In this paper, we study a power control game over a collision channel. Each player has an energy state. When choosing a higher transmission power, the chances of a successful transmission (in the presence of other interference) increases at the cost of a larger decrease in the energy state of the battery. A central feature in these games is that of the limitation on battery life. Natural questions that arise concern the behavior of mobile users in the presence of interference. How should a mobile user behave given his initial energy state? We study this dynamic game when restricting to simple non dynamic strategies that consist on choosing a given power level that is maintained during the lifetime of the battery. We identify a surprising paradox which we call the Hawk and Dove resource abundance paradox.