One again the Internet has come together for a viral global cyber event — The Button. I am talking about the mysterious Lost-esque button on Reddit which became an Internet phenomenon.

Reddit, as we know, has an enormous amount of web traffic. A button appeared on Reddit on April Fools day. It was accompanied by a simple timer. Whenever someone presses the button, the timer resets to 60 seconds, and starts counting down. Every user/account created before April 1st on Reddit had a single chance t0 press the button. This meant the number of possible clicks on the button were finite. If the timer hits zero and runs out, the game ends and the button would not respond to any more presses.

Users who pressed the button ("pressers") got a color flair depending on the exact timer value (0–60 seconds) when they pressed it.​



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The purpose of the button has been widely debated in press. Was is it an experiment to check if we can wait for a minute ? Was it an art project? A way to show advertisers how engaged the user base is? An existential representation of life? Can it be a lesson in for public policy? Why is society so fascinated that they can't wait to press it? Should we be worried about this? What does it all mean… especially when over ONE million netizens have pressed the Button; given seemingly zero associated reward incentive.

What can a pointless Button tell us about how our beliefs and ideological theories survive in today's competitive environments? A lot, actually.

This post is not a revelation of the grand theory for the button — why it was born or what happened when it died. I doubt even the Reddit mods know that. Instead, I show that analyzing the click data provided by Reddit indicates that the evolution of community strategies around the button mimics aspects of biological evolution in competitive environments. User reaction, interaction and community formation around the fictive purpose of the button directly leads to this result.

The Button is a massive psychological and social experiment, probably the biggest ever of its kind on the Internet. Insights we can extract from this data are useful in various scenarios, from gamification in your app to understanding how very simple rules can actively engage (even obsess) online communities.

For those who haven't been following the entire story, several color-coded communities, coalitions and cults had mobilized on Reddit with specific missions for the Button. Overall these rivalries lay in a spectrum between: (1) prolong the life of the button or (2) expire the button as quickly as possible. Here are some of the button coalitions based on the pressed timer values (or color flair):



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As the button presses dwindled there was murmur of the imminent Pressiah — the last person to press the button before the timer expires. Apparently, scientists on Reddit had warned that one of the bots could become the Pressiah, which is incredible to think what happens when a machine makes the final push. Was the Pressiah a bot?

Here are the three overarching questions surrounding the Button game:

1) How long will the button survive? Why were estimates made from initial data so off, and why did it not survive the entire duration of what's mathematically possible.

2) Why did ad hoc communities and coalitions form in the game? Do redditors have a natural propensity to cooperate, or did the game design generate partial cooperation as an unintentional by product.

3) What was the impact of BOTS and ZOMBIES playing the game ? Because you know, every digital community has its share of bots who "engage."

To answer these questions, I will use the time series of button presses data released by Reddit, which essentially contains the <press_time> and <flair_received> for each of the ~1.008 Million presses. I do not have the user info related to each press. Remember, for the button to survive, it must receive at least one click per minute.

Life Of The Button

There were many predictions as to how long the button would survive. 1) If we discount the fact that there are co-presses, that people are not always rational and there is only one universal strategy (to extend button life), then the mathematically ideal lifetime of the button is N*59, where N is the # of Reddit active user accounts created before April 1. This end-date would be a whopping 15 years, October 30, 2031 to be exact! 2) We know ~1M people pressed the button. In fact, even if all of the ~1 million pressers had decided to wait for a zero sec press, this button would have lived till March 1, 2017!

Other predictions tried to use a saturation model to extrapolate the clicks/minute on the button based on the initial data. The decay in the number of clicks predicted that the button would expire within 12.3 days, i.e. on April 13th. This exponential decay model went wrong because it failed to account for the other competing strategies from different flair coalitions.

In reality, the button lived from April 1 to June 5th and accumulated around ~1 M presses over its lifetime. However, almost 30% of the all clicks on the button occurred within the first 24 hours of inception.



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In fact, within two days 50% of the pressers had already clicked it. In a span of one fortnight since launch, 75% of pressers had a colored flair.

The button would still survive for another 50 days, contrary to the predictions. Just 10% of the pressers sustained it during the entire of the last month. This is simply staggering, because it hints at the possibility of strategic cooperation in a set of users who were not fundamentally amassed to cooperate. Without cooperation and formation of coalitions to pre-plan button presses, the life of the button would have expired significantly earlier.

When the button finally expired on June 5th, it was 65 days old. Here is a chart of how the different flair pressers clicked the button over time.



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It is not surprising to see the lower value flairs (more prized) did not flourish in the early days. In fact, the rise of each flair curve follows the exact order as the color ranks in the flair guide, i.e., yellow leads orange because yellow (32s-22s) comes before orange (22s-12s).

Most people believe the Button is a massive social experiment, which is probably true. But it is a much bigger experiment in collective decision theory — the strategy of when to press it. To understand the strategic decisions made by different flair coalitions in the game, we must dive deep into Game Theory.

So, how can we frame this problem in terms of Game Theory? By assuming each colored flair line that you see above is a strategy. Unlike casual usage, a "strategy" in game theory does not necessitate previous knowledge or interaction among individuals to decide on it. Two independent yet identical choices still belong to the same strategy. So all presses that fell into one flair color can be considered a strategy of its own.

Strategies And What Cooperation Means



I first tried to simulate the game and analyze button pressing strategies by drawing parallels to the "centipede game," a classic game theory problem. You might think the name of this game carries some deeper meaning but it really does not. In a centipede game model, the sequence of decision patterns in the game looks like a centipede, thus its name. My first task was to figure out the utility of a single press. We could formulate it as inversely proportional to what the press-timer value is. So if you pressed at 59 secs, your utility could be 100/(1+59) ~ 1.667. If you pressed at zeroth sec, you would gain an utility of 100.



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Every Nash Equilibrium (NE) in this game is known to possess the feature of first-stage defection with sub-game perfect equilibrium, i.e. theory suggests there will be immediate defection and zero cooperation. The game should continue to future stages. This solution is uniquely rational. It is what Classical Game Theory (CGT) tells us to expect.

However, we see that the flair press data for the button differs from this theory i.e. first-stage defection (press immediately or at 59) is certainly untrue for most of the latter 70% pressers beyond the first 2 days. If the centipede game and Nash Equilibria held, then we would have seen zero cooperation. The button would have expired in less than a week, because users would have pressed it immediately (assuming all users did not learn about in on the first day). But this is hardly true for the data. And in fact, it is known to scientists that experimental results of the centipede game deviate wildly from these theoretical prediction (> 50% times), i.e. players instead choose to cooperate. Thus, CGT does not provide us any explanation for the existence of partial cooperation in the Button game.

When the evidence changes, theories must also change. We need a new theory of why cooperation occurs in the Button game. Scientist suggest that deviations from the NE occurs due the possibility of "reputation" and/or incomplete information in the game.

The Game Has Changed

A cooperative game is a game where groups of players ("coalitions") may enforce cooperative behavior, hence the game is a competition between coalitions of players, rather than between individual players.

There are four critical design patterns in the game which lead to partial cooperation instead of first stage defection (as predicted by NE):

1) Finite population of players (Stochastic evolution in finite populations need not select a strictly dominant strategy, hence the "classical" need to kill all alternatives strategies other than the dominant is invalid).

2) Belonging to a flair and the flair color-ranking (the concept of reputation, first reason to not defect in centipede games)

3) Simultaneous presses all get same flair (meaning both players can defect and split rewards, increasing chances of cooperation)

4) Players are unaware of each other's flair allegiance (incomplete information, second reason not to defect in centipede games)

So if CGT does not explain the data, what does? Remember we only have the "when-pressed" data (frequency of clicks) available to us (as opposed to the who-pressed). So why do I think the frequency of presses is important? Because it lets us model the problem in terms of Evolutionary Game Theory (EGT) — where we can study how strategies evolve over time. EGT differs from the classical version by focussing more on the frequency with which each strategy is adopted by the population instead of overall number of competing strategies.

Evolutionary Game Algorithms not only consider the number of competing strategies as parameters, but also what percentage of the population adopted each strategy and how the sequence of adoption affects subsequent strategies.

I will skip the math for brevity and borrow some results from EGT. First, according to EGT there be several evolutionary paths, and the sequence of adoption of strategies and the numbers that adopt each strategy are critical in deciding where the final equilibrium will arise. If the population is finite, the evolutionary paths can "get stuck," where the population exhibits partial cooperation leading up to the equilibrium. Thus, many strategies will be born and will die before the final dominant strategy takes over and the final equilibrium is found.



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To simulate the evolutionary strategies, I used a simple genetic algorithm that determines dominant strategy among the six flairs (more later on how to calculate this). I then fitted an exponential trend-line for the points in each of the flair categories. The trend-line represent the rise of the strategies over time. If you run the algorithm, the result shows the game reaching an equilibrium ~52 days since onset.

Just like NE of the CGT case, at this final equilibrium point here in EGT — the game is supposed to end. The final dominant strategy (red) has taken over and there is no newer competing strategy. This is when and where the evolutionary paths would have reached the equilibrium. So at this point, the game should have ended. This is where the button should have died. In fact, it did…

…and this is when the first zombie bot saved The Button.

Zombie Bot Salvation



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A red flair coalition called the "Knights of the Button" had created The Zombie Project— a group of users who donated their reddit accounts so that the presses can be performed at precisely the zero second tick by a server at some undisclosed location. Some of these reddit accounts had been "shadow banned" where their activity invisible to all other users. Knights members, however, realized that such accounts could still press the Button. This zombie army could theoretically save the button every time it was about to die.

So on May 23rd, 52 days after origin, the button timer did hit zero — just as the EGA predicts. And it was precisely at this moment that the Knight's Zombie count reduced by one, saving the button with a zero-sec press. It appears more than 1000 zombies rescued the button at various instances between the 52nd and 65th day. But since zombies cannot count we will never know how many there actually were. The Necromancer, who built the zombie bot army, claimed that less than 10% of the available zombies had been exploited till June 5th.

So why could the zombies not protect the button eternally? Because one of the zombies was not qualified. This is also why zombies need background checks before getting enlisted. But for now, let's talk a little more EGA. How did we come to decide which strategy is dominant and how it fits EGT. Why does sequence matter?

Evolution In Cooperative Games

The beauty of coalitions is that although cooperation proceeds jointly, the individual action of pressers are chosen independently and non-cooperatively. At the individual level, the incentive still is to get a lower flair for Internet status symbol. In fact we can see this in the data. Notice the similar pattern over each flair category for the press-times. If we look at the pressed time within each flair (Pressec), we see a rise in presses towards the boundaries of each flair. More community members press when they enter a new flair.



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The critical aspect to understand here is that in EGT, unlike CGT, weakly dominated strategies are not eliminated immediately. Instead, such games tend to have a sequential structure where one coalition will choose its action followed by another coalition — which is why we see one flair strategy take over from another as time passes by.

Also according to EGT, this dynamic will not carry the game directly to some unique equilibrium. Instead, it can carry the the population through series of stages, brought upon by the elimination of the current dominating strategies. This is evident if you look at the green, yellow, orange and red flair strategies. Certain strategies will become weak and go extinct (and in effect that population might die out, which is exactly what we see in the graphs).



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Hence, the current dominant strategy in one phase eventually dies and a new strategy arises quickly, which in turn becomes dominant and gets eliminated in time. When certain strategies go extinct, whats left is the final dominant strategy — in this case, the Red.

You can also calculate that red is the final dominant strategy using a simple algorithm. It is just a fancy way of representing that the dominating strategy of each user is the strategy where the utility is greatest:



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How long does each intermediate strategy phase last? The time it takes a new strategy to take dominance over the previous one in this case is approximately ~11 days. Every time. This constance can be attributed to similar size of the population, the length of the overall game and the initial state of the population. Yellow, orange, green and red flairs all had similar size of participants (12K ~ 14K) and they were all initially were suppressed in the non-cooperative stage.

This is what evolution does — it tests alternative strategies for the utility to survive and selects dominant one after several phases.

Button Dies Due To Robot Zombie Malfunctio n



When we choose unqualified zombies, we lose. As the Knights of the Button obtained thousands of zombie reddit accounts, one failed because it was created after April 1. Apparently the software was designed to only check if a zombie candidates had previously pressed the button; not when if it was created after the game began. Thus, without this programming bug which made a zombie invalid, the button would have lived longer. Pro tip: Background check your zombies !

People are saying the Button is meaningless, but that's not the point. The Button isn't supposed to do "what we expect" — and therein lies its greatest ulterior hallmark and what makes it such a compelling social experiment.

This post originally appeared on Medium.