Quadratic State-Dependent Utility Model for Decision-Making under Cognitive and Affective Constraints

This paper proposes a formally tractable extension of the standard utility framework in which preferences depend on endogenous decision-relevant states. We introduce a five-dimensional state vector incorporating material consumption \(\:\left(C\right)\) alongside bounded rationality \(\:\left(R\right)\), affective state \(\:\left(E\right)\), contextual valuation \(\:\left(A\right)\), and idiosyncratic preference components \(\:\left(F\right)\). Preferences are represented by a quadratic utility function with interpretable interaction effects, preserving scalar maximisation and standard concavity conditions while allowing for amplification, attenuation, and substitution mechanisms across cognitive and affective dimensions. The model provides a unified decision-theoretic representation of how internal states modulate marginal evaluation and choice without violating global concavity. We derive conditions under which affective states interact with rational deliberation in a stable manner, and we show how interactions among \(\:(R,E,A,F)\) generate state-dependent valuation patterns consistent with framing and context effects. A numerical illustration and a simulation of the \(\:R\)–\(\:E\) interaction space highlight the analytical flexibility of the framework. The proposed representation is intended as a general tool for decision theory, offering a basis for comparative statics, experimental design, and future empirical implementation of state-dependent preferences under cognitive and affective constraints. JEL classification: D01, D87, D91, C02.