Additional Complexities of Using the Hawk-Dove Game to explain Biodiversity
https://phys.org/news/2018-08-tackling-great-paradox-biodiversity-game.html
https://phys.org/news/2016-08-unbalance-nutrients-threatens-biodiversity.html#nRlv
https://arxiv.org/pdf/1711.00755.pdf
In the article “Tackling the Great Paradox of Biodiversity with Game Theory,” scientists suggested that a possible model for explaining the biodiversity of an environment, despite the limited number of resources, would be a well known Hawk-Dove game in which two animals can either choose the strategy of the hawk or the dove. Below is a possible payoff matrix for the Hawk-Dove game.
The article continued to generalize that this game can be used to describe how two species can survive from one resource, four species can survive from two resources, and so on. However, in the article “An Unbalance in Nutrients Threatens Plant Biodiversity” seems to offer contradictory evidence in which scientists actually added resources into an environment which in turn decreased the biodiversity. They concluded that an imbalance of resources favored a particular species that would come to dominate the environment causing the less-favored species to potentially die off. Therefore, can game theory still be used to explain the biodiversity paradox?
“Diversity, Stability, and Reproducibility in Stochastically Assembled Microbial Ecosystems” possibly provides an explanation not only as to why there is an even greater biodiversity in the real world than suggested in “Tackling the Great Paradox of Biodiversity with Game Theory”, but also for the contradiction above where increased resources decreased biodiversity. In regards to an even greater biodiversity, their model incorporated another factor in that when a species consumes a resource, it is not completely used and there is a metabolic byproduct which then becomes an additional resource for other species. Therefore in this model, resources are being added just like in the experiment described in “An Unbalance in Nutrients Threatens Plant Biodiversity”. However, the increased resources didn’t lead to decreased biodiversity, at least not in the long run. The mathematical model incorporating the metabolic byproduct showed that there were “extinction avalanches” where chain effects caused extinctions; however, in the long run it became relatively stable and diverse.
Through analyzing this hawk-dove game, one realizes that it is a multiple equilibria game. However, as a more realistic model, the payoffs could differ while still holding the general idea of the “aggressive strategy” (hawk) and “passive strategy” (dove). Differing the payoffs more closely models real-life situations because not all species value the same resource equally so their “payoff” of a resource differs. This can result in a game with no pure Nash equilibrium; hence the introduction of mixed strategies. In class we discussed the Matching Pennies game and realized that there is an additional element of randomization and an equilibrium can be reached through randomizing behavior through choosing a probability rather than a direct choice. The same idea can be applied to the game of resources in contributing to biodiversity. Since the players might not have a pure Nash equilibrium, mixed strategies are introduced creating a randomization factor. As a result, addition of resources, extinction of species, and other changes to the environment will change the game by changing the payoff matrix resulting in a possible initial decrease in biodiversity as shown in “An Unbalance in Nutrients Threatens Plant Biodiversity”, but then a new equilibrium is established which will lead to increased biodiversity and stability as suggested in “Diversity, Stability, and Reproducibility in Stochastically Assembled Microbial Ecosystems”. A possible reason why game theory as discussed in class cannot completely explain this biodiversity phenomenon is because we assumed complete information where all players understood the possible strategies and their payoffs in response to the other player. In actuality, species will have incomplete information which changes their behaviors as well. Regardless, game theory seems to provide a very solid foundation to explaining the biodiversity that arises from a limited-resource environment.