Queens of the honey bee, Apis mellifera (L.), exhibit extreme polyandry, mating with up to forty-five different males (drones). This increases the genetic diversity of their colonies and consequently their fitness. After copulation, drones leave a mating sign in the genital opening of the queen which has been shown to promote additional mating of the queen. On one hand, this signing behavior is beneficial for the drone because it increases the genetic diversity of the resulting colony. On the other hand, it decreases the proportion of the drone's personal offspring among colony members which is detrimental to the drone. We analyze the adaptiveness and evolutionary stability of this drone's behavior with a game-theoretical model. We find that theoretically both the strategy of leaving a mating sign and the strategy of not leaving a mating sign can be evolutionary stable, depending on natural parameters. However, for most scenarios, including all biologically plausible ones, based on empirical data the signing strategy is not favored. We conclude that leaving a sign is not in the interest of the drone unless it serves biological functions other than increasing subsequent queen mating chances.