This paper studies a power control game over a collision channel. Each player has an energy state and balances energy conservation and transmission success. When opting for higher transmission power, the chances of a successful transmission in the presence of interference increases at the cost of a larger drop in energy. We study this dynamic game when restricting to simple non-dynamic strategies: a power level is chosen at start-up and maintained during the lifetime of the battery. A thorough analysis of the existence and characterization of the equilibria of this evolutionary Hawk-Dove game is conducted. Moreover, we study the stability of our results under various classes of evolutionary dynamics, including replicator dynamics and Brown-von Neumann-Nash (BNN) dynamics and identify various surprising paradoxes. Simulation results validate our theoretical claims.