Semi-dynamic Hawk and Dove game, applied to power control

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 chance 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. We study this dynamic game when restricting to simple non-dynamic strategies that consist of choosing a given power level that is maintained during the lifetime of the battery. We identify a surprising paradox in our Hawk-Dove game which we term the initial energy paradox.