and environmental outcomes for society. Maybe our Parliaments could adopt some ideas from Game of Thrones with the next Question Time? That will make Paul Keating’s rippers look tame.

Climate Change Negotiations

For my sins, I have followed climate change negotiations, or you may know them by their riveting official name of the ‘United Nations Framework Convention on Climate Change: Conference of the Parties [insert year]’. You may not be aware that the decision rule for the treaty negotiations is unanimity. That means that all 193 member States of the United Nations have to agree. For anyone who has been to a meeting, this seems laughable. Yet, somehow we have persisted with this flawed system despite the obvious lack of progress in addressing a global threat.

With a unanimity rule, it is a Nash Equilibrium for a recalcitrant nation to hold the negotiations hostage by holding out.

Australia did this successfully in the negotiation of the 1997 Kyoto Protocol by actually negotiating an increase in emissions when the goal was actually to reduce carbon emissions. Since then, negotiations to replace the Kyoto Protocol have often fail at the last minute. Because countries know that if they hold out for a better deal they increase their leverage and either get some thing like the ‘Australia clause’ or nothing happens. This strategy is attractive for countries that are not likely to suffer disproportionately from climate change. Unfortunately, this imposes the cost of delay on countries that are least likely to be able to cope with it such as small island countries, Africa, South East Asian countries and low-lying poor countries such as Bangladesh. Unfortunately, I don’t think this will change until either the decision rule changes or it becomes clear that everyone will suffer under climate change.

More Examples?

I only scratched the surface here. You can probably think of others where a Nash Equilibrium explains why a sub-optimal result persists. Just off the top of my head, the property speculation prior to the Great Recession is a case where it was a Nash Equilibrium to keep on investing in property because it appear it would go up infinitely. I’m sure you can think of others. Or, if you see a seemingly illogical situation, maybe you should ask, ‘what would John Nash think?’