Finite-Capacity Prospect Theory: State-Dependent Risk Preferences under Resource, Attention, and Boundary-Risk Constraints

This paper develops a state-dependent version of Prospect Theory in which loss aversion, reference adaptation, and probability weighting vary with resource buffers, attention constraints, and boundary-risk context. Prospect Theory is usually treated as a descriptive account of deviations from expected-utility rationality. This paper proposes a finite-capacity bridge model: bounded agents operating under scarcity, limited attention, finite memory, and finite update capacity should exhibit state-dependent risk preferences. The model introduces a vector-valued resource buffer, perceived distance to a constraint threshold, event-class-dependent probability weighting, and a nudge-bandwidth model. It predicts that loss aversion should rise under scarcity and downside exposure, reference baselines should adapt more slowly under depletion, and probability weighting should become more distorted for low-capacity agents and boundary-relevant rare events. The paper includes deterministic synthetic simulations and a replication package, but does not fit human-subject data. It is intended as a theoretical working paper and empirical identification framework for future tests of state-dependent Prospect Theory.