Evolutionary Stable Strategies

Evolutionary stability is asking the question what strategies are stable under ongoing interaction and competition with others? As such it tells us something about the equilibrium to an evolutionary game

The concept of an Evolutionarily Stable Strategy(ESS) applies to evolutionary processes where agents adopt a strategy and then learn of its comparative success through its interaction with other agents in an evolutionary process. An ESS is a strategy such that any player adopting any different (mutant) strategy will do no better than the average of all other players, all of whom are playing the same ESS strategy.1
Because evolutionary games are dynamic, meaning that creatures’ strategies change over time, what is best for one creature to do often depends on what others are doing. It is legitimate for us to then ask, are there any strategies within a given game that are stable and resistant to invasion? In studying evolutionary games one thing that biologists and others have been particularly interested in is this idea of evolutionary stability, which are evolutionary games that lead to stable situations or points of stasis for contending strategies. Just as equilibrium is the central idea within static noncooperative games, the central idea in dynamic games is that of evolutionarily stable strategies, as those that will endure over time.2

Evolutionary Game

As an example, we can think about a population of seals that go out fishing every day. Hunting for fish is energy consuming and thus some seals may adopt a strategy of simply stealing the fish off those who have done the fishing. So if the whole population is fishing then if an individual mutant might be born that follows a defector strategy of stealing, it would then do well for itself because there is plenty of fishing happening. This successful defector strategy could then reproduce creating more defectors. At which point we might say that this defecting strategy is superior and will dominate. But of course, over time we will get a tragedy of the commons situation emerge as not enough seals are going out fishing. Stealing fish will become a less viable strategy to the point where they die out and those who go fishing may do well again. Thus the defector strategy is unstable, and likewise, the fishing strategy may also be unstable. What may be stable in this evolutionary game is some combination of both.
The Evolutionarily Stable Strategy is very much similar to Nash Equilibrium in classical Game Theory, with a number of additions. Nash Equilibrium is a game equilibrium where it is not rational for any player to deviate from their present strategy. An evolutionarily stable strategy here is a state of game dynamics where, in a very large population of competitors, another mutant strategy cannot successfully enter the population to disturb the existing dynamic.3 Indeed, in the modern view, equilibrium should be thought of as the limiting outcome of an unspecified learning or evolutionary process that unfolds over time. In this view, equilibrium is the end of the story of how strategic thinking, competition, optimization, and learning work, not the beginning or middle of a one-shot game.
Therefore, a successful stable strategy must have at least two characteristics. One, it must be effective against competitors when it is rare – so that it can enter the previous competing population and grow. Secondly, it must also be successful later when it has grown to a high proportion of the population – so that it can defend itself.This, in turn, means that the strategy must be successful when it contends with others exactly like itself. A stable strategy in an evolutionary game does not have to be unbeatable, it only has to be uninvadable and thus stable over time. A stable strategy is a strategy that when everyone is doing it no new mutant could arise which would do better, and thus we can expect a degree of stability.

Unstable Cycling

Unstable cycles are situations in games where no strategy evolves to become stable and the system continues to cycle through a given strategy set.

Of course, we don’t always get stable strategies emerge within evolutionary games. One of the simplest examples of this is the game rock-paper-scissors. The best strategy is to play a mixed random game, where one plays any of the three strategies one-third of the time. However in biology, many creatures are incapable of mixed behavior — they only exhibit one pure strategy. If the game is played only with the pure Rock, Paper and Scissors strategies the evolutionary game is dynamically unstable: Rock mutants can enter an all scissor population, but then – Paper mutants can take over an all Rock population, but then – Scissor mutants can take over an all Paper population – and so on.
Using experimental economic methods, scientists have used the Rock, Paper, Scissors game to test human social evolutionary dynamical behaviors in the laboratory. The social cyclic behaviors, predicted by evolutionary game theory, have been observed in various lab experiments. Likewise, it has been recorded within ecosystems, most notably within a particular type of lizard5 that can have three different forms, creating three different strategies, one of being aggressive, the other unaggressive and the third somewhat prudent. The overall situation corresponds to the Rock, Scissors, Paper game, creating a six-year population cycle as new mutants enter and become dominant before another strategy invades and so on.

1. (2017). Www2.warwick.ac.uk. Retrieved 14 May 2017, from http://www2.warwick.ac.uk/fac/soc/economics/staff/academic/ireland/ess.pdf

2. (2017). Www2.warwick.ac.uk. Retrieved 14 May 2017, from http://www2.warwick.ac.uk/fac/soc/economics/staff/academic/ireland/ess.pdf

3. (2017). Www2.warwick.ac.uk. Retrieved 14 May 2017, from https://www2.warwick.ac.uk/fac/cross_fac/complexity/study/msc_and_phd/co923/cooperation.pdf

4. Taylor, P. D. (1979). Evolutionarily Stable Strategies with Two Types of Players J. Appl. Prob. 16, 76-83.

5. Alonzo, S., & Sinervo, B. (2001). Mate choice games, context-dependent good genes, and genetic cycles in the side-blotched lizard, Uta stansburiana. Behavioral Ecology And Sociobiology, 49(2-3), 176-186. doi:10.1007/s002650000265