A game-theoretic framework models boundedly rational interactions under scarcity. Agents interact with limited resources and cognitive biases stemming from power asymmetries. No hierarchy is imposed.
Hierarchy emerges anyway. Bias in interactions — not in rules, not in initial conditions, but in the interaction process itself — generates stable inequality patterns. The nonlinear dynamics reveal periods of stability alternating with rapid hierarchical shifts: long plateaus where the ranking barely changes, punctuated by cascading reorganizations.
The framework models the spectrum from extreme capitalism to egalitarianism by tuning a single parameter: the degree to which prior advantage amplifies interaction outcomes. Different redistribution mechanisms — social welfare versus universal basic income — produce qualitatively different trajectories through the hierarchy space.
The structural insight: you don't need structural inequality to produce persistent inequality. You need biased interaction. Two agents who are identical in every way except their interaction history will diverge because early advantages compound through the interaction mechanism itself.
This is distinct from preferential attachment, where the rich get richer through explicit size-dependent advantage. Here, the bias is in how the interaction plays out, not in who gets to interact. The hierarchy isn't designed. It precipitates — like a crystal forming from a supersaturated solution. The supersaturation is scarcity. The nucleation site is bias.