Evolutionary Game Theory Introduction
Evolutionary Game Theory takes the ideas of Game Theory and applies them to the world of biology. It helps us understand:
- How behaviors change over time through natural selection
- Why certain ways of acting become common in a group
The success of a strategy depends on the environment and on what other animals do!
It is useful in biology, economics, social sciences, and even in artificial intelligence. Let's dive into an example to see how Evolutionary Game Theory helps us understand strategic behavior in nature.
It is useful for studying biology, economics, and even Artificial Intelligence. Let's look at a famous example to see how it works.
Hawk-Dove Game
In this game the animals have two strategies:
Hawk Strategy
(aggressive)
Dove Strategy
(peaceful)
When two animals compete (for food or anything), they use one of those two strategies.
Here's what happens:
- Hawk vs. Hawk: Both fight and get hurt. They both lose "fitness points" (energy or health), costing them −2 each
- Hawk vs. Dove: The Hawk scares the Dove away. The Hawk wins the resource (+3 points) and the Dove gets 0, but stays safe
- Dove vs. Dove: They share! Each gets a small win of +1 point
Which strategy is better?
... think about it for a moment ...
Being a Hawk seems like a winning move because you get the most points against a Dove. But if everyone is a Hawk, everyone ends up injured and losing points!
We can look at their scores in a payoff table:
The success of each strategy depends on how many hawks and doves there are in the population.
Example: Calculating the Balance Between Hawks and Doves
Using the above payoff table, and
- p = the percent of Hawks
- 1 − p = the percent of Doves
A Hawk:
- meets a Hawk p of the time and loses 2 points
- meets a Dove 1 − p of the time and gains 3 points
A Dove:
- meets a Hawk p of the time and gets 0 points
- meets a Dove 1 − p of the time and gains 1 point
At the balance point, Hawks and Doves score the same:
3 − 5p = 1 − p
3 − 1 = 5p − p
2 = 4p
p = 1/2
So in our case, about half the animals will be aggressive and about half peaceful.
The "Self-Correcting" Nature:
If the Hawk population rises to 60% (p=0.6), the Hawk score becomes 3−5(0.6)=0, while the Dove score is 1−0.6=0.4.
Since Doves are now doing better, the number of Hawks will naturally decrease back toward 50%.
This is called a stable equilibrium!
This balance, where neither strategy is favored overall, leads to an evolutionary stable strategy (ESS) where both strategies coexist.
In biology, a Strategy is a behavior that's passed down through genes.
- It could be "always attack" (Hawk)
- It could be "always share" (Dove)
- Or it could be a mix, like "only attack if the other one does"
Evolutionary Stable Strategy (ESS)
An ESS is a strategy that, if used by most of the population, can't be taken over by any other strategy due to its stability.
In the Hawk-Dove game, nature finds a balance ... a mix of Hawks and Doves that works together to keep the group stable.
Simply put, any deviation from the ESS by a small amount will often result in a worse general outcome, heading things back toward the stability of the original strategy.
If the group moves away from this balance, natural selection pushes it back. It's like a self-adjusting system!
Example: Altruism in Nature
Imagine a group where animals can either be Selfish or Altruistic (helpful).
- Two Altruists help each other and both get 4 points
- If an Altruist meets a Selfish animal, the Altruist gets 0 and the Selfish one gets 6
- Two Selfish animals don't help at all and get 2 points each
Here's the table for this setup:
Even though being selfish might seem better for one individual, the population often settles into a mix.
These balances show why some animals are helpful to each other in the wild!
Continuing the Journey
This is just the start!
There's so much to learn about how animals, plants, and even bacteria interact using these "games."
Summary
Evolutionary Game Theory shows us that nature is like a giant, ongoing game.
Strategies aren't chosen by "thinking", they are chosen by survival.
If a behavior helps an animal survive and have babies, that strategy continues to the next generation.