Quantum Game Theoretic Analysis of Kabaddi


  • Swati Singh Dayalbagh Educational Institute, Agra, Uttar Pradesh, India.


Nash equilibrium, Pareto Optimal, Quantum Game Simulator


The paper attempts to quantize Kabaddi using game-theoretic analysis. The authors' design payoff matrices using classical game theory. There are multiple pure and mixed strategy Nash equilibria for the matrices. The dilemma resolves using the quantization of Kabaddi, and we obtain a unique solution to the payoff matrix. It also shows how a player can modify another player's winning by choosing its angles.

Author Biography

Swati Singh, Dayalbagh Educational Institute, Agra, Uttar Pradesh, India.

Research Scholar in Physics with specialization in Electronics, Dayalbagh Educational Institute, Agra, Uttar Pradesh, India.


Kyriienko, O., Paine, A. E., & Elfving, V. E. (2021). Solving nonlinear differential equations with differentiable quantum circuits. Physical Review A, 103(5), 052416.

Li, Y., Zhao, Y., Fu, J., & Xu, L. (2021). Reducing food loss and waste in a two-echelon food supply chain: A quantum game approach. Journal of Cleaner Production, 285, 125261.

Yuan, B. (2021). Study on the exit strategy selection mechanism of venture capital based on the quantum game. AIMS Mathematics, 6(7), 6882-6897.

Elgazzar, A. S. (2021). Coopetition in quantum prisoner’s dilemma and COVID-19. Quantum Information Processing, 20(3), 1-13.

Naskar, J., & Maioli, A. C. (2020). Quantum Multiplayer Colonel Blotto Game. arXiv preprint arXiv:2008.00762.

Emeriau, P. E., Howard, M., & Mansfield, S. The Torpedo Game: Quantum Advantage, Wigner Negativity, and Sequential Contextuality in a Generalized Random Access Code. Quantum, 2(3), 4.

Chen, J., Jian, J., & Hong, S. (2020). Quantum repeated pricing game. Quantum Information Processing, 19(2), 1-10.

Alonso-Sanz, R. (2019). Quantum Memory. In Quantum Game Simulation (pp. 175-192). Springer, Cham.

Yoo, W. S. (2019). Quantum voting and its physical interpretation. arXiv preprint arXiv:1912.05356.

Banik, M., Bhattacharya, S. S., Ganguly, N., Guha, T., Mukherjee, A., Rai, A., & Roy, A. (2019). Two-qubit pure entanglement as optimal social welfare resource in the Bayesian game. Quantum, 3, 185.

Ge, W., Jacobs, K., Eldredge, Z., Gorshkov, A. V., & Foss-Feig, M. (2018). Distributed quantum metrology with linear networks and separable inputs. Physical review letters, 121(4), 043604.

Albarelli, F., Rossi, M. A., Tamascelli, D., & Genoni, M. G. (2018). Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment. Quantum, 2, 110.

Solmeyer, N., Dixon, R., & Balu, R. (2018). Quantum routing games. Journal of Physics A: Mathematical and Theoretical, 51(45), 455304.

Trisetyarso, A., & Hastiadi, F. F. (2018, October). Quantum games of quadruple helix ecosystem. In 2018 International Symposium on Electronics and Smart Devices (ISESD) (pp. 1-4). IEEE.

Kaur, H., & Kumar, A. (2018). The game-theoretic perspective of ping-pong protocol. Physica A: Statistical Mechanics and its Applications, 490, 1415-1422.

Samadi, A. H., Montakhab, A., Marzban, H., & Owjimehr, S. (2018). Quantum Barro–Gordon game in monetary economics. Physica A: Statistical Mechanics and its Applications, 489, 94-101.

Kaur, H., & Kumar, A. (2018). The game-theoretic perspective of ping-pong protocol. Physica A: Statistical Mechanics and its Applications, 490, 1415-1422.

Bao, N., & Halpern, N. Y. (2017). Quantum voting and violation of Arrow's impossibility theorem. Physical Review A, 95(6), 062306.

Zabaleta, O. G., Barrangú, J. P., & Arizmendi, C. M. (2017). Quantum game application to spectrum scarcity problems. Physica A: Statistical Mechanics and its Applications, 466, 455-461.

O'Brien, K. L. (2016). Climate change and social transformations: is it time for a quantum leap?. Wiley Interdisciplinary Reviews: Climate Change, 7(5), 618-626.

Drabik, E., & Młodzianowski, P. (2016). Some remarks about financial market modelling using a minority game approach. Economics, 4(5), 216-223.

Tesař, J. (2015). Quantum theory of international relations: approaches and possible gains. Human Affairs, 25(4), 486-502.

Zhenzhou, L., Ming, Z., Hong-Yi, D., Xi, C., & Boyang, L. (2015, July). Quantization makes investors avoid the moral hazard. In 2015 34th Chinese Control Conference (CCC) (pp. 8315-8318). IEEE.

Khrennikova, P. (2014, June). Quantum-like modelling of the nonseparability of voters' preferences in the US political system. In International Symposium on Quantum Interaction (pp. 196-209). Springer, Cham.

Chen, Y., Qin, G., & Wang, A. M. (2014). Quantization of the location stage of the Hotelling model. arXiv preprint arXiv:1410.2779.

Szopa, M. (2014). How Quantum Prisoner’s Dilemma Can Support Negotiations.

GAO, T., & CHEN, Y. The Fluctuations of Stock Market in a Quantum Paradigm.

Zabaleta, O. G., & Arizmendi, C. M. (2014). Quantum game techniques are applied to wireless networks communications. Journal of Advances in Applied and Computational Mathematics, 1, 3-7.

Jiménez, E. H. (2012). Cancer treatment is an entangled cooperative game. International Journal of Biological Engineering, 2(2), 9-17.

Gonçalves, C. P. (2012). Risk Mathematics and Quantum Games on Quantum Risk Structures-A Nuclear War Scenario Game. arXiv preprint arXiv:1211.6683.

Pedram, P. (2012). The minimal length uncertainty and the quantum model for the stock market. Physica A: Statistical Mechanics and its Applications, 391(5), 2100-2105.

Brindha, G. R., Anand, S., Prakash, S., & JoePrathap, P. M. (2012). Optimization of task allocation using quantum game theory with artificial intelligence. In Proceedings of the International Conference on Information Systems Design and Intelligent Applications 2012 (INDIA 2012) held in Visakhapatnam, India, January 2012 (pp. 1-10). Springer, Berlin, Heidelberg.

Houshmand, M., Houshmand, M., & Mashhadi, H. R. (2011). A Game-Theoretic Approach to Study the Quantum Key Distribution BB84 Protocol. International Journal of Quantum Information, 9(04), 1133-1146.

Mihara, T. (2011). Information sharing using entangled states and its applications to quantum card tricks. Decision support systems, 50(2), 522-528.

Sharif, P., & Heydari, H. (2011). Quantum solution to a three-player Kolkata restaurant problem using entangled qutrits. arXiv preprint arXiv:1111.1962.

Zabaleta, O. G., & Arizmendi, C. M. (2010). Quantum dating market. Physica A: statistical mechanics and its applications, 389(14), 2858-2863.

Zhang, C., & Huang, L. (2010). A quantum model for the stock market. Physica A: Statistical Mechanics and Its Applications, 389(24), 5769-5775.

Leaw, J. N., & Cheong, S. A. (2010). Strategic insights from playing quantum tic-tac-toe. Journal of Physics A: Mathematical and Theoretical, 43(45), 455304.

Anand, A., Behera, B. K., & Panigrahi, P. K. (2020). Solving Diner's dilemma game, circuit implementation, and verification on IBMQ simulator. arXiv preprint arXiv:2010.12841.

Scarpa, G. (2009, October). Network games with quantum strategies. In International Conference on Quantum Communication and Quantum Networking (pp. 74-81). Springer, Berlin, Heidelberg.

Altepeter, J. B., & Kumar, P. (2009). Quantum Strategies: Proposal to Experimentally Test a Quantum Economics Protocol. NORTHWESTERN UNIV EVANSTON IL DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE.

Salimi, S., & Soltanzadeh, M. M. (2009). Investigation of quantum roulette. International Journal of Quantum Information, 7(03), 615-626.

Bleiler, S. A. (2009). Quantized poker. arXiv preprint arXiv:0902.2196.

Aerts, D., D'Hooghe, B., Posiewnik, A., Pykacz, J., Dehaene, J., & De Moor, B. (2008). How to play two-player restricted quantum games with ten cards. International Journal of Theoretical Physics, 47(1), 61-68.

Lawless, W. F., Bergman, M., Louçã, J., Kriegel, N. N., & Feltovich, N. (2007). A quantum metric of organizational performance: Terrorism and counterterrorism. Computational and Mathematical Organization Theory, 13(3), 241-281.

Miakisz, K., Piotrowski, E. W., &Sładkowski, J. (2006). Quantization of games: Towards quantum artificial intelligence. Theoretical Computer Science, 358(1), 15-22.

Pakula, I., Piotrowski, E. W., & Sladkowski, J. (2006, February). Quantum market games: Implementing tactics via measurements. In Journal of Physics: Conference Series (Vol. 30, No. 1, p. 009). IOP Publishing.

Flitney, A. P., & Abbott, D. (2005). A semi-quantum version of the game of life. In Advances in Dynamic Games (pp. 667-679). Birkhäuser Boston.

Lo, C. F., & Kiang, D. (2003). Quantum oligopoly. EPL (Europhysics Letters), 64(5), 592.

Guinea, F., & Martin-Delgado, M. A. (2003). Quantum Chino's game: winning strategies through quantum fluctuations. Journal of Physics A: Mathematical and General, 36(13), L197.

Ozdemir, S. K., Shimamura, J., Morikoshi, F., & Imoto, N. (2003). Samaritan's Dilemma: Classical and quantum strategies in Welfare Game. arXiv preprint quant-ph/0311074.

Piotrowski, E. W., Sładkowski, J., & Syska, J. (2003). Interference of quantum market strategies. Physica A: Statistical Mechanics and its Applications, 318(3-4), 516-528.

Piotrowski, E. W., & Sładkowski, J. (2002). Quantum bargaining games. Physica A: Statistical Mechanics and its Applications, 308(1-4), 391-401.

Piotrowski, E. W., & Sładkowski, J. (2001). Quantum-like approach to financial risk: quantum anthropic principle. arXiv preprint quant-ph/0110046.

Segre, G. (2001). Law of excluded quantum gambling strategies. arXiv preprint quant-ph/0104080.

Miyake, A., & Wadati, M. (2001). Geometric strategy for the optimal quantum search. Physical Review A, 64(4), 042317.

Chen, Z. (2001). Quantum Finance: The finite-dimensional case. arXiv preprint quant-ph/0112158.

Ahmad Nawaz and A H Toor, Generalized quantization scheme for two-person non-zero-sum games, J. Phys. A: Math. Gen. 37 (2004) 11457–11463

Marinatto L and Weber T 2000 Phys. Lett. A 272 291–303 (Preprint quant-ph/0004081)

Eisert J, Wilkens M and Lewenstein M 1999 Phys. Rev. Lett. 83 3077

Eisert, J., Wilkens, M., Lewenstein, M., Quantum Games and Quantum Strategies, Physical Review Letters 83 (1999) 3077.

Ma Y J, Long G L, Deng F G, Lee F and Zhang S-X 2002 Phys. Lett. A 301 117

- Vlachos, P., & Karafyllidis, I. G. (2009). Quantum game simulator, using the circuit model of quantum computation. Computer Physics Communications, 180(10), 1990-1998.

Avis, D., Rosenberg, G. D., Savani, R., & Von Stengel, B. (2010). Enumeration of Nash equilibria for two-player games. Economic theory, 42(1), 9-37.

Game Theory Solver 2x2 Matrix Games, n.d.,(https://mindyourdecisions.com/GameSolver.html)