Animals Play Coordination Games - Coordination Part I
Counting cicadas, flirtatious fireflies, and bourgeois butterflies
Prime Time for Cicadas
Magicicada septendecim, the Pharaoh cicada, emerges from the ground in mind-numbing numbers every seventeen years in the eastern United States. The first scientific report of the swarm was in volume one of the vaunted publication, Philosophical Transactions of the Royal Society. In this report, we learn the following:1
A great observer, who hath lived long in New England relate[d]…that some few years since there was such a swarm of a certain sort of insects in the English colony that for the space of 200 miles they poisoned and destroyed all the trees of that country…
The pattern has been known for some time. The polymath Benjamin Banneker was among the first to note the odd frequency, recording the insect swarms in 1749, 1766, and 1783. Some closely related species emerge every 13 years in similarly eye-popping numbers.
The more mathematically inclined readers will have noticed that both numbers are prime, divisible only by themselves and one. The most promising explanation—which is still subject to debate—for both the swarming itself and the frequency with which it occurs illustrates the central point of this post: animals play coordination games.
Let’s take the two pieces separately. First, why do all the cicadas emerge at the same time? The key is that the predators that eat the cicadas can only eat so many of them. All species reach a point of satiety past which they just can’t eat anymore, something that happens far too early on Thanksgiving day in my house because of all the amazing food my mom has ready when we arrive. In any case, the way to understand the swarming is to look at it from the standpoint of any individual cicada, call him Cecil. If Cecil comes out the year before all his pals, the predators around him are all hungry, which is bad for him. But, if Cecil emerges when billions of his closest friends do, there’s a much better chance he’ll live because the predators who might otherwise eat him have gorged on his friends.
From the perspective of Cecil, and each individual cicada, their best move is to emerge when everyone else does. Evolution acted on cicada life cycles, causing this convergence.
Indeed, the coordination is even better than that. Cicadas emerge when the temperature hits around 64 degrees. By using an environmental trigger, the cicadas can coordinate precisely when during the key year they emerge. For all that follows, it’s important to keep in mind the idea that a cicada can’t do better by switching to a new strategy, emerging in an off year or at a different temperature. This is a hallmark of coordination games: players can’t do better by switching away from what others are doing. Cicadas are still in competition with each other—for food, mates, etc.—but the fact that they are competing does not preclude the possibility that for some games, coordinating is the best strategy for each and all.
Ok, next, why do these guys come out every 17 years? Interestingly, this is an example of a game in which there is an incentive—really, a selection pressure—to disco-ordinate. This hypothesis begins with the observation that many populations go through regular boom and bust cycles. A particular population does well, birth rates increase, the density of the organism increases, taxing food supplies, leading to a population bust. Suppose some predator population booms every two or three years. If the cicadas emerged, say, every 8 years, then the predator booms could synch up to the cicada cycle, exploiting them just when their numbers are greatest. Prime numbers avoid this problem. Additionally, the prime numbers ensure that the broods on different cycles emerge in the same year only very rarely which, by coincidence, is happening this year, for the first time in 221 (13x17) years.
(You might also wonder why the cycle times are so long. Could it be that the long delay thwarts parasites, with short life cycles? Suppose you have a parasite that evolves to be very good at exploiting just the one cicada adult host. By disappearing for a long period of time, the cicadas leave the parasite host-less for many generations, perhaps enough to go extinct or evolve toward exploiting a different host. Still, the larvae have to come up eventually to reach the adult life stage and reproduce, which is why the interval can’t be 101.)
Cicadas aren’t the only species to play the coordination game this way. The Olive Ridley sea turtle arrives in the thousands to lay eggs on the beach where they were born, possibly using an olfactory signal to coordinate when to arrive. They’re using the same solution—overwhelming numbers—to the same problem: predators.
Coordination Game Theory
Ok, let’s make all this talk a bit formal, to provide an easy way to look at and think about other examples. Let’s take the simplest possible coordination game. Adam and Bob are on opposite sides of a two-lane bridge. Each faces a very simple choice: drive on the right side or on the left side. We can make a little grid to illustrate the game—choices and consequences—as follows, putting the result of their respective choices in the appropriate box in the grid.
For the duration, I’ll use numbers to reflect the outcomes, listing them for the row player first (Adam’s Outcome, Bob’s Outcome). Here, they get one point for crossing safely, zero for dying in a fiery crash.
A key point, as we will see in other coordination games, is that Adam and Bob are indifferent to which side they are on—the payoffs are the same in both—but they do care about being on the same side. Just as in the cicada case, if, say, Adam drives on the right, Bob can’t do any better than driving on the right. This is called an equilibrium because it’s stable in the sense that there is no advantage to switching. I try to avoid too much technical language in these posts, but the equilibrium concept is crucial for understanding and analyzing coordination games, so the term will appear frequently in this series.
In particular, the logic of equilibrium can be applied to evolution. You can think of evolution as “trying” different strategies in different games. In the case of the cicadas, genes that cause the cicada’s offspring to emerge at the same time as others do better and propagate. This trait is stable because any change from the equilibrium—seventeen years or what have you—is punished for the reasons described above. The equilibrium concept is useful for predicting what strategies will be seen over evolutionary time. Solving for an equilibrium in a game tells you which strategies are evolutionarily stable.2
Those Flirtatious Flies & Bourgeois Butterflies
How, you might be wondering, does this relate to fireflies?
I’m so glad you asked.
There are approximately 2,000 different species of firefly. Given this diversity, a critical adaptive problem is for fireflies to identify and mate with another member of their species, since cross-species mating does not yield viable offspring. Both male and female fireflies face this adaptive problem, creating a coordination game.
To solve this problem, natural selection led to a trait: a fancy bioluminescent tail that generates a series of flashes a male uses to identify himself to a potential partner. The pattern of these flashes—how many flashes, how long, etc.—vary across species but are, of course, unique to each species. The trait loses utility as a coordination device if different species use the same pattern. When a male flashes, he’s making a particular sort of proposal. When a female detects the correct flash pattern, she counter-signals her own unique pattern if she is inclined.
Let’s pause to note a few facts.
First, as in other coordination games, no firefly can do better by changing patterns. Once there is a unique pattern within a species, a firefly that deviates is simply going to be excluded from mating, an evolutionary dead end. One needs just the right key, as it were, to unlock the mating.
Second, and I really cannot stress this enough, the specific details of the signals don’t matter. Dot dot dash. Dash dot dot. As long as everyone knows and uses the same pattern, the content of the pattern—what it looks like—doesn’t matter. This is crucial for the coming discussion. As long as there is coordination, the content is irrelevant. To anticipate somewhat, when you see what seem to be a collection of arbitrary contents, a good guess is that you’re looking at the result of a coordination game.
Now, there might be other reasons, beyond the game itself, that some patterns are better than others. Maybe a long flashing pattern is more likely to attract predators. In that case, everything else equal, we would still expect to see unique patterns across species, but by and large, these patterns will be brief. This phenomenon is called equilibrium selection. Coordination games by themselves often allow for equally possible equilibria. In the cicada case, 13 years and 17 years might well be equally good, for example. Then, in addition, there are other forces that push strategies in one direction or another. For those who like the tables, here is one way to think about it, below. I’ll start using green font to indicate the equilibria.
In this game, Flynn and Flo, both flies, want to choose the same option as the other. However, some coordination points—dot-dash—are better than others—dot-dot-dot-dash—because they are brief and don’t attract predators. If—and it’s a big if—natural selection acts in such a way that it can “find” the dot-dash equilibrium, that’s very stable. But it’s important to note that if evolution just happens to reach, say, dot-dot-dot-dash first, it might be hard to get unstuck from it. Remember, fireflies that switch will be at a disadvantage and will be more likely to be selected out.3
Up to this point, I’ve addressed games that are symmetrical. Some coordination games are not symmetrical: the players have unequal payoffs when they coordinate. Suppose two organisms both want a resource—food, territory, mate, etc.—but both cannot have it. Each would prefer the resource but—here is the coordination part—neither wants to get into a costly fight to settle who gets it. For example, stag beetles wrestle one another with their large mandibles, using the match to figure out who would win an all-out fight, without either participant inflicting or incurring much actual damage.
The Speckled Wood Butterfly (Pararge aegeria), a denizen of dappled woodland areas, defends sunlight patches, which are valuable to attract mates. If it were possible, it would be in each butterfly’s interest to choose who gets the patch without having to go through with a fight for it, as in the beetle case. This advantage to avoiding conflict, of course, explains why many species display to one another—to determine who would win a fight if it were to occur.
Is there another way?
Simplifying somewhat, it has been suggested that these butterflies play a very simple strategy to avoid fights.4 This strategy, dubbed “bourgeois,”5 is to defend a patch if you were there first, but to retreat if you weren’t. It’s called bourgeois because using the strategy looks like butterflies are respecting property rights: whoever got there first “owns” the space. When all use this strategy, as long as the timing on a patch isn’t exactly the same, all are spared the cost of a fight.
It's important to note that, in theory—if not in fact6—the reverse strategy, anti-bourgeois, in which the 2nd butterfly to arrive gets the territory, would work just as well to avoid conflict. The key, as with all coordination problems, is for all involved to use the same strategy, whatever the content of the strategy.
Real-time Coordination
Coordination games aren’t only played over evolutionary time. Some are played in real time. We’ve already seen, in the cicada case, that the insects emerge when the temperature reaches a certain point. This strategy, using a signal in the world to choose when to act is an example of what is called a correlated equilibrium.7 The observed behavior is correlated with some information the organisms can perceive. Traffic lights, in the human world, are an example, as we’ll discuss in future posts.
Cicadas aren’t the only ones. Fish school, cows herd, and wolves pack, and the coordination of starlings in a murmuration is something to behold. If you haven’t watched one of these videos, or seen it in real life, click through because it’s pretty spectacular.
When organisms synchronize their movements like this, it’s likely that they are playing some sort of coordination game. In the case of herds, schools, and murmurations, the explanation is likely to do with the advantage that individuals get from being around other individuals. Large groups of organisms moving together can make it more difficult for predators to focus on a single individual to attack. There are, of course, other possible explanations for this and similar behavior. When I was traveling in South Africa, I was lucky to see roughly a bajillion vultures—and a few hyenas—all clustered around the carcass of a dead buffalo. They weren’t coordinating with each other; they were all foraging using the same strategy, exploiting a large, non-moving food source.
For the present purpose, however, the point is simply that these sorts of cases illustrate additional examples in which the individual’s best strategy—in real time—is to do what all the others are doing. They coordinate because the alternative, not coordinating, entails a cost. As always, this doesn’t mean that the organisms involved aren’t also competing with one another. They are. The advantage to coordinating with others is, nonetheless, the best move from the perspective of each individual.
Before concluding, it’s important to note that while there are some really interesting coordination games in nature, I’m not saying that they are everywhere. The conditions have to be just right for the structure of a coordination game to apply.
Conclusions
In this post, I laid out the grid for coordination games. The first thing that must be borne in mind is that coordination games don’t announce themselves. When I show you the payoffs, I’ve sort of flipped to the answer key in the back of the book. What we have to go on is observation, usually of behavior, whether non-human or human. A huge part of the challenge in animal behavior—and psychology—is to figure out the game that organisms are playing. For example, I recently suggested that people at protests are playing a signaling game. Once you figure out the game, you can make real progress in understanding and explaining otherwise puzzling behavior.
An important takeaway from this piece is the following. A big clue that you are seeing the results of a coordination game is observing within-group commonalities and between-group differences. Fireflies signal their species. They are all playing a signaling game. But species differ in the content of their signals. The coordination game explains why signals are the same within a species but different between them. These differences constitute arrivals at different equilibria.
Contrast this with the array of ways in which species are similar. The famous examples of bird wings and bat wings illustrate the point. When the problem is the same for everyone, you get the same solution. There aren’t multiple equilibria to be selected. Wings are a winning design for (natural) flight. Full stop.
Finally, when you have all these equilibria to choose from, you can get a staggering variety of contents, many of them seemingly arbitrary. If a species can use anything—colors, flashes, audio calls, scents, etc.—to coordinate, then you’ll see an ebullience of these contents. Again, there might be forces pushing toward one equilibrium or another, but coordination games frequently result in arbitrary conventions, such as stopping on red and going on green.
We’ll visit many more coordination games in the posts to come.
REFERENCES
On cicadas.
Campos, P. R., De Oliveira, V. M., Giro, R., & Galvao, D. S. (2004). Emergence of prime numbers as the result of evolutionary strategy. Physical review letters, 93(9), 098107.
Kon, R. (2012). Permanence induced by life-cycle resonances: The periodical cicada problem. Journal of biological dynamics, 6(2), 855-890.
Webb, G. F. (2001). The prime number periodical cicada problem. Discrete and Continuous Dynamical Systems-B, 1(3), 387-399.
On game theory
Aumann, R. J. (1974). Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics, 1(1), 67-96.
Maynard Smith, J. (1974). The theory of games and the evolution of animal conflicts. Journal of theoretical biology, 47(1), 209-221.
Maynard Smith, J. (1982). Evolution and the theory of games. Cambridge University Press
Schelling, T. C. (1960). The strategy of conflict. Harvard University Press.
On the Bourgeois strategy
Davies, N. B. (1978). Territorial defence in the speckled wood butterfly (Pararge aegeria): The resident always wins. Animal Behaviour, 26, 138-147.
Sherratt, T. N., & Mesterton‐Gibbons, M. (2015). The evolution of respect for property. Journal of evolutionary biology, 28(6), 1185-1202.
I have changed the orthography to modern practice (e.g., observer for Obferver).
Maynard Smith, 1982.
For the technically inclined, this is obviously a reference to the issue of local maxima. Equilibrium selection has to bridge maxima and the likelihood it will depends on the specifics.
Davies, 1978.
Maynard Smith, 198
Sherratt and Mesterton‐Gibbons (2015) write: “Despite these predictions, anti-Bourgeois behaviour is rare in nature…” (p. 1185)
Aumann, 1974; Schelling, 1960
I am not looking forward to any cooperating cicadas this year! Nor even any noncooperating cicadas. Dread the whole concept with two new horses, in fact.
Richard Dawkins in The Selfish Gene gives an example of a Mexican social spider that uses the anti-bourgeois strategy