abstract: Need-based transfers (NBTs) are a form of risk-pooling in which binary welfare exchanges occur to preserve the viable participation of individuals in an economy, e.g. reciprocal gifting of cattle among East African herders or food sharing among vampire bats. With the broad goal of better understanding the mathematics of such binary welfare and risk pooling, agent-based simulations are conducted to explore socially optimal transfer policies and sharing network structures, kinetic exchange models that utilize tools from the kinetic theory of gas dynamics are utilized to characterize the wealth distribution of an NBT economy, and a variant of repeated prisoner’s dilemma is analyzed to determine whether and why individuals would participate in such a system of reciprocal altruism. From agent-based simulation and kinetic exchange models, it is found that regressive NBT wealth redistribution acts as a cutting stock optimization heuristic that most efficiently matches deficits to surpluses to improve short-term survival; however, progressive redistribution leads to a wealth distribution that is more stable in volatile environments and therefore is optimal for long-term survival. Homogeneous sharing networks with low variance in degree are found to be ideal for maintaining community viability as the burden and benefit of NBTs is equally shared. Also, phrasing NBTs as a survivor’s dilemma reveals parameter regions where the repeated game becomes equivalent to a stag hunt or harmony game, and thus where cooperation is evolutionarily stable. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2018