  Allocation games are zero-sum games that model the distribution of resources
among multiple agents. In this paper, we explore the interplay between an
\textit{subjective identity} and its impact on notions of fairness in
allocation. The sense of identity in agents is known to lead to responsible
decision-making in non-cooperative, non-zero-sum games like Prisoners' Dilemma,
and is a desirable feature to add into agent models. However, when it comes to
allocation, the sense of identity can be shown to exacerbate inequities in
allocation, giving no rational incentive for agents to act fairly towards one
another. This lead us to introduce a sense of fairness as an innate
characteristic of autonomous agency. For this, we implement the well-known
Ultimatum Game between two agents, where their sense of identity association
and their sense of fairness are both varied. We study the points at which
agents find it no longer rational to identify with the other agent, and uphold
their sense of fairness, and vice versa. Such a study also helps us discern the
subtle difference between responsibility and fairness when it comes to
autonomous agency.
