Game theory: Red Queen effect, dictatorless dystopias, and capitalism

Whether you realize it or not, you are participating in a multiplayer game right now. They don’t just lurk behind glistening screens or on board games that result in incessant squabbling — they manifest themselves in every interaction with multiple people/agents/actors. 

This was probably the most difficult model for me to articulate. Partly because it seems so esoteric, yet it’s so deeply woven into the nature of all competing systems.

The applicability of game theory ranges from something as a simple two-player game, to evolution, competition, cooperation, self-sustaining systems, and basically anything that with two or more agents. 

While it might seem difficult to grasp initially, it’s definitely worth trying. Trust me, once you learn to see the underlying mechanics, it becomes impossible to un-see in everything else.

I won’t delve into classic scenarios like prisoner’s dilemma, there are many explanations you can easily Google to find. The basic premise is this, there is usually an optimal global outcome within the possibility space, but if everyone moves incrementally to maximize their own payoff (which they would do since they are motivated by self-interest), they eventually fall into a suboptimal outcome for everyone, including themselves. That region of possibility space, where no one can move in any direction to further improve their own outcome without giving up an advantage, is known as the Nash equilibrium. 

Airport annoyances

Let’s start with a very relatable example. Everyone knows it’s annoying to pick up your bulky suitcase from a crowded luggage belt. People tend to stand frustratingly close to the conveyor belt, which makes it hard to pick yours up when it arrives. Wouldn’t it be easier if everyone just collectively agreed to stand one meter away from it? Whoever needs to actually pick theirs up can then stand forward and do so with ease. So why doesn’t that happen?

If we all started out one meter away, any person that stands slightly closer to the belt has a slight advantage of picking up their suitcase more easily when it comes. Especially when it’s crowded, every individual might start to think the same way and will be incentivized to move forward ever so slightly. This happens until everyone is huddled at the luggage belt and there is no incremental advantage left. 

There are two important things to note here. One is that when everyone does this, not only is the incremental advantage lost, everybody is slightly worse off. Secondly, there is no central control, no one individually decides to make things worse for everyone. The individual self-interested decisions lead to these inevitable outcomes. This is the nature of game theory dynamics.

The Red Queen effect

_“Well, in our country,” said Alice, still panting a little, “you’d generally get to somewhere else—if you run very fast for a long time, as we’ve been doing.”

“A slow sort of country!” said the Queen. “Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!”_

- Lewis Carroll, Through the looking-glass (Sequel to Alice’s Adventures in Wonderland)

The trees in the Californian Redwood forest are a sight to behold. Sturdily piercing towards the heavens, their massive trunks dwarf humans standing next to them, and their heights easily surpass 100 meters.

While they might be captivating sight, you might ask: “Why is there a need for them to grow to such extreme heights?” A common answer would be: “To get more sunlight, of course”. 

But if you think about it, you’ll know that isn’t true. You start to realize that the amount of sunlight, captured as billions of energetic photons raining down from the sky, still remains the same per square meter regardless of the height of the trees. In terms of efficiency, these gigantic trees with their enormous trunks are an exuberance of biological excess. Growing higher does not increase the overall amount of sunlight received. It does, however, allow you to capture more sunlight than your neighbors.

A similar principle applies here. If they all started out 1 meter from the ground, they would all enjoy the same, blissful experience bathing themselves with sunlight while spending minimal energy and resources to wasteful growing. But all it would take is one gene variation to randomly appear and give that particular tree a modest boost in height. Now it’s taking in more sunlight relative to the energy required to grow that little bit more. The gears of natural selection kick in, that tree reproduces successfully with its height and energetic advantage, and next thing you know, those without those genes lose out on sunlight. Repeat this process over thousands of generations, and you get a whole bunch of very tall trees, wasting vast amounts of biological material and energy to grow and compete and grow and compete, all while receiving the same amount of sunlight they would have gotten if they all happily agreed to stay close to the ground. 

It’s not just trees that wastefully compete this way. Life itself it a gigantic game amongst replicators. Ruthless competition between species and amongst species drives an endless race. Think about the cheetahs and antelopes, foxes and rabbits, all continuously upgrading their biomechanics through natural selection to run a little bit faster, to have a little more agility. Natural selection is almost a euphemism here; you get unselected by starving to death or being eaten alive. This is the endless treadmill of adaptation, all just to survive and prevent the species from going extinct.

As the red queen said, you have to run as fast as you can just to stay in the same place.

Game theory writ large into self-sustaining systems

Dictatorless dystopia

Imagine a hypothetical world where everyone is forced to self-administer 5 units of electric shocks per hour for 10 hours every day. Definitely unpleasant, but not severe enough for any long-lasting damage. Getting caught with the failure to do so results in you getting 20 excruciating units of electric shock. Worse still, if you catch someone not doing it and you yourself get caught with the failure to report it, you receive a  lethal dose of 50 units of electric shock. Any talk about even adjusting this system must also be reported and will be swiftly dealt with through 50 units.

This is the thought experiment posed by the artificial intelligence philosopher Nick Bostrom. You can see that in this absurd situation, regardless of how it came to be, the most logical choice is to self-administer the shocks in compliance. Even if everyone personally hated it, they could not gather the simultaneous consensus of everyone under this regime to rid themselves of the system. With the very act of subverting the system carrying such a high penalty, it would make no sense to take that risk upon yourself. They would all be slaves to this unpleasant nightmare while realizing that they are the very source and recipient of each other’s misery. 

This is known as the coordination problem. Everyone behaves in a way that maximizes their own self-interest (lowest risk of receiving a high shock) through preference falsification, which results in a poorer global outcome (they are unable to completely free themselves). There is no need for a central command or dictator to enforce this cycle. It exists as a self-sustaining, independent system that perpetuates misery.

The tragedy of everything

A common game theory scenario is the tragedy of the commons, where there is a shared resource and the best outcome is for everyone to share it at the expense of maximizing their own interest. For example, in a pristine plot of grassland that produces 200 units of grass, 10 farmers can let their cows graze on 20 units of grass every year. However, if the plot of land is overgrazed beyond 300 units, it only produces 100 units of grass the next year. Every farmer initially agrees to stick to 20 units, but one of the farmers decides instead to take 30 units and realises that he is able to grow 33% more cows.

Another farmer notices this and starts doing the same and initially the effect is small so the plot of land remains relatively pristine. But one by one, farmers take notice of their neighbours fattened cows and all of them start grazing on 30 units. This leads to the inevitable outcome of an overgrazed plot of land, and they all receive a measly 10 units the next year. The problem eventually returns again when the grasslands recover and each farmer is faced with the incentive to overgraze just a little.

This applies to every single public resource and commodity that is non-excludable and rivalrous (forests, fresh air and water etc). At a global scale, pollution and climate change form the biggest games that are being played. The players, individual countries, are trading-off pollution caps to economic growth. Because of these dynamics, we’re inevitably heading towards the overgrazing scenario. Unfortunately for us, the grassland is the very planet that we inhabit and the end results are likely cataclysmic and irreversible.

Capitalism 

In a small town with only two grocery shops, both of them receive 100 customers paying $10 each every month. Shop A’s owner says to himself: I think I want to earn more money, I need to find more customers. He does some research online and figures out the price for a billboard ad. He figures that with the right placement, he can probably persuade more customers to come to his shop.

He decides to spend $50 on a monthly billboard advertisement, this brings him 120 (versus 100) customers which equates to an extra $200 in revenue. Assuming the overall demand is fixed and it’s a zero sum game, shop B loses out and only gets 80 customers the next month. 
Shop B realises this and starts to spend $50 as well, gaining back his market share to 100 customers a month. At the end of it, they are both back to where they started at 100 customers each, but both earning $50 less each month.

This game might continue to escalate, with Shop A or B increasing the spend on ads ever so slightly to gain more revenue until their profit margins reach a threshold and they cannot afford to do so anymore. You might say, why don’t they just coordinate and stop running ads altogether? It might be a simple solution in our hypothetical world, but multiply this by hundreds of thousands of businesses in the same game, with increasing competition at a global multiplayer level, and you’ll realise that coordination is simply impossible. 

Greed in this case isn’t just a selfish motivation, it’s a survival mechanism that’s essential in coping in an environment with competition. If you don’t control every dollar to maximise your revenue and minimise cost, someone else will come and take your slice of the pie. 
The point I’m trying to make here with trees, dystopias and businesses/capitalism, is that many of these phenomena do not require an overarching system that is controlled by some agent. These forces manifest themselves through individual incentives and decisions without anyone “signing” up to be part of anything or being controlled by anyone.

The dynamics act like an constant invisible nudge, pulling the system towards an inevitable slide towards the Nash equilibrium. Like gravity, it’s virtually inescapable without implementing an even larger body to force coordination (aka government). While I used to have strong libertarian views about maximising freedom especially within the context of business, game theoretic concepts and technological monopolies probably form the most persuasive arguments against unbridled capitalism without government intervention.

Alturism

It seems like almost every consequence of game theory has led to poor outcomes overall, but this isn’t actually true. I’d like to end off with something slightly more positive.

Why do people behave nicely? It’s actually a game-theoretic solution with tit-for-tat mechanics.

In order to explain this, it seems like I’ll have to make a short digression into the classic prisoner’s dilemma after all.

Imagine a scenario where two gang members A and B are suspected of a crime and kept in separate interrogation rooms. They are faced with two choices, rat their partner out or confess to the crime. If they both confess to committing the crime and don’t rat their fellow partner, they both receive 2 years of prison each. However, if:

1. Person A decides to rat B out and B confesses, A will receive 0 years and B will receive 10 years.
2. Similarly, if B decides to rat A out and A chooses to confess, B will receive 0 years and A will receive 10 years.
3. If they both end up ratting on each other, they will both receive 4 years.

In this scenario, the “ideal” case to maximise the best outcome for both would be to simply cooperate (both confess). This will lead to the least total amount of years spent in prison between them (2 years x 2 = 4 years). 

However, the optimal solution from each person’s point of view is to defect (rat their partner out). 

A) If your partner chooses cooperation and you choose to defect, you get away with 0 years instead of 2 years if you chose to cooperate instead. B) If your partner chooses to defect and you choose to defect, you get 4 years instead of 10 if you chose to cooperate instead.

As you can see regardless of which option your partner chooses, you are better off taking the defect option. Since your partner will also think the same way, it’s likely both will end up with 4 years, which happens to be the Nash equilibrium.

You might be thinking, game theory will inevitably lead to selfish, uncooperative behaviour! How do you ever get to altruism?

There is one key ingredient missing. The optimal solution for this game is to defect only if the game is played ONCE. However, in the lives of social animals, games are continuous and never-ending. In almost all social species, cooperation is essential for survival. 

The correct amount to reciprocate (cooperate) or defect (either to punish or take advantage) get put through the tests of survival and eventually form evolutionary stable strategies. Refuse to cooperate and not care about others, and your genes will quickly be removed from the gene pool. Cooperate too often without defecting, and you will quickly be exploited with your genes being similarly removed from the pool. Being nice and doing good deeds isn’t a purely social construct, it’s an evolutionary strategy that has helped us survive and flourish within rich, interdependent relationships that are necessary to build tribes and societies. This is a massive oversimplification of the types of strategies available, but its safe to say that for the majority, there’s a deeply innate drive that’s been programmed into our genes to do good and genuinely care about others.

End

Hopefully you have some new perspective on multipolar regimes, cooperation/conflict, competing incentives, self-sustaining systems, and the dynamics of game theory to spot this occurring the world around you. Whether it’s something as complex as financial systems or as trivial as taking turns to do the dishes, as long as there are two competing interests, you’re bound to find something interesting if you look hard enough!