Bees, Graphs and Equilibriums in Nature
Game theory isn’t restricted to human activities. It can also be found in nature, as we saw in class with the Hawk and Dove problem. Another notable example is Honey Bees. Honey Bees are extremely efficient in their social structure. Their hives are extremely interconnected and the bees work as a group to maintain them. They divide up the tasks like collecting pollen, feeding the larvae and making the wax for the hive. The bees’ efficiency is extremely important to humans as well. The bees are the most efficient form of pollination, which is crucial to the survival of crops and other plants. It is because of this that honey bees are studied frequently.
Identifying the queen can be done using a graph. We will make the nodes of this graph the different bees, not distinguishing the queen, and the edges will be the interactions between the different bees. Many worker bees’ jobs are to attend to the queen, which will cause them to have an edge between them and the queen. This means that the queen will be the bee that is connected to most bees.
The survival of a bee colony depends on the survival and health of its queen. Even though the queen bee is important, the bees will kill the previous queen at the point when she becomes inefficient. After doing this, they must pick the larva that has the best chance of becoming queen to condition into the role. (In reality there will be more chosen but to model this is simplified). The choice between the different larvae can be modeled with a Nash Equilibrium. There will be two larvae being compared, and the choices will be to choose or to not choose. The reward can be modeled as a measure of the predicted efficiency. When the Nash equilibrium is calculated, it will decide whether to pick entirely different larvae to look at when both are not chosen, pick one of the larvae, or pick both and let them fight to the death if they both survive.
While these models are greatly simplified to fit the material we have learned in class, the models explore how the material can be expanded to real life.
Sources:
https://scialert.net/fulltext/?doi=tasr.2011.1352.1359 (I didn’t end up talking about this one because it seems a lot more complicated than what we’re learning in class but it’s really cool to read. It’s about taking a model for the bee’s foraging patterns, assuming it’s a nash equilibrium with full information, then applying it to different scenarios)
https://www.orkin.com/stinging-pests/bees/honey-bee-queen
https://www.perfectbee.com/learn-about-bees/the-life-of-bees/the-role-of-the-worker-bee