The multi-dimensional nature of social exclusion requires several perspectives in understanding its causes and consequences. Focus on the topic is largely centred around questions of material deprivation. However, as poverty and inequality are inextricably linked to questions of access and inclusion, a holistic approach is required. Consequently, we explore how imposed relational asymmetries which manifest as differences in the ability to exercise personal agency and in turn, engender wealth inequalities, affect social cooperation in future interactions. To do this, we generate wealth inequalities through two Prisoner's Dilemma games, where one party is excluded from participating in the determination of the outcomes of the game. The effects of this asymmetry in social participation on ex post cooperation is examined using a Public Goods game. We find that the presence of prior asymmetric influence in social decision-making subsequently reduces contributions to the public good, independent of endowment level. This reduction in social welfare is driven by the under-contribution from players who were excluded in prior social interactions. Simply put, the data shows that a history of social exclusion reduces subsequent public goods provision, independent of material inequality.