Evolutionary Game Theory for the Children

Adults also welcome

Last November I published a “children’s book for all ages” called Game in the Garden. It’s about evolutionary game theory.

In choosing this style, which was very different from the dense 486 pages of my first book, my hope was to convey certain ideas and lessons in a way which could be universally appreciated. In that sense, I want the book to stand on its own and have something to offer to readers—whether they are 5 years old or 50.

However, I’m not going to make you do all the heavy lifting by yourself. That’s why I decided to write a sort of “teacher’s edition”. In this post I’ll go point-by-point and explain the key ideas brought to life by the story’s playful flowers.

I decided that this was an important subject for a book because games have the power to change the world. Playing is important. And the more we understand our actions and interactions, the more good we can do for the world. In fact, this is one of the subjects I’m most passionate about because it seems to be the glue which holds all other subjects together. In all of my philosophical work, I aim to marry values and actions. When we learn about the theory of games and how to play purposefully, we are afforded the opportunity to actualize the best versions of ourselves, live more meaningfully, and create a more beautiful future.

I hope this short story gives you a taste of all that games have to offer us, and that you are inspired to take games more seriously. After all, playing is not just for children.

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Game in the Garden: Teacher’s Edition:

There was a garden full of flowers, and each was unique.

When analyzing a game, we generally begin by defining key elements like the players, the goals and boundaries of the game, rules, and strategies. In our garden game, there are different kinds of flowers whose dynamic interactions form a complex system.

They all had their rules for when to smell stinky and when to smell sweet.

The “moves” or choices within this game involve the flowers either being sweet or stinky. These are meant to correspond to any number of our real-world games where players often have choices with different degrees of personal benefit along with socially desirable or undesirable outcomes. Sweet and stinky may also be compared to “cooperate” and “defect”, respectively, in a setting like the Prisoner’s Dilemma.

But they mostly agreed: It’s good to be sweet.

In many games, there are outcomes which the vast majority prefer over other outcomes. And so we can often describe games teleologically.

For a garden to make that lovely sweet smell, three in four flowers need to work hard.

To reach the socially desirable outcome, in this garden game and in many real games, generally requires a minimum level of participation. For example, if too many people cheat a tax system, a government might cease to function.

That’s why flowers always follow a rule. It springs up when they ask: If you do this or that, what will I do?

Game theory is deeply connected to counterfactual thinking. Strategy selection is largely a process of considering what other players could do, predicting what they will do, and considering possible outcomes from all potential interactions.

There were red flowers who stayed sweet no matter what. “Being sweet isn’t easy, but it’s right,” says the red flower. Through the seasons, certain flowers didn’t do their share of work. But the red flower says, “Just be you.” Through the seasons, red flowers were always sweet.

Red flowers correspond to a strategy we can call “always cooperate” or “always nice”. This indicates a strategy which is maximally altruistic and prosocial, but is susceptible to being taken advantage of by free-riders. In a Prisoner’s Dilemma, for example, two red flowers would do well playing together, but would not do well when more selfish strategies proliferate. This is generally not an evolutionarily stable strategy because of its weakness to defection or free-riding.

There were blue flowers who started sweet, but watched how others moved. If they were stinky, so were the blues. The blue flower says, “I’ll be sweet if you are too!” Through the seasons, back and forth went blue.

Blue flowers correspond to a “tit-for-tat” strategy. A blue flower would start out cooperative/nice, and then afterwards copy the most recent move of the flower it played with. In other words, two blue flowers together would act much like red flowers—always cooperating through acts of reciprocity. However, when matched with selfish strategies, it will not be taken advantage of in the way reds are. Because of this dynamic balance, tit-for-tat is usually a strong and evolutionarily stable strategy.

There were yellow flowers who were sweet once, but after that: never. If others were stinky once, yellow flowers would stay stinky forever. The yellow flower says, “I tried to be sweet, but the world is stinky!” Through the seasons, yellow flowers stopped being sweet.

Yellow flowers correspond to a strategy called “grim trigger”. This strategy starts off like the blue flower’s tit-for-tat. Yellow flowers begin by being cooperative/nice, but are also sensitive to the behaviors of other flowers. Unlike the blue flowers, however, yellow flowers permanently alter their behavior if they encounter defection—or whatever the antisocial strategy is in the real games we play. A grim trigger strategy can be evolutionarily stable, but weaker than other strategies like tit-for-tat.

And there were pink flowers who wanted to cheat. They said it was silly to try to be sweet. The pink flower says, “I’ll get a sweet garden that I didn’t earn!” Through the seasons, pinks enjoyed sweetness, but gave none in return.

Pink flowers to correspond to an “always defect” strategy. They are the opposite of red flowers. Pinks are maximally selfish and/or antisocial, while reds are maximally altruistic and/or prosocial. This class of strategies is also highly connected to ideas like free-riding, a race to the bottom, the tragedy of the commons, and multipolar traps. “Always defect” is also the Nash Equilibrium for the one-shot Prisoners Dilemma—i.e. without expanding the game into its iterated form or adding superrationality to the players, defection is a highly stable and dependable strategy. Because of the game mechanics in our present setting, where only three out of four flowers need to be sweet in order to have a viable garden, there is an ongoing pull towards free-riding and pink flowers will proliferate to fill that niche.

All through the years, season through season, many gardens grew like these. Each was filled with reds, blues, yellows, and pinks. And there were different amounts of these flowers in each.

Now that the main players and strategies have been introduced, we can move onto considering a plethora of gardens. The idea is that there are separate instances of the garden game going on, but that in some larger way they are all connected. Much like how our cities have unique identities, but share a common planet. Systems within metasystems.

The more sweet the whole garden, the more it would spread.

A garden with three out of four flowers being sweet is viable and will survive and spread at least a little. But we are led to consider how higher levels of sweetness (or cooperation or prosociality) can make a garden thrive more than others.

But being sweet was more work than being stinky, so flowers would get tired quickly.

In the garden game, and in many of our own games, we find behaviors/strategies which are collectively desirable and sometimes necessary for basic survival, that are also personally costly. This often creates tensions between selfish and altruistic behaviors.

So some flowers were too tired to spread. And none were more tired than always-sweet reds.

Red flowers solidify the idea that prosocial strategies can come with costs and be personally draining. We should imagine that a garden full of red flowers would be healthy, but would spread relatively slowly. A mostly red garden is also the most susceptible to being infiltrated by pink flowers or others with less cooperative strategies. In other words, a small cluster of pink flowers within a red garden would not need to exert their own energy being sweet; they would free-ride on the efforts of reds. And, as a result, that small cluster would spread much faster than the surrounding red flowers—at least until some critical point where there is not enough sweetness to sustain more growth.

This illustrates how a dynamic balance of strategies opens up different niches. Red flowers open a niche for pink flowers to thrive, at least for a time. When pink flowers overshoot the limits of the garden, they open a niche for prosocial flowers like reds and blues to grow in their place.

So all through the years, season through season, some flowers and gardens spread more quickly than others. Many years later, a bird flew above. Looking down, what did she discover? Fields full of flowers, with mostly the blues. Sweetness for sweetness outshines other rules.

We take a bird’s-eye view and consider the entire landscape. Game theory can be applied to single moments or long evolutionary timescales. Getting to the game theoretic moral of this story, the bird sees a proliferation of blue flowers. This is due to the strength of tit-for-tat in a competitive field of other strategies. Its success can be summarized as: It never does worse than the strategies around it. A blue flower will do at least as well as a pink flower, and won’t get taken advantage of like the red flower.

This outcome is backed by a well-known experiment by Robert Axelrod on the evolution of cooperation. He created a tournament in which different strategies, encoded in computer programs, played and competed and cooperated like the flowers in my story. The tournament simulated an iterated version of a Prisoner’s Dilemma—many rounds of the game were played and the scores from each were totaled together at the end. The tit-for-tat strategy was the winner.

These types of findings provide compelling evidence that reciprocally altruistic strategies can thrive in a hostile world and provide a pathway to cooperation which is largescale, noncoercive, and evolutionarily stable.

It is also worth appealing to more personal substantiations of these findings: I believe we are intrinsically prosocial and have the capacity to value the wellbeing of others as much or more than our own. It seems intuitively appealing that we should play nice, be altruistic, and act coherently with the holistic wellbeing of the universe. Only in certain circumstances must we deviate into the defensive stance of our tit-for-tat strategy.

There are many real games in which there is a utopian aspiration to be like the red flowers of this story. It is, after all, the nicest flower. But it is also naive. In proper terms, it is not an evolutionarily stable strategy. Game theory teaches us that strategies like tit-for-tat create the best balance between our natural altruistic drive and the presence of antisocial strategies which, if left unchecked, malignantly consume and destroy whole systems.

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Conclusion

One of my hopes is that the flowers in this story help people understand how valuable it is to see the world through the lens of games. If you are reading this, I think there must be something about the future which you would like to be different, and better, than the present. And I believe that if we hear the wisdom of the flowers in this story, we can make life better for everyone through the power of play.