Transitivity of an entangled choice

Makowski, Marcin; Piotrowski, Edward W.

doi:10.1088/1751-8113/44/7/075301

Cited by 11 publications

(9 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper considers a simple model of a repeated game in which, at each stage, both players divide between themselves a set consisting of three goods. With reference to the earlier results [10][11][12][13][14][15] influenced by the remarks of Hugo Steinhaus [16], the players are referred to as "cats" and goods are referred to as "foods". The main goal of our analysis is to examine how the rules of the game affect the type of optimal strategies for the players (whether they are transitive or intransitive).…”

Section: Introductionmentioning

confidence: 99%

Do Transitive Preferences Always Result in Indifferent Divisions?

Makowski

Piotrowski

Sładkowski

2015

Entropy

Self Cite

View full text Add to dashboard Cite

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with the rationality of choice and is considered useful in building rankings. Intransitive preferences are considered paradoxical and undesirable. This problem is discussed by many social and natural scientists. A simple model of a sequential game in which two players choose one of the two elements in each iteration is discussed in this paper. The players make their decisions in different contexts defined by the rules of the game. It appears that the optimal strategy of one of the players can only be intransitive (the so-called relevant intransitive strategy)! On the other hand, the optimal strategy for the second player can be either transitive or intransitive. A quantum model of the game using pure one-qubit strategies is considered. In this model, an increase in the importance of intransitive strategies is observed: there is a certain course of the game where intransitive strategies are the only optimal strategies for both players. The study of decision-making models using quantum information theory tools may shed some new light on the understanding of mechanisms that drive the formation of types of preferences.

show abstract

Section: Introductionmentioning

confidence: 99%

Do Transitive Preferences Always Result in Indifferent Divisions?

Makowski

Piotrowski

Sładkowski

2015

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, it is worthwhile mentioning that applications of quantum games in cognitive science have been generalized to contextuality scenarios (e.g. [44][45][46][47]), in which intransitive and transitive preferences have been studied. In fact, the bistable framework exhibits some potential to model contextuality [29] and future work will be directed to the modelling of contextuality in games.…”

Section: Discussionmentioning

confidence: 99%

Bistable probabilities: a unified framework for studying rationality and irrationality in classical and quantum games

et al. 2020

View full text Add to dashboard Cite

This article presents a unified probabilistic framework that allows both rational and irrational decision-making to be theoretically investigated and simulated in classical and quantum games. Rational choice theory is a basic component of game-theoretic models, which assumes that a decision-maker chooses the best action according to their preferences. In this article, we define irrationality as a deviation from a rational choice. Bistable probabilities are proposed as a principled and straightforward means for modelling (ir)rational decision-making in games. Bistable variants of classical and quantum Prisoner’s Dilemma, Stag Hunt and Chicken are analysed in order to assess the effect of (ir)rationality on agent utility and Nash equilibria. It was found that up to three Nash equilibria exist for all three classical bistable games and maximal utility was attained when agents were rational. Up to three Nash equilibria exist for all three quantum bistable games; however, utility was shown to increase according to higher levels of agent irrationality.

show abstract

“…Nevertheless, there occur several choice situations where time transitivity may be violated even in a probabilistic form. Then one says that there is dynamic preference intransitivity [ 114 , 115 , 116 , 117 , 118 , 119 , 120 ].…”

Section: Dynamic Preference Intransitivitymentioning

confidence: 99%

Evolutionary Processes in Quantum Decision Theory

Yukalov

2020

Entropy

View full text Add to dashboard Cite

The review presents the basics of quantum decision theory, with an emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. How an operationally-testable, rational choice between alternatives differs from a choice decorated by irrational feelings is elucidated. Quantum-classical correspondence is emphasized. A model of quantum intelligence network is described. Dynamic inconsistencies are shown to be resolved in the frame of the quantum decision theory.

show abstract

Transitivity of an entangled choice

Cited by 11 publications

References 30 publications

Do Transitive Preferences Always Result in Indifferent Divisions?

Do Transitive Preferences Always Result in Indifferent Divisions?

Bistable probabilities: a unified framework for studying rationality and irrationality in classical and quantum games

Evolutionary Processes in Quantum Decision Theory

Contact Info

Product

Resources

About