We present a variety of issues in modern economics where applied mathematics is needed. These include economic equilibrium prob- lem where Oxed point theory for Markov operators, and for ordered sets is needed; the emergent Oeld of behavioral economics (Nobel Memorial Prize in Economics 2017) where more mathematical research is needed, for ex- ample, to capture cognitive decision-making, a§ecting economic data, and hence econometric modeling processes. We will focus on a promising venue, namely, quantum probability as a measure of uncertainty, since, unlike Kol- mogorov probability, quantum probability, borrowed from quantum physics, is non-additive and non-commutative, thus avoiding Ellsbergis paradox (of von Neumannis expected utility) and capturing order e§ects of human judge- ments, respectively. Evoking the development of the framework of quantum probability as behavioral probability, as well as a quantum stochastic calculus for, say, Onancial econometrics, we will discuss various important mathemati
We present a variety of issues in modern economics where applied mathematics is needed. These include economic equilibrium prob- lem where Oxed point theory for Markov operators, and for ordered sets is needed; the emergent Oeld of behavioral economics (Nobel Memorial Prize in Economics 2017) where more mathematical research is needed, for ex- ample, to capture cognitive decision-making, a§ecting economic data, and hence econometric modeling processes. We will focus on a promising venue, namely, quantum probability as a measure of uncertainty, since, unlike Kol- mogorov probability, quantum probability, borrowed from quantum physics, is non-additive and non-commutative, thus avoiding Ellsbergis paradox (of von Neumannis expected utility) and capturing order e§ects of human judge- ments, respectively. Evoking the development of the framework of quantum probability as behavioral probability, as well as a quantum stochastic calculus for, say, Onancial econometrics, we will discuss various important mathemati
We present a variety of issues in modern economics where applied mathematics is needed. These include economic equilibrium prob- lem where Öxed point theory for Markov operators, and for ordered sets is needed; the emergent Öeld of behavioral economics (Nobel Memorial Prize in Economics 2017) where more mathematical research is needed, for ex- ample, to capture cognitive decision-making, a§ecting economic data, and hence econometric modeling processes. We will focus on a promising venue, namely, quantum probability as a measure of uncertainty, since, unlike Kol- mogorov probability, quantum probability, borrowed from quantum physics, is non-additive and non-commutative, thus avoiding Ellsbergís paradox (of von Neumannís expected utility) and capturing order e§ects of human judge- ments, respectively. Evoking the development of the framework of quantum probability as behavioral probability, as well as a quantum stochastic calculus for, say, Önancial econometrics, we will discuss various important mathemati
Abstract Foundations of Quantum Economics unfolds a coherent theoretical thread, replacing the rational-agent premise of mainstream economics with the quantum-person hypothesis: before observation, decision-makers sustain multiple conflicting options encoded in probability amplitudes, and a decision corresponds to collapse triggered by measurement. The book first lays cognitive and mathematical foundations, demonstrating that human judgement inherently exhibits quantum features including superposition, interference and order dependence. Classical probability theory fails for non-commutative economic events, making Hilbert spaces and probability amplitudes indispensable languages for economic inquiry. It then reconstructs causality, information, uncertainty and risk, arguing that economic causes are not uniquely fixed before the collapse of consensus; uncertainty is endogenous to the system, and risk represents the spread of superposed distributions rather than exogenous noise. Built upon this architecture, the work revisits core microeconomic notions such as value, utility, game interaction, supply and demand, property rights, institutions and innovation. All conventional theories are recovered as special limits under zero interference and single eigenstates, while superposition and entanglement furnish fresh explanatory power for economic anomalies. The analysis further expands into macroeconomics, interpreting growth, business cycles, money, fiscal policy, trade and welfare as coherent superposition, phase transition and collapse of collective cognition and consensus, and concludes with the renovation of econometrics and economic governance. The book’s central thesis holds that superposition, interference, observation and collapse are not metaphors borrowed from quantum physics, but intrinsic properties of human cognition and economic practice. Economic realities are not predetermined facts waiting to be discovered; instead, they are generated through human cognition, consensus and practice in the act of measurement. Quantum economics is far more than a cosmetic revision of existing models. It constitutes a shift of research programme, abandoning Laplacian determinism and reconceiving the economy as an open, generative process. The book articulates five interconnected layers: the quantum person as ontological starting point, quantum features of cognition, superposition of collective consensus, endogenous uncertainty, and quantuminformed governance. It reminds researchers and policymakers that economic observation and policy intervention are performative, capable of reshaping the very system they examine. Economics abandons the pursuit of a single, determinate optimum and embraces endogenous uncertainty; policymakers cease to be omniscient system engineers and become prudent stewards of consensus and designers of measurement bases. This volume establishes the unified bedrock for the whole quantum economics series and calls for a new, more honest and realistic economics embedded within the economic process itself.
The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance has produced valuable results. The principal movement which has steered this research direction is known under the name of `econophysics'. In this paper, we illustrate and advance some of the findings that have been obtained by applying the mathematical formalism of quantum mechanics to model human decision making under `uncertainty' in behavioral economics and finance. Starting from Ellsberg's seminal article, decision making situations have been experimentally verified where the application of Kolmogorovian probability in the formulation of expected utility is problematic. Those probability measures which by necessity must situate themselves in Hilbert space (such as `quantum probability') enable a faithful representation of experimental data. We thus provide an explanation for the effectiveness of the mathematical framework of quantum mechanics in the modeling of human decision making. We want to be explicit though that we are not claiming that decision making has microscopic quantum mechanical features.
Since its emergence in the 1970s, behavioral economics has integrated psychological insights into economics—drawing on Kahneman and Tversky's prospect theory, Thaler's psychological accounting and boost theory, and Schiller's behavioral finance—thereby dismantling the myth of the "homo economicus" and revealing systematic cognitive biases inherent to human decision-making. However, classical behavioral economics has been constructed from a collection of fragmented "effects" and "biases," lacking a unified, axiomatic mathematical framework; moreover, the frequent practice among researchers to selectively apply individual effects has undermined the discipline's predictive power and theoretical coherence. This book is the first academic monograph in the world to systematically expound on quantum behavioral economics—a new paradigm devised specifically to overcome this fundamental dilemma. It introduces concepts such as Hilbert spaces, state vectors, superposition, entanglement, measurement collapse, quantum probability, interference effects, unitary evolution, decoherence, non-commutative observables, and quantum phase transitions into the foundational bedrock of behavioral economics: that preferences and beliefs coexist in a superposition prior to decision-making; that decision-making consists of constructing measurements to extract definite preferences via measurement collapse; and that the beliefs and behaviors of individuals are entangled, exhibiting non-local quantum correlations. Furthermore, it posits that the sequence in which information is presented and the framing effects are intrinsic properties of quantum decision-making—rather than mere "biases." This book comprises six parts and thirty chapters: Part I, "Paradigm Revolution," establishes the philosophical foundations, the quantum subject hypothesis, and the analytical framework; Part II develops quantum probabilistic judgments, quantum heuristics, quantum prospect theory, quantum decision-making under uncertainty, and quantum framing effects; Part III explores quantum preferences, quantum utility, quantum choice theory, quantum endowment effects and loss aversion, as well as the current state of quantum research and default effects; Part IV extends the scope to quantum social preferences, quantum altruism, quantum trust and cooperation, quantum game theory, and quantum public goods games; Part V examines quantum intertemporal choice, quantum hyperbolic discounting, quantum self-control, quantum procrastination and addiction, and quantum habit formation and behavioral change across temporal dimensions; Part VI demonstrates the application of framing in finance, markets, public policy, and health domains, while offering insights into the future of this discipline. This work pursues three overarching objectives: theoretical unification and depth, originality and authority, and seamless readability. It is intended for graduate students, faculty, and researchers in behavioral economics, decision science, psychology, and finance, as well as for public policy makers and practitioners in financial markets to provide new paradigm-based analytical tools.
Since the beginning of the 21st century, a new interdisciplinary research movement has started, which aims at developing quantum math-like (or simply quantum-like) models to provide an explanation for a variety of socio-economic processes and human behaviour. By making use of mainly the probabilistic aspects of quantum theory, this research movement has led to many important results in the areas of decision-making and finance. In this article, we introduce a novel and more exhaustive approach, to analyze the socio-economic processes and activities, than the pure quantum math-like modelling approach, by taking into account the physical foundations of quantum theory. We also provide a plausibility argument for its exhaustiveness in terms of what we can expect from such an approach, when it is applied to, for example, a generic socio-economic decision process.
Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes.To overcome these difficulties, economists have introduced an interesting distinction between risk and ambiguity depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations.On the other hand, evidence of everyday life suggests that context plays a fundamental role in human decisions under uncertainty.Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework.In this paper we introduce the notion of contextual risk with the aim of modeling a substantial part of the situations in which usually only ambiguity is present.More precisely, we firstly introduce the essentials of an operational formalism called the hidden measurement approach in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts.Within the hidden measurement approach we propose a sphere model as a mathematical tool for situations in which contextual risk occurs.We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it.This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.