Evolutionarily Stable Strategy and Game Theory

This article is an excerpt from the Shortform book guide to "The Selfish Gene" by Richard Dawkins. Shortform has the world's best summaries and analyses of books you should be reading.

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What is an Evolutionarily Stable Strategy? How does game theory help identify strategies that might be stable?

An Evolutionarily Stable Strategy is a population configuration that leads to the best survival for a population. If an individual deviates, they will be less likely to succeed than those who conform.

Read on to understand what an Evolutionarily Stable Strategy is and how game theory can help explain it.

What Is an Evolutionarily Stable Strategy?

Populations of animals will naturally tend toward an Evolutionarily Stable Strategy, or ESS. The ESS of a population is the most stable possible configuration of members; by definition, any member of the population who doesn’t conform to the ESS will not be as successful as others.

For example, imagine that a hypothetical species has two possible strategies when confronted with a rival: Fight or bluff. Furthermore, imagine that each member of that species engages in only one of those behaviors—the same one every time without fail. 

If two fighters meet, they will fight until one is severely injured or killed. If a fighter meets a bluffer, the bluffer will run and the fighter will win without suffering injuries. If two bluffers meet, they will engage in a drawn-out contest until one backs down. 

Applying Game Theory

(Shortform note: Game theory is the study of strategic decision-making through mathematical models.)

We can apply Game Theory to find the Evolutionarily Stable Strategyfor this species by assigning arbitrary point values to the outcomes. Let’s say that being injured is -100 points, wasting time on a lengthy contest is -10 points, and winning a contest (whether fighting or bluffing) is worth +50 points. In a more realistic model the numbers would be based on a huge number of factors, but this arbitrary setup will do as an example.

Running the Numbers

At a glance, it would seem that the Evolutionarily Stable Strategy is for every member of the species to be a bluffer. Each contest between two bluffers, or peaceful individuals, would then result in each member losing 10 points due to wasting time; however, the winner would also gain 50 points, for a total gain of 40. Neither one would suffer the penalty for being injured, because such a contest wouldn’t turn to violence. 

Assuming that each creature has a 50/50 chance of winning any given contest, all members of the species would gain an average of 15 points per contest—50 points for winning one, minus 20 for the cost of engaging in two contests, divided by two. This is the best possible outcome for the entire population.

(Shortform note: For a real-world example of a bluffing contest, think about two dogs meeting: They may stare each other down, bare their teeth, and growl, but it would be very unusual for them to immediately start fighting. Each is trying to get the other to back down.)

However, this all-bluffing strategy could only work if evolution existed for the good of the species, rather than the individual. This is because a single selfish individual could easily take advantage of the situation.

In a population of bluffers, a single fighter would win the full 50 points for every contest it participates in, making it vastly more successful than its bluffing counterparts. Plus, it would only be a matter of time before a mutant or deviant member of the population became a fighter and began spreading that strategy through its offspring. Therefore, while having everyone be a bluffer is the best strategy, it is not the stable strategy. 

Having every member be a fighter would also be highly unstable, because every member of the population would lose an average of 25 points per contest. Assume again that each creature has a 50/50 chance of winning a fight. Then, in two fights you could expect it to win one (+50 points) and lose one (-100 points for being injured). -50 points across two fights averages out to -25 per fight. 

Right now it might seem like there isn’t a stable strategy; that the population is bound to oscillate between bluffers and fighters as the situation keeps changing. However, this hypothetical species can reach an equilibrium. 

After doing a lot of math, it turns out that the ideal composition for this arbitrary population is a 5:7 ratio of bluffers to fighters. The average gain from a contest in that population is 6.25 for fighters and bluffers alike. While that’s clearly much lower than the 15 average in a population of all bluffers, the population will be stable.

If, by chance, the number of fighters starts to increase, they will encounter and injure each other more often, so the bluffers will gain an advantage until equilibrium is restored. Similarly, if the number of bluffers happens to increase, fighters will gain an advantage until the population is back to that 5:7 ratio. 

The model works equally well if we assume that—instead of being a pure fighter or pure bluffer—every member of the population can act as either. As long as they perform those behaviors in the same 5:7 ratio, the population will be just as stable.

Is There a Conditional Evolutionarily Stable Strategy?

The previous model assumes that there are only two possible strategies, but in reality there are several others besides pure fighting and pure bluffing. For instance, a bully will act like a fighter unless the target fights back, in which case it runs like a bluffer. A retaliator is just the opposite—it acts like a bluffer unless it’s attacked, in which case it will fight back. A prober-retaliator usually acts like a retaliator, but will occasionally try to escalate the fight to see if its target runs. These are called conditional strategies: Strategies that depend on what the other creature does.

Interestingly, retaliation is the only strategy that, by itself, leads to a stable population. If two retaliators engage in a contest, it won’t escalate to a real fight. However, if a fighter emerges in a population of retaliators, it won’t be successful because every target will fight back. Prober-retaliator is almost, but not quite, as stable as true retaliation, simply because it leads to fights and injuries slightly more often. 

The retaliator strategy explains why so many animals engage in contests that aren’t true fights—they bluff unless their opponent tries to escalate to a real fight, in which case they fight back. A conditional Evolutionarily Stable Strategy may work.

Evolutionarily Stable Strategy and Game Theory

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  • Why organisms don't matter, only genes do
  • How all life forms begin with a replicating molecule
  • How species need to balance aggression and pacifism to survive

Rina Shah

An avid reader for as long as she can remember, Rina’s love for books began with The Boxcar Children. Her penchant for always having a book nearby has never faded, though her reading tastes have since evolved. Rina reads around 100 books every year, with a fairly even split between fiction and non-fiction. Her favorite genres are memoirs, public health, and locked room mysteries. As an attorney, Rina can’t help analyzing and deconstructing arguments in any book she reads.

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