  We analyze, using a dynamical systems approach, the replicator dynamics for
the asymmetric Hawk-Dove game in which there is a set of four pure strategies
with arbitrary payoffs. We give a full account of the equilibrium points and
their stability and derive the Nash equilibria. We also give a detailed account
of the local bifurcations that the system exhibits based on choices of the
typical Hawk-Dove parameters and . We also give details on the connections
between the results found in this work and those of the standard two-strategy
Hawk-Dove game. We conclude the paper with some examples of numerical
simulations that further illustrate some global behaviours of the system.
