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Palgrave Macmillan UK eBooks

Quantum-Like Type Indeterminacy: A Constructive Approach to Preferences à la Kahneman and Tversky

Ariane Lambert‐Mogiliansky

Published Jan 1, 2017• 2 citations
Publisher

Abstract

Develop an example with 2 DS mention result for 1 DS and commuting DS from ALMZZ and from measurable systems too. Write in words about cognitive dissonance. Dynamic decision making conceptual and some formal description on one page and end with game with QL-players as a generalization. Make the point in distinction with RUM and conditional preferences. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1057/978-1-137-49276-0_11

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Develop an example with 2 DS mention result for 1 DS and commuting DS from ALMZZ and from measurable systems too. Write in words about cognitive dissonance. Dynamic decision making conceptual and some formal description on one page and end with game with QL-players as a generalization. Make the point in distinction with RUM and conditional preferences. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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., realized, and not merely revealed) only when the action takes place. An agent is described by a state that is a superposition of potential types (or preferences or behaviors). This superposed state is projected (or "collapses") onto one of the possible behaviors at the time of the interaction. In addition to the main goal of modelling uncertainty of preferences that is not due to lack of information, this formalism seems to be adequate to describe widely observed phenomena of noncommutativity in patterns of behavior. We explore some implications of our approach in a comparison between classical and type indeterminate rational choice behavior. The potential of the approach is illustrated in two examples.
We develop a framework for the analysis of strategic interactions under the constructive preference perspective à la Kahneman and Tversky formalized in the Type Indeterminacy model. The players are modeled as systems subject to measurements and characterized by quantum-like uncertain preferences. The decision nodes are modeled as, possibly non-commuting, operators that measure preferences modulo strategic reasoning. We define a Hilbert space of types spanned by the players' eigentypes representing their potential preferences in different situations. We focus on pure strategy TI games of maximal information where all uncertainty stems from the intrinsic indeterminacy of preferences. We show that preferences evolve in a non-deterministic manner with actions along the play: they are endogenous to the interaction. We propose the notion of cashing-on-the-go to compute a player's utility, and the Type Indeterminate Nash Equilibrium as a solution concept relying on best-replies at the level of the eigentypes. We illustrate an example exhibiting the phenomenon of the manipulation of rivals' preferences.
We develop a basic framework encoding preference relations on the set of possible strategies in a quantum-like fashion. The Type Indeterminacy model introduces quantum-like uncertainty affecting preferences. The players are viewed as systems subject to measurements. The decision nodes are, possibly non-commuting, operators that measure preferences modulo strategic reasoning. We define a Hilbert space of types and focus on pure strategy TI games of maximal information. Preferences evolve in a non-deterministic manner with actions along the play: they are endogenous to the interaction. We propose the Type Indeterminate Nash Equilibrium as a solution concept relying on best-replies at the level of eigentypes.
1. IntroductionIl est aujourd’hui bien connu que les acteurs en situation de choix ou de décision se comportent quelquefois de manière apparemment irrationnelle, constat que l’on qualifie d’anomalies comportementales. Ces anomalies peuvent se manifester de différentes manières. Confronté aux mêmes possibilités, un agent peut, par exemple, faire un choix différent selon la manière dont le choix lui est présenté, ou selon le contexte dans lequel il est placé alors que les différents contextes ...
The authors present the theory of quantum measurements in a humanities friendly way. The most general process of decision-making is represented with the aid of the formalism of quantum apparatuses and instruments. This measurement formalism generalizes the standard one based on the von Neumann–Lüders projection postulate. Generalized quantum observables are mathematically represented as positive operator valued measures (POVMs) and state transformers resulting from the feedback of measurements to the states of systems that are given by quantum instruments. The quantum scheme of indirect measurements (a special realization of quantum instruments) is applied to model decision-making as resulting from the interaction between the belief and decision states. The authors analyze the specific features of quantum instruments which are important for cognitive and social applications. In particular, the state transformers given by quantum instruments are in general less invasive than the state projections. Thus quantum-like decision-making need not be viewed as a kind of state collapse. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.