Discovery of Economic Collusion by Metrics of Quantum Entanglement
Keywords:
collusion, cartel, decision making, quantum cognition, quantum entanglement, behavioral modeling, recommendation systemsAbstract
An effective economy requires prompt prevention of misconduct of legal entities. With the ever-increasing transaction rate, an important part of this work is finding market collusions based on statistics of electronic traces. We report a solution to this problem based on a quantum-theoretical approach to behavioral modeling. In particular, cognitive states of economic subjects are represented by complex-valued vectors in space formed by the basis of decision alternatives, while decision probabilities are defined by projections of these states to the corresponding directions. Coordination of multilateral behavior then corresponds to entanglement of the joint cognitive state, measured by standard metrics of quantum theory. A high score of these metrics indicates the likelihood of collusion between the considered subjects. The resulting method for collusion discovery was tested with open data on the participation of legal entities in public procurement between 2015 and 2020 available at the federal portal https://zakupki.gov.ru. Quantum models are built for about 80 thousand unique pairs and 10 million unique triples of agents in the obtained dataset. The reliability of collusion discovery was defined by comparison with open data of Federal antimonopoly service available at https://br.fas.gov.ru. The achieved performance allows the discovery of about one-half of known pairwise collusions with a reliability of more than 50%, which is comparable with detection based on classical correlation and mutual information. For three-sided behavior, in contrast, the quantum model is practically the only available option since classical measures are typically limited to the bilateral case. Half of such collusions are detected with a reliability of 40%. The obtained results indicate the efficiency of the quantum-probabilistic approach to modeling economic behavior. The developed metrics can be used as informative features in analytic systems and algorithms of machine learning for this field.
References
1. Ferguson A.G. Policing predictive policing. Washington University Law Review. 2017. vol. 94. no. 5. p. 1109.
2. Yang F. Oxford Research Encyclopedia of Criminology and Criminal Justice Oxford University Press. 2019. vol. 44. no. 1. pp. 57–61.
3. McDaniel J., Pease K. Predictive Policing and Artificial Intelligence Routledge, Taylor & Francis Group. 2021. 330 p.
4. Berk R. Artificial Intelligence, Predictive Policing, and Risk Assessment for Law Enforcement Annual Review of Criminology. 2021. vol. 4. no. 1. pp. 209–237.
5. Oficial’nyj sajt Federal’naja Antimonopol’naja sluzhba. Available at: fas.gov.ru (accessed: 09.2022). (In Russ.).
6. Yuriev R.N., Alodjants A.P. [The problem of collusion of bidders and ways to solve it in the framework of digital economics paradogms and by using quantum probability theory]. Sovremennaya nauka: aktualnye problemy teorii i praktiki – Modern Science: Actual Problems of Theory and Practice. Series: Natural and technical sciences. 2021. no. 10. pp. 139–149. (In Russ.).
7. Bajari P., Ye L. Deciding Between Competition and Collusion. Review of Economics and Statistics. 2003. vol. 85. no. 4. pp. 971–989.
8. Ballesteros-Perez P., Skitmore M., Das R., del Campo-Hitschfeld M. Quick Abnormal-Bid-Detection Method for Construction Contract Auctions. Journal of Construction Engineering and Management. 2015. vol. 141. no. 7. p. 04015010.
9. Huber M., Imhof D. Machine learning with screens for detecting bid-rigging cartels. International Journal of Industrial Organization. 2019. vol. 65. pp. 277–301.
10. Garcia Rodriguez M., Rodriguez-Montequin V., Ballesteros-Perez P., Love P., Signor R. Collusion detection in public procurement auctions with machine learning algorithms. Automation in Construction. 2022. vol. 133. p. 104047.
11. Nasledov A.D. Matematicheskie metody psihologicheskogo issledovanija. Analiz i interpretacija dannyh [Mathematical methods of psychological research. Data analysis and interpretation]. Rech’, 2004. p. 392. (In Russ.).
12. Harchenko M.A. Korreljacionnyj analiz [Correlation analysis]. VGU, 2008. 31p. (In Russ.).
13. Marchenko V.M., Mozhej N.P., Shinkevich E.A. Jekonometrika i jekonomiko- matematicheskie metody i modeli [Econometrics and economic-mathematical methods and models]. Minsk: BGTU, 2011. p. 157. (In Russ.).
14. Kremer N.Sh. Teorija verojatnostej i matematicheskaja statistika [Theory of Probability and Mathematical Statistics]. M: Yuniti. 2012. (In Russ.).
15. Killworth P., Russell H. Informant Accuracy in Social Network Data III: A Comparison of Triadic Structure in Behavioral and Cognitive Data. Social Networks. 1979. vol. 2. pp. 19–46.
16. Morgenstern O., Schwodiauer G. Competition and collusion in bilateral markets. Zeitschrift fur Nationalokonomie. 1976. vol. 36. no. 3–4. pp. 217–245.
17. Thomas C., Wilson B. A Comparison of Auctions and Multilateral Negotiations. The RAND Journal of Economics. 2002. vol. 33. no. 1. p. 140.
18. Uddin S., Hossain L. Dyad and Triad Census Analysis of Crisis Communication Network. Social Networking. 2013. vol. 2. no. 1. pp. 32–41.
19. Holland P., Leinhardt S. The Statistical Analysis of Local Structure in Social Networks. Sociological Methodology. 1974. p. 45.
20. Martean L. The Triangle and the Eye inside the Circle: Dyadic and Triadic Dynamics in the Group. Group Analysis. 2014. vol. 47. no. 1. pp. 42–61.
21. Razmi P., Oloomi Buygi M., Esmalifalak M. A Machine Learning Approach for Collusion Detection in Electricity Markets Based on Nash Equilibrium Theory. Group Analysis. vol. 9. no. 1. pp. 170–180.
22. Ball P. The physical modelling of society: a historical perspective. Physica A: Statistical Mechanics and its Applications. 2002. vol. 314. no. 1–4. pp. 1–14.
23. Jorion P. Accounting for human activity through physics. Cybernetics and Systems. 2004. vol. 35. no. 2–3. pp. 275–284.
24. Galam S. Sociophysics. A Physicist’s Modeling of Psycho-political Phenomena Boston, MA: Springer US. 2012. p. 439.
25. Maldonado C. Quantum Theory and the Social Sciences Momento. 2019. no. 59E. pp. 34–47.
26. Meghdadi A., Akbarzadeh-T., Javidan K. A Quantum-Like Model for Predicting Human Decisions in the Entangled Social Systems IEEE Transactions on Cybernetics. pp. 1–11.
27. Meyer D.A. Quantum Strategies. Physical Review Letters. 1999. vol. 82. no. 5. pp. 1052–1055.
28. Eisert J., Wilkens M., Lewenstein M. Quantum Games and Quantum Strategies. Physical Review Letters. 1999. vol. 83. no. 15. pp. 3077–3080.
29. Marinatto L., Weber T. A quantum approach to static games of complete information. Physics Letters A. 2000. vol. 272. pp. 291–303.
30. Yukalov V., Yukalova E., Sornette D. Role of collective information in networks of quantum operating agents. Physica A. 2022. vol. 598. p. 127365.
31. Pothos E., Perry G., Corr P., Matthew M., Busemeyer J. Understanding cooperation in the Prisoner’s Dilemma game. Personality and Individual Differences. vol. 51. no. 3. pp. 210–215.
32. Pelosse Y. The Intrinsic Quantum Nature of Nash Equilibrium Mixtures. Journal of Philosophical Logic. 2016. vol. 45. no. 1. pp. 25–64.
33. Baatique B.E. Quantum finance. Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge. 1998.
34. Khrennikov A. Quantum-psychological model of the stock market Problems and Perspectives in Management. 2003. pp. 136–148.
35. Bagarello F. Stock markets and quantum dynamics: A second quantized description. Physica A: Statistical Mechanics and its Applications. 2007. vol. 386. no. 1. pp. 283–302.
36. Choustova O. Quantum probability and financial market Information Sciences. 2009. vol. no. 5. pp. 478–484.
37. Goncalves C.P. Quantum financial economics – risk and returns Journal of Systems Science and Complexity. 2013. vol. 26. no. 2. pp. 187–200.
38. Tahmasebi F., Meskinimood S., Namaki A., Vasheghani Farahani S., Jalalzadeh S., Jafari G. Financial market images: A practical approach owing to the secret quantum potential. EPL (Europhysics Letters). 2015. vol. 109. no. 3. p. 30001.
39. Orrell D. A quantum model of supply and demand Physica A: Statistical Mechanics and its Applications. 2020. vol. 539. p. 122928.
40. Athalye V., Haven E. Socio-Economic Sciences: Beyond Quantum Math-like Formalisms Quantum Reports. 2021. vol. 3. no. 4. pp. 656–663.
41. Khrennikov A. Social laser model: from color revolutions to Brexit and election of Donald Trump Kybernetes. 2018. vol. 47. no. 2. pp. 273–288.
42. Tsarev D., Trofimova A., Alodjants, A., Khrennikov A. Phase transitions, collective emotions and decision-making problem in heterogeneous social systems Scientific Reports. 2019. vol. 9. no. 1. p. 18039.
43. Alodjants A., Bazhenov A., Khrennikov A., Bukhanovsky A. Mean-field theory of social laser Scientific Reports. 2022. vol. 12. no. 1. p. 8566.
44. Slovohotov Ju.L. [Physics and sociophysics. Part 2. Networks of social interactions. Econophysics]. Problemy upravlenija – Management issues. 2012. no. 2. pp. 2–31. (In Russ.).
45. Haven E., Khrennikov A. Quantum Social Science. NY: Cambridge University Press.
46. Orrell D. A Quantum Theory of Money and Value Economic Thought. 2016. vol. 5. no. 2. pp. 19–28.
47. Khrennikov A., Haven E. Quantum-like Modeling: from Economics to Social Laser. Asian Journal of Economics and Banking. 2020. vol. 4. no. 1. pp. 87–99.
48. Orrell D. The value of value: A quantum approach to economics, security and international relations. Security Dialogue. 2020. vol. 51. no. 5. pp. 482–498.
49. Surov I.A., Alodjants A.P. Modeli prinjatija reshenij v kvantovoj kognitivistike [Decision models in quantum cognitive science]. SPb.: Universitet ITMO, 2018. 63 p. (In Russ.).
50. Peres A. Unperformed experiments have no results American Journal of Physics. 1978. vol. 46. no. 7. pp. 745–747.
51. Bell J.S. Against “measurement”. Physics World. 1990. vol. 3. pp. 32–41.
52. Ballentine L. Propensity, Probability, and Quantum Theory. Foundations of Physics. vol. 46. no. 8. pp. 973–1005.
53. Surov I. Quantum Cognitive Triad: Semantic Geometry of Context Representation. Foundations of Science. 2020. vol. 26. no. 4. pp. 947–975.
54. Horodecki R., Horodecki P., Horodecki M., Horodecki K. Quantum entanglement. Reviews of Modern Physics. 2009. vol. 81. no. 2. pp. 865–942.
55. Hill S., Wootters W. Entanglement of a Pair of Quantum Bits. Physical Review Letters. vol. 78. no. 26. pp. 5022–5025.
56. Surov I., Semenenko E., Platonov A., Bessmertny I., Galofaro F., Toffano Z., Khrennikov A., Alodjants A. Quantum semantics of text perception. Scientific Reports. vol. 11. no. 1. p. 4193.
57. Caves C., Fuchs C., Rungta P. Entanglement of Formation of an Arbitrary State of Two Rebits. Foundations of Physics Letters. 2001. vol. 14. no. 3. pp. 199–212.
58. Wootters W. Entanglement of formation of an arbitrary state of two qubits. Physical Review Letters. 1998. vol. 80. no. 10. pp. 2245–2248.
59. Vidal G., Werner R. Computable measure of entanglement. Physical Review A. 2002. vol. 65. no. 3. p. 032314.
60. Vedral V. The role of relative entropy in quantum information theory. Reviews of Modern Physics. 2002. vol. 74. no. 1. pp. 197–234.
61. Eisert J., Plenio M. A comparison of entanglement measures. Journal of Modern Optics. vol. 46. no. 1. pp. 145–154.
62. Miranowicz A., Grudka A. A comparative study of relative entropy of entanglement, concurrence and negativity. Journal of Optics B: Quantum and Semiclassical Optics. vol. 6. no. 12. pp. 542–548.
63. Vereshhagin N.K., Shhepin E.V. Informacija, kodirovanie i predskazanie [Information, coding and prediction]. M.: FMOP MCNMO, 2012. p. 236. (In Russ.).
64. Coffman V., Kundu J., Wootters W. Distributed entanglement. Physical Review A. 2000. vol. 61. no. 5.
65. Gao X. Fei S. Wu K. Lower bounds of concurrence for tripartite quantum systems. Physical Review A. 2006. vol. 74. no. 5.
66. Nakahara H., Amari S. Information-Geometric Measure for Neural Spikes. Neural Computation. 2002. vol. 14. no. 10. pp. 2269–2316.
67. Fawcett T. An introduction to ROC analysis. Pattern Recognition Letters. 2006. vol. 27. no. 8. pp. 861–874.
68. Gubanov D.A., Novikov D.A., Chhartishvili A. Social’nye seti: modeli informacionnogo vlijanija, upravlenija i protivoborstva [Social networks: models of information influence, control and confrontation]. M: Fizmatlit. 2010. p. 228. (In Russ.).
69. Vitali S., Glattfelder J.B., Battiston S. The Network of Global Corporate Control. PLoS ONE. 2011. vol. 6. no. 10.
70. Sedakov D., Filonov P. Razvedka set’ju: kak sistema Avalanche pomogaet specsluzhbam i biznesu [Network intelligence: how the Avalanche system helps intelligence agencies and businesses]. Forbes. 2015. (In Russ.).
71. Dorofeev A.V., Markov A.S. [Structured monitoring of open personal data on the Internet]. Monitoring pravoprimenenija – Law enforcement monitoring. 2017. no. 18. pp. 30–39. (In Russ.).
72. Pil’kevich S.V., Mazhnikov P.V. [Modern research in the field of monitoring and data analysis of social networks]. Zashhita informacii. Insajd – Protection of information. Inside. 2018. no. 70. pp. 41–53. (In Russ.).
73. Masalovich A.I. [Verona is a computer program for intelligent monitoring of the Internet and express analysis of open data No. RU 2021660918]. 2021. (In Russ.).
74. Johansson J., Nation P., Nori F. QuTiP: An open-source Python framework for the dynamics of open quantum systems. Computer Physics Communications. 2012. vol. 183. no. 8. pp. 1760–1772.
75. Aleksandrowicz G. et al. Qiskit: An Open-source Framework for Quantum Computing. Zenodo. 2019. DOI: 10.5281/zenodo.2562111.
76. Surov I. Quantum core affect. Color-emotion structure of semantic atom. Frontiers in Psychology. 2022. vol. 13.
77. Lebon G. [Psychology of peoples and masses]. Akademicheskij proekt – Academic project. 2021. p. 272. (In Russ.).
78. Kozhisseri S., Surov I. Quantum-probabilistic SVD: complex-valued factorization of matrix data. Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2022. vol. 22. no. 3. pp. 567–573.
79. Gnidko K.O., Lomako A.G. [Modeling Individual and Group Behaviorsubjects of mass communication in p-adic coordinate systems for indicating the level of contamination of consciousness]. Voprosy Kiberbezopasnosti – Issues of Cybersecurity. 2017. no. 15. pp. 54–68. (In Russ.).
80. Ivanov O.S., Pil’kevich S.V., Gnidko K.O., Lohvickij V.A., Dudkin A.S., Sabirov T.R. [Substantiation of the terminological basis for research on the forms of manifestation of contamination of the human psyche]. Vestnik Rossijskogo novogo universiteta. Serija: Slozhnye sistemy: modeli, analiz i upravlenie – Bulletin of the Russian New University. Series: Complex systems: models, analysis and control. 2019. pp. 69–76. (In Russ.).
81. Yanshin P.V. [Study of the emotional state of the group]. Sbornik nauchnyh trudov uchenyh Moskovskogo gorodskogo pedagogicheskogo universiteta i Bakinskogo slavyanskogo universiteta – Collection of scientific works of scientists of the Moscow City Pedagogical University and Baku Slavic University. Ed.: Mylnikov M. 2010. pp. 278–288. (In Russ.).
82. Petrenko V.F. Osnovy psihosemantiki [Fundamentals of psychosemantics]. M.: Eksmo. 2010. (In Russ.).
2. Yang F. Oxford Research Encyclopedia of Criminology and Criminal Justice Oxford University Press. 2019. vol. 44. no. 1. pp. 57–61.
3. McDaniel J., Pease K. Predictive Policing and Artificial Intelligence Routledge, Taylor & Francis Group. 2021. 330 p.
4. Berk R. Artificial Intelligence, Predictive Policing, and Risk Assessment for Law Enforcement Annual Review of Criminology. 2021. vol. 4. no. 1. pp. 209–237.
5. Oficial’nyj sajt Federal’naja Antimonopol’naja sluzhba. Available at: fas.gov.ru (accessed: 09.2022). (In Russ.).
6. Yuriev R.N., Alodjants A.P. [The problem of collusion of bidders and ways to solve it in the framework of digital economics paradogms and by using quantum probability theory]. Sovremennaya nauka: aktualnye problemy teorii i praktiki – Modern Science: Actual Problems of Theory and Practice. Series: Natural and technical sciences. 2021. no. 10. pp. 139–149. (In Russ.).
7. Bajari P., Ye L. Deciding Between Competition and Collusion. Review of Economics and Statistics. 2003. vol. 85. no. 4. pp. 971–989.
8. Ballesteros-Perez P., Skitmore M., Das R., del Campo-Hitschfeld M. Quick Abnormal-Bid-Detection Method for Construction Contract Auctions. Journal of Construction Engineering and Management. 2015. vol. 141. no. 7. p. 04015010.
9. Huber M., Imhof D. Machine learning with screens for detecting bid-rigging cartels. International Journal of Industrial Organization. 2019. vol. 65. pp. 277–301.
10. Garcia Rodriguez M., Rodriguez-Montequin V., Ballesteros-Perez P., Love P., Signor R. Collusion detection in public procurement auctions with machine learning algorithms. Automation in Construction. 2022. vol. 133. p. 104047.
11. Nasledov A.D. Matematicheskie metody psihologicheskogo issledovanija. Analiz i interpretacija dannyh [Mathematical methods of psychological research. Data analysis and interpretation]. Rech’, 2004. p. 392. (In Russ.).
12. Harchenko M.A. Korreljacionnyj analiz [Correlation analysis]. VGU, 2008. 31p. (In Russ.).
13. Marchenko V.M., Mozhej N.P., Shinkevich E.A. Jekonometrika i jekonomiko- matematicheskie metody i modeli [Econometrics and economic-mathematical methods and models]. Minsk: BGTU, 2011. p. 157. (In Russ.).
14. Kremer N.Sh. Teorija verojatnostej i matematicheskaja statistika [Theory of Probability and Mathematical Statistics]. M: Yuniti. 2012. (In Russ.).
15. Killworth P., Russell H. Informant Accuracy in Social Network Data III: A Comparison of Triadic Structure in Behavioral and Cognitive Data. Social Networks. 1979. vol. 2. pp. 19–46.
16. Morgenstern O., Schwodiauer G. Competition and collusion in bilateral markets. Zeitschrift fur Nationalokonomie. 1976. vol. 36. no. 3–4. pp. 217–245.
17. Thomas C., Wilson B. A Comparison of Auctions and Multilateral Negotiations. The RAND Journal of Economics. 2002. vol. 33. no. 1. p. 140.
18. Uddin S., Hossain L. Dyad and Triad Census Analysis of Crisis Communication Network. Social Networking. 2013. vol. 2. no. 1. pp. 32–41.
19. Holland P., Leinhardt S. The Statistical Analysis of Local Structure in Social Networks. Sociological Methodology. 1974. p. 45.
20. Martean L. The Triangle and the Eye inside the Circle: Dyadic and Triadic Dynamics in the Group. Group Analysis. 2014. vol. 47. no. 1. pp. 42–61.
21. Razmi P., Oloomi Buygi M., Esmalifalak M. A Machine Learning Approach for Collusion Detection in Electricity Markets Based on Nash Equilibrium Theory. Group Analysis. vol. 9. no. 1. pp. 170–180.
22. Ball P. The physical modelling of society: a historical perspective. Physica A: Statistical Mechanics and its Applications. 2002. vol. 314. no. 1–4. pp. 1–14.
23. Jorion P. Accounting for human activity through physics. Cybernetics and Systems. 2004. vol. 35. no. 2–3. pp. 275–284.
24. Galam S. Sociophysics. A Physicist’s Modeling of Psycho-political Phenomena Boston, MA: Springer US. 2012. p. 439.
25. Maldonado C. Quantum Theory and the Social Sciences Momento. 2019. no. 59E. pp. 34–47.
26. Meghdadi A., Akbarzadeh-T., Javidan K. A Quantum-Like Model for Predicting Human Decisions in the Entangled Social Systems IEEE Transactions on Cybernetics. pp. 1–11.
27. Meyer D.A. Quantum Strategies. Physical Review Letters. 1999. vol. 82. no. 5. pp. 1052–1055.
28. Eisert J., Wilkens M., Lewenstein M. Quantum Games and Quantum Strategies. Physical Review Letters. 1999. vol. 83. no. 15. pp. 3077–3080.
29. Marinatto L., Weber T. A quantum approach to static games of complete information. Physics Letters A. 2000. vol. 272. pp. 291–303.
30. Yukalov V., Yukalova E., Sornette D. Role of collective information in networks of quantum operating agents. Physica A. 2022. vol. 598. p. 127365.
31. Pothos E., Perry G., Corr P., Matthew M., Busemeyer J. Understanding cooperation in the Prisoner’s Dilemma game. Personality and Individual Differences. vol. 51. no. 3. pp. 210–215.
32. Pelosse Y. The Intrinsic Quantum Nature of Nash Equilibrium Mixtures. Journal of Philosophical Logic. 2016. vol. 45. no. 1. pp. 25–64.
33. Baatique B.E. Quantum finance. Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge. 1998.
34. Khrennikov A. Quantum-psychological model of the stock market Problems and Perspectives in Management. 2003. pp. 136–148.
35. Bagarello F. Stock markets and quantum dynamics: A second quantized description. Physica A: Statistical Mechanics and its Applications. 2007. vol. 386. no. 1. pp. 283–302.
36. Choustova O. Quantum probability and financial market Information Sciences. 2009. vol. no. 5. pp. 478–484.
37. Goncalves C.P. Quantum financial economics – risk and returns Journal of Systems Science and Complexity. 2013. vol. 26. no. 2. pp. 187–200.
38. Tahmasebi F., Meskinimood S., Namaki A., Vasheghani Farahani S., Jalalzadeh S., Jafari G. Financial market images: A practical approach owing to the secret quantum potential. EPL (Europhysics Letters). 2015. vol. 109. no. 3. p. 30001.
39. Orrell D. A quantum model of supply and demand Physica A: Statistical Mechanics and its Applications. 2020. vol. 539. p. 122928.
40. Athalye V., Haven E. Socio-Economic Sciences: Beyond Quantum Math-like Formalisms Quantum Reports. 2021. vol. 3. no. 4. pp. 656–663.
41. Khrennikov A. Social laser model: from color revolutions to Brexit and election of Donald Trump Kybernetes. 2018. vol. 47. no. 2. pp. 273–288.
42. Tsarev D., Trofimova A., Alodjants, A., Khrennikov A. Phase transitions, collective emotions and decision-making problem in heterogeneous social systems Scientific Reports. 2019. vol. 9. no. 1. p. 18039.
43. Alodjants A., Bazhenov A., Khrennikov A., Bukhanovsky A. Mean-field theory of social laser Scientific Reports. 2022. vol. 12. no. 1. p. 8566.
44. Slovohotov Ju.L. [Physics and sociophysics. Part 2. Networks of social interactions. Econophysics]. Problemy upravlenija – Management issues. 2012. no. 2. pp. 2–31. (In Russ.).
45. Haven E., Khrennikov A. Quantum Social Science. NY: Cambridge University Press.
46. Orrell D. A Quantum Theory of Money and Value Economic Thought. 2016. vol. 5. no. 2. pp. 19–28.
47. Khrennikov A., Haven E. Quantum-like Modeling: from Economics to Social Laser. Asian Journal of Economics and Banking. 2020. vol. 4. no. 1. pp. 87–99.
48. Orrell D. The value of value: A quantum approach to economics, security and international relations. Security Dialogue. 2020. vol. 51. no. 5. pp. 482–498.
49. Surov I.A., Alodjants A.P. Modeli prinjatija reshenij v kvantovoj kognitivistike [Decision models in quantum cognitive science]. SPb.: Universitet ITMO, 2018. 63 p. (In Russ.).
50. Peres A. Unperformed experiments have no results American Journal of Physics. 1978. vol. 46. no. 7. pp. 745–747.
51. Bell J.S. Against “measurement”. Physics World. 1990. vol. 3. pp. 32–41.
52. Ballentine L. Propensity, Probability, and Quantum Theory. Foundations of Physics. vol. 46. no. 8. pp. 973–1005.
53. Surov I. Quantum Cognitive Triad: Semantic Geometry of Context Representation. Foundations of Science. 2020. vol. 26. no. 4. pp. 947–975.
54. Horodecki R., Horodecki P., Horodecki M., Horodecki K. Quantum entanglement. Reviews of Modern Physics. 2009. vol. 81. no. 2. pp. 865–942.
55. Hill S., Wootters W. Entanglement of a Pair of Quantum Bits. Physical Review Letters. vol. 78. no. 26. pp. 5022–5025.
56. Surov I., Semenenko E., Platonov A., Bessmertny I., Galofaro F., Toffano Z., Khrennikov A., Alodjants A. Quantum semantics of text perception. Scientific Reports. vol. 11. no. 1. p. 4193.
57. Caves C., Fuchs C., Rungta P. Entanglement of Formation of an Arbitrary State of Two Rebits. Foundations of Physics Letters. 2001. vol. 14. no. 3. pp. 199–212.
58. Wootters W. Entanglement of formation of an arbitrary state of two qubits. Physical Review Letters. 1998. vol. 80. no. 10. pp. 2245–2248.
59. Vidal G., Werner R. Computable measure of entanglement. Physical Review A. 2002. vol. 65. no. 3. p. 032314.
60. Vedral V. The role of relative entropy in quantum information theory. Reviews of Modern Physics. 2002. vol. 74. no. 1. pp. 197–234.
61. Eisert J., Plenio M. A comparison of entanglement measures. Journal of Modern Optics. vol. 46. no. 1. pp. 145–154.
62. Miranowicz A., Grudka A. A comparative study of relative entropy of entanglement, concurrence and negativity. Journal of Optics B: Quantum and Semiclassical Optics. vol. 6. no. 12. pp. 542–548.
63. Vereshhagin N.K., Shhepin E.V. Informacija, kodirovanie i predskazanie [Information, coding and prediction]. M.: FMOP MCNMO, 2012. p. 236. (In Russ.).
64. Coffman V., Kundu J., Wootters W. Distributed entanglement. Physical Review A. 2000. vol. 61. no. 5.
65. Gao X. Fei S. Wu K. Lower bounds of concurrence for tripartite quantum systems. Physical Review A. 2006. vol. 74. no. 5.
66. Nakahara H., Amari S. Information-Geometric Measure for Neural Spikes. Neural Computation. 2002. vol. 14. no. 10. pp. 2269–2316.
67. Fawcett T. An introduction to ROC analysis. Pattern Recognition Letters. 2006. vol. 27. no. 8. pp. 861–874.
68. Gubanov D.A., Novikov D.A., Chhartishvili A. Social’nye seti: modeli informacionnogo vlijanija, upravlenija i protivoborstva [Social networks: models of information influence, control and confrontation]. M: Fizmatlit. 2010. p. 228. (In Russ.).
69. Vitali S., Glattfelder J.B., Battiston S. The Network of Global Corporate Control. PLoS ONE. 2011. vol. 6. no. 10.
70. Sedakov D., Filonov P. Razvedka set’ju: kak sistema Avalanche pomogaet specsluzhbam i biznesu [Network intelligence: how the Avalanche system helps intelligence agencies and businesses]. Forbes. 2015. (In Russ.).
71. Dorofeev A.V., Markov A.S. [Structured monitoring of open personal data on the Internet]. Monitoring pravoprimenenija – Law enforcement monitoring. 2017. no. 18. pp. 30–39. (In Russ.).
72. Pil’kevich S.V., Mazhnikov P.V. [Modern research in the field of monitoring and data analysis of social networks]. Zashhita informacii. Insajd – Protection of information. Inside. 2018. no. 70. pp. 41–53. (In Russ.).
73. Masalovich A.I. [Verona is a computer program for intelligent monitoring of the Internet and express analysis of open data No. RU 2021660918]. 2021. (In Russ.).
74. Johansson J., Nation P., Nori F. QuTiP: An open-source Python framework for the dynamics of open quantum systems. Computer Physics Communications. 2012. vol. 183. no. 8. pp. 1760–1772.
75. Aleksandrowicz G. et al. Qiskit: An Open-source Framework for Quantum Computing. Zenodo. 2019. DOI: 10.5281/zenodo.2562111.
76. Surov I. Quantum core affect. Color-emotion structure of semantic atom. Frontiers in Psychology. 2022. vol. 13.
77. Lebon G. [Psychology of peoples and masses]. Akademicheskij proekt – Academic project. 2021. p. 272. (In Russ.).
78. Kozhisseri S., Surov I. Quantum-probabilistic SVD: complex-valued factorization of matrix data. Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2022. vol. 22. no. 3. pp. 567–573.
79. Gnidko K.O., Lomako A.G. [Modeling Individual and Group Behaviorsubjects of mass communication in p-adic coordinate systems for indicating the level of contamination of consciousness]. Voprosy Kiberbezopasnosti – Issues of Cybersecurity. 2017. no. 15. pp. 54–68. (In Russ.).
80. Ivanov O.S., Pil’kevich S.V., Gnidko K.O., Lohvickij V.A., Dudkin A.S., Sabirov T.R. [Substantiation of the terminological basis for research on the forms of manifestation of contamination of the human psyche]. Vestnik Rossijskogo novogo universiteta. Serija: Slozhnye sistemy: modeli, analiz i upravlenie – Bulletin of the Russian New University. Series: Complex systems: models, analysis and control. 2019. pp. 69–76. (In Russ.).
81. Yanshin P.V. [Study of the emotional state of the group]. Sbornik nauchnyh trudov uchenyh Moskovskogo gorodskogo pedagogicheskogo universiteta i Bakinskogo slavyanskogo universiteta – Collection of scientific works of scientists of the Moscow City Pedagogical University and Baku Slavic University. Ed.: Mylnikov M. 2010. pp. 278–288. (In Russ.).
82. Petrenko V.F. Osnovy psihosemantiki [Fundamentals of psychosemantics]. M.: Eksmo. 2010. (In Russ.).
Published
2023-03-17
How to Cite
Semenenko, E., Belolipetskaya, A., Yuriev, R., Alodjants, A., Bessmertny, I., & Surov, I. (2023). Discovery of Economic Collusion by Metrics of Quantum Entanglement. Informatics and Automation, 22(2), 416-446. https://doi.org/10.15622/ia.22.2.7
Section
Mathematical Modeling and Applied Mathematics
Copyright (c) Евгений Константинович Семененко, Анна Геннадьевна Белолипецкая, Родион Николаевич Юрьев, Игорь Александрович Бессмертный, Александр Павлович Алоджанц, Илья Алексеевич Суров
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