Animals use a wide variety of strategies to reduce or avoid aggression in conflicts over resources. These strategies range from sharing resources without outward signs of conflict to the development of dominance hierarchies, in which initial fighting is followed by the submission of subordinates. Although models have been developed to analyse specific strategies for resolving conflicts over resources, little work has focused on trying to understand why particular strategies are more likely to arise in certain situations. In this paper, we use a model based on an iterated Hawk–Dove game to analyse how resource holding potentials (RHPs) and other factors affect whether sharing, dominance relationships, or other behaviours are evolutionarily stable. We find through extensive numerical simulations that sharing is stable only when the cost of fighting is low and the animals in a contest have similar RHPs, whereas dominance relationships are stable in most other situations. We also explore what happens when animals are unable to assess each other’s RHPs without fighting, and we compare a range of strategies for contestants using simulations. We find (1) that the most successful strategies involve a limited period of assessment followed by a stable relationship in which fights are avoided and (2) that the duration of assessment depends both on the costliness of fighting and on the difference between the animals’ RHPs. Along with our direct work on modelling and simulations, we develop extensive software to facilitate further testing. It is available at https://bitbucket.org/CameronLHall/dominancesharingassessmentmatlab/.