When I cut, you choose method implies intransitivity

Makowski, Marcin; Piotrowski, Edward W.

doi:10.1016/j.physa.2014.05.074

Cited by 6 publications

(5 citation statements)

References 29 publications

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“…Concerning the crucial Aumann’s agreement theorem 25 , Khrennikov and Basieva 26 show how agents using a quantum probability system for decision-making can indeed agree to disagree even if they have common priors, and their posteriors for a given event are common knowledge. In addition, Lambert-Mogiliansky et al 27 show how violations of transitivity of preferences in observed choices emerge naturally when dealing with non-classical agents, in line with the works by Makowski et al 28 29 who analyze how an agent achieves the optimal outcome through a sequence of intransitive choices in a quantum-like context.…”

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confidence: 62%

Quantum stochastic walks on networks for decision-making

Martínez-Martínez

Sánchez-Burillo

2016

Sci Rep

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Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

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confidence: 62%

Quantum stochastic walks on networks for decision-making

Martínez-Martínez

Sánchez-Burillo

2016

Sci Rep

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“…It turns out that intransitive relevant strategies are not only characteristic of quantum models. In the paper [15] the offering player (nature) has been replaced by a rational player. In this game, both players (Cat 1 and Cat 2) divide the set of three foods according to the "I cut, you choose" method [39,40] (see Figure 1).…”

Section: Hugo Steinhaus Mentionsmentioning

confidence: 99%

“…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

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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.

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“…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

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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.

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When I cut, you choose method implies intransitivity

Cited by 6 publications

References 29 publications

Quantum stochastic walks on networks for decision-making

Quantum stochastic walks on networks for decision-making

Do Transitive Preferences Always Result in Indifferent Divisions?

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

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