Related papers: Dynamic consistency of expected utility under non-…
The cognitive state of mind concerning a range of choices to be made can effectively be modelled in terms of an element of a high-dimensional Hilbert space. The dynamics of the state of mind resulting form information acquisition is…
The ideas about decision making under ignorance in economics are combined with the ideas about uncertainty representation in computer science. The combination sheds new light on the question of how artificial agents can act in a dynamically…
We present the mathematical model of decision making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioral, and geo-political factors). To describe interaction of agents…
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…
In the present article we use the quantum formalism to describe the effects of risk and ambiguity in decision theory. The main idea is that the probabilities in the classic theory of expected utility are estimated probabilities, and thus do…
The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion…
We formulate and prove an Agreement Theorem for quantum mechanics (QM), describing when two agents, represented by separate laboratories, can or cannot maintain differing probability estimates of a shared quantum property of interest.…
In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach…
This paper delves into recent advancements in Quantum Reinforcement Learning (QRL), particularly focusing on non-commutative environments, which represent uncharted territory in this field. Our research endeavors to redefine the boundaries…
In their target article, \citet{WangBusemeyer13} [A quantum question order model supported by empirical tests of an a priori and precise prediction. \emph{Topics in Cognitive Science}] discuss question order effects in terms of incompatible…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
In this paper we propose to use elements of the mathematical formalism of Quantum Mechanics to capture the idea that agents' preferences, in addition to being typically uncertain, can also be indeterminate. They are determined (i.e.,…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
We consider a family of conditional nonlinear expectations defined on the space of bounded random variables and indexed by the class of all the sub-sigma-algebras of a given underlying sigma-algebra. We show that if this family satisfies a…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…
Expected Utility: Algebraic Expected Utility In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von Neumann-Morgenstern setting, i.e. uncertainty…
In this paper we extend Savage's theory of decision-making under uncertainty from a classical environment into a non-classical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and…
Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several…
{\it Ellsberg thought experiments} and empirical confirmation of Ellsberg preferences pose serious challenges to {\it subjective expected utility theory} (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions…