You go head-to-head with your arch nemesis to the only game that matters - rock, paper, scissors. With everything on the line, you would be wise to plan ahead and try to contemplate a winning strategy. Much to your horror, the strategy you came up with was no match for your opponent who only plays rock every turn!
Replicator dynamics is the subfield of evolutionary biology that frames how various species survive in a shared ecosystem and studies how their various strategies change over time. This approach turns out to be a very effective approach to modelling natural selection in ecosystems. At the same time, the resulting dynamics are increasingly complicated and chaotic as more and more species and strategies enter the ecosystem.
When the number of strategies in the ecosystem is less than or equal to three, the ways competing strategies play out over time are completely classified. In this project, we will explore how these results can be extended for four or more strategies in an ecosystem as well as the emergent chaos that comes with it. We will also try to understand how these models can be adapted if we account for other things besides natural selection.
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