  The introduction of concepts of Game Theory and Ordinary Differential
Equations into Biology gave birth to the field of Evolutionary Stable
Strategies, with applications in Biology, Genetics, Politics, Economics and
others. In special, the model composed by two players having two pure
strategies each results in a planar cubic vector field with an invariant
octothorpe. Therefore, in this paper we study such class of vector fields,
suggesting the notion of genericity and providing the global phase portraits of
the generic systems with a singularity at the central region of the octothorpe.
