Special Issue "Decision Making, Classical and Quantum Optimization Methods"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: 30 September 2021.

Special Issue Editors

Prof. Dr. Ewa Roszkowska
E-Mail Website
Guest Editor
Faculty of Economics and Finance, University of Bialystok, 15-062 Bialystok, Poland
Interests: negotiation; negotiation support; multicriteria decision making; fuzzy multicriteria decision making
Special Issues and Collections in MDPI journals
Prof. Dr. Marek Szopa
E-Mail Website
Guest Editor
Department of Operations Research College of Informatics and Communication University of Economics in Katowice Ul, Bogucicka 3, 40-287 Katowice, Poland
Interests: game theory; quantum games; matching markets; fair share; quantum communication; application of game theory to negotiation and decision making

Special Issue Information

Dear Colleagues,

The development of technology opens up new possibilities of using it to optimize decision making. Methods based on artificial intelligence and machine learning will in the future set the standards for optimization of decisions in key areas of the economy and human life.

Advances in quantum information processing also open up new opportunities. Quantum methods allow achieving new ways of strategy randomization and offer a classically unavailable level of information security.

The aim of the project is to explore various theoretical methods of decision optimization based both on the classical and quantum approach.

The scope of the project includes the development of tools and techniques to optimize decisions by:

  • A scoring system for negotiation analysis and building a negotiation template and its rating system that reflect the structure of the negotiation problem and the negotiator’s preferences;
  • Game theory and the application of fair-share and matching algorithms (Shapley, Roth);
  • Quantum game theory models to obtain more Pareto-efficient equilibria in interactive decision making;
  • Bayesian methods for decision optimization;
  • Entropy-based measures in machine learning;
  • Fuzzy multicriteria decision analysis.

Prof. Dr. Ewa Roszkowska
Prof. Dr. Marek Szopa
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • decision optimization
  • game theory
  • quantum game theory
  • negotiation
  • machine learning
  • Pareto efficiency

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:


Open AccessArticle
Efficiency of Classical and Quantum Games Equilibria
Entropy 2021, 23(5), 506; https://doi.org/10.3390/e23050506 - 22 Apr 2021
Viewed by 127
Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoners dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash [...] Read more.
Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoners dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert–Wilkens–Lewenstein formalism and the Frąckiewicz–Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counter-parts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied. Full article
(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

1. Title: Fuzzy representation of principal’s preferences in representative negotiations and its links to the agent’s decision-making profiles

Authors: Wachowicz Tomasz, Roszkowska Ewa, Piasecki Krzysztof

Abstract: The paper is focused on the problem of building the scoring systems by agents for their principals in the representative negotiations, where the agents may differ in their decision making profiles. We empirically verify how the information processing style may affect the way the agents interpret the preferential information provided to them by the principals and how they construct the scoring systems based on such information. To find a general representation of the principal’s preferences by agents from different mixes of cognitive styles we will apply the notion of the generalized fuzzy scoring system. In our study, the fuzzy numbers will be applied to aggregate the structure of the scoring systems suggested by various agents into one representation of such a scoring system describing reliably the group of agents of uniform cognitive style. The concordance of such generalized fuzzy scoring systems with the principal's preferences will also be tested to find, which agents of what decision-making style, if any, are most prone to assure the best representation of the principal's preferences in the future negotiation process.

2. Title: Shapley-based estimation of a company value – concept, algorithms and parameters

Authors: Jacek Mercik, Barbara Gładysz , Izabella Stach,Jochen Staudacher 

Abstract: The goodwill is assessed in many ways (e.g. stock exchange value, accounting value, replacement value, etc.) depending on the needs that such an assessment serves. None of the methods takes into account the full complexity of ownership dependencies in a given company. The owners of the company may, for example, also be owners or co-owners of other business entities with or without economic relations with the analyzed company. The aim of the article is to propose a new method of valuation of the company, taking into account its ownership relations with other companies. For this purpose, the concept of Shapley's value was used as the basis for assessing such dependent companies.

The proposed assessment of the company's market value meets, by definition, the conditions related to Shapley's value for cooperative games. The use of Shapley's value results from its universality. It should be noted, however, that there are many different modifications to this value in the literature (e.g. Banzhaf (1965, 1968), Coleman (1971), Rae (1969), Brams-Lake (1977), Deegan-Packel (1978), Holler (1982). ), Johnston (1978), Gehrlein-Fishburn (1986), Mercik, (2001), et al.). Their diversity is mainly related to the diversity of assumptions related to the coalition formation process and the assessment of the contribution of a given coalition participant to the entire system.

The proposed assessment of the value of both the market and the company requires (if it is to be a realistic method) solving the problem of Shapley value calculation algorithms for multi-argument cooperative games for large numbers of players. The paper presents proposals for such algorithms along with their computational complexity assessment and approximation proposals. We also test the stability of solutions to changing external parameters and the dynamics of connections in a given market.

Back to TopTop