A model for a population-game with multiple asymmetry is studied, in which the participants are assumed to be different from one another both in size and in status as owners or non-owners of a territory. Only owners can reproduce, hence natural selection is assumed to operate in favor of the increase of ownership-time. Conditions for the evolutionary stability of the Bourgeois Principle of owner-priority, despite difference in body size, are characterized. It is shown that ownership-priority tends to be at least partially replaced by strength-priority as the availability of habitats, the expected longevity of potential intruders and the harm inflicted on the loser of an aggressive confrontation decrease, and as the expected longevity of the owner increases. It is further established that the combined effect of all these parameters can be characterized by a single parameter, referred to as the concord coefficient of the population. Finally, when this parameter reaches a certain critical level, only strength-priority can prevail. If the concord coefficient decreases below this critical level, no priority-rule can remain stable in the population, in which case aggressive confrontations cannot be avoided, at least in certain situations. In this case, it is shown that aggression emerges first among low-rank individuals.