If you want a biological basis for the mating system then you have a couple of choices. If you want the males to be the determining force (male-male competition) there is typicaly some type of a harem structure where one male controls access to many females. The control is achieved by control of a resource (resource polygyny) which is typically territory. This territory can be large and be the territory contorlled by the male, or it can be small and something that the female needs for reproduction (think elephant seals and the beach masters). This will typically result in males fighting extensively for the best territory leaving the females little choice regarding their mates. There is also harem polygyny, where the males coerce females into their harems (sometimes quite forcefully) and defend their harems from all other males.
The more common aspect of mating is female choice where females chose the males with whom they will mate. The focus of the choice is generally associated with the extended phenotype, healthy males, or good genes. The extended phenotype would be the quality of the resources that the male can provide (an extension of his phenotype that the female finds enticing - in this case treasure, territory quality, etc) determines if a female will mate with the specific male. Look up bower birds (https://m.youtube.com/watch?v=MZFzH3dWsbA ) for a great example of this or the nuptial gifts of crane flies. In the healthy male example females judge the parasite or disease load of a male based on either morphological features or behaviors, and chooses the males least likely to infect her during courtship and mating. a classic example of this is the snood (https://en.m.wikipedia.org/wiki/Snood_(anatomy)) on the turkey. The length of the snood is highly correlated to the parasite burden found in the male. Choose the male with the longest snood and you choose the male least impacted by parasites. Parasites are an energy drain, so it is difficult to produce a large snood with a heavy parasite burden. Lastly females can chose males based on good genes. Under this model, females evaluate the quality of the male based on morphological or behavioral (less often behavioral) characteristics of the males. An example of this is the eye spots found on the tails feathers of male peacocks. Females prefer males with a greater area of eyespots, and the survival of chicks to adulthood are significantly greater for chicks born to fathers who have greater eyespot area. The pigments of the eyespots are very expensive to make biochemically, so a male that can make lots of eyespots must be a high quality male and likely to pass on those traits to your babies.
Last suggestion in my long-winded exposition is that the best territories are rarely the largest. The most dominant individuals will take the highest qualtity territories. Territory quality its typically related to the density of needed resources. The higher the density of the resources, the higher the quality of the territory. It takes significant time and energy to patrol territories. Thus, the dominant individual will first choose the area with the highest density of resources, which will often result in it being the smallest. They now spend the minimal amount of time patrolling their territory while gaining the maximum amount of resources.
Just some suggestions for how dragons are likely to behave based on what we see in the real world. Sorry for the lenght of the post, but behavioral ecology in particularly fascinating!
