Can Game Theory be Applied to Evolution?
Introduction
Throughout this course we’ve explored many topics directly and indirectly related to game theory, trying to find different fields where game theory can either be applied for efficiency, or theorizing how game theory could have been applied to find a better or more efficient solution. However while researching different potential topics for this blog, I found one that could possibly be the most influential and fundamentally important which is evolution.
Evolutionary Game Theory
Evolutionary game theory has been a long studied topic and was believed to first stem from biology, with the initial concept of evolutionary stable strategy. This was first introduced by Maynard Smith and Price and developed further by Maynard Smith. They go as far to suggest that evolutionary stability is potentially as important to evolutionary theory as Darwin was.
As always, the underlying premise can be simplified to a game focused around a large population that are repeatedly matched in pairs to play. There are some simple ground rules for the game, specifically that regardless of the identities of the players the payoffs for certain strategies are static. Also players cannot make decisions based off of external factors, the only goal is to obtain the highest payoff since that is the metric which natural selection is favoring in our example. This idea is just a premise for natural evolution and many more specific games stemmed from this basic premise.
With this process, we can envision a repeat basic scenario where the population has a “common” strategy that has been developed and is working consistently. In the event that a new “mutant” strategy appears, there are two branching scenarios. Either the common strategy has a higher payoff, and the mutant strategy will naturally be eliminated. Or the opposite, and the common strategy will shrink and eventually be eliminated. With this idea we can also reach some Nash equilibria, i.e. some strategies that fare as well as the common strategy which is the candidate for evolutionary stability.
The Hawk-Dove Game
A common interpretation for evolutionary stability is the Hawk-Dove game introduced by Maynard Smith. In the game, both players want to contest a necessary resource ‘V’. In the case where one player is aggressive and the other is not, the former would get the entirety of V and the latter would get nothing. If both choose to be non aggressive they split the V, and if both choose to be aggressive they split the V, but incur an injury C with the restriction that C > V. This means they will both suffer a net loss of V. This game eventually boils down to a stable strategy which is a mixed strategy where Hawk is played with the probability of (V/C)^2.
The interesting idea here is that the same evolutionary stable outcome can be arrived at from similar population configurations. This is known as the replicator dynamic. Basically implicating that the amount of people using a given strategy will grow at a rate qual to the difference between the average payoff of that strategy and the average payoff of the population (people converge to the better strategy naturally) this can be better understood if the payoff is more related to natural reproduction than simply vital resources. For example, if we have a case where V/C percentage of the players play hawk, this will result in an evolutionary stable strategy however instead of every player having a mixed strategy relying on probability, we have a portion of the population playing hawk (V/C) and a portion playing Dove (1 – V/C). This will also lead to a very similar end state but derived from very different evolutionary strategies.
Conclusion
There are many more examples where game theory and our understanding of Nash Equilibrium can be applied to genetics and natural selection. This can help us to greatly better understand the overarching systems in nature, or even simply thinking of something that we’ve overlooked for generations in a new light. Some other interesting examples are the joint venture game, as well as the coordination game which both have their own intricacies to be analyzed.
Sources
https://pubs.aeaweb.org/doi/pdfplus/10.1257/0895330027256
https://physics.mcmaster.ca/~higgsp/756/WarOfAttrition.pdf
2 replies on “Can Game Theory be Applied to Evolution?”
I find this very interesting since I have never looked at evolution this way. This gives a completely different view of what evolution means and what “survival of the fittest” means. I have never thought of it as a game where the mutant “strategy” could have a higher payoff than the common payoff, which would result in majority of the population “playing” the mutant strately.
It is very interesting how a simple concept like nash equilibrium can be used in a vast array of fields and help us get a quick idea. For example any relationship between species based on how they act on situations such as sharing resource and actions stemming from the results of it can be explained clearly but using nash equilibrium we also see the reasons and why one chooses it. It’s such an interesting tool to explain evolution.