Over the last half-century, myriad fruitful applications have been found for evolutionary game theory in computational research. One such application is running game theoretic simulations as a method of uncovering theoretical “minimal conditions” for unfairness to arise in populations of agents, with the intent of analogizing these computational results to actual human contexts. Different models deploying different structural assumptions and using different parameters might uncover different minimal conditions, and there is rich potential for novel implementations to yield further results. In this dissertation, I build on existing work by others using such game theoretic simulations to run and analyze my own simulations. These simulations implement discrete populations of agents playing best responses, initially unstructured and later embedded into a lattice network. Agents in these populations play the Nash demand game with each other, communicating only through pre-play signalling regarding which of two groups, or “labels”, they belong to. In the process, I arrive at four different categories of findings. First, I find that in a networkless population, minor exogenous interventions into the initial conditions (including designating a small number of agents as “tyrants”) can be sufficient to consistently produce unfair outcomes. Second, when a population is embedded into a network, I find that asymmetries in how “far” groups are willing to go to play with other agents can be a minimal condition for unfairness, in favour of the group that is willing to go further. Third, and conversely, I find that when this same population is able to rearrange the network by changing places, the group that prefers playing with closer agents actually does better. Finally, I find that there is a tendency for emergent self-organization to occur, especially when one group has asymmetric ability to move, and conversely, there is little tendency for self-segregation within the simulation as designed. Many of these results appear to be parasitic on the Cultural Red King and Red Queen effects attested in prior research by others, while some are mechanically independent.