Quantum-Fuzzy Relational Dynamics in the Iterated Prisoner’s Dilemma: Competitive Prediction with Stronger Recovery, Coupling, and Resilience Effects
Resumo
Modeling socially interdependent decision processes remains a major challenge in computational intelligence, particularly when behavior is influenced by emotional ambiguity, inter-agent coupling, and recovery after disruption. This paper introduces a quantum-fuzzy benchmark for emotion-aware relational dynamics in the Iterated Prisoner’s Dilemma. Emotional variables are represented through fuzzy membership degrees and encoded into quantum-fuzzy relational states, enabling controlled analysis of cooperation, betrayal, recovery, coupling, and robustness under perturbation. We compare three settings: a classical fuzzy baseline, a quantum-fuzzy model, and a classifier-augmented quantum-fuzzy variant. On the predictive benchmark, the quantum-fuzzy model is competitive and slightly outperforms the classical baseline, achieving the best F1-score (0.8153 vs. 0.8039) and accuracy (0.7672 vs. 0.7610), while the augmented variant performs similarly. The main gains, however, appear in relational dynamics. Quantum-fuzzy models recover cooperation much faster after betrayal, reduce collapse rates, respond more strongly to inter-agent coupling, and show higher resilience under relational shocks, with recovery time dropping from 5.91 to 2.28 and 1.43, and resilience increasing from 0.0466 to 0.2256. Overall, the results suggest that quantum-fuzzy encoding contributes less through predictive gains and more through improved relational adaptation in emotionally interdependent environments.Referências
Axelrod, R. and Hamilton, W. D. (1981). The evolution of cooperation. Science, 211(4489):1390–1396.
Busemeyer, J. R. and Bruza, P. D. (2012). Quantum models of cognition and decision. Cambridge University Press.
Farias, G. P., Dimuro, G. P., Peter, G. D., and De Manuel Jerez, E. (2013). A bdi-fuzzy agent model for exchanges of non-economic services based on the social exchange theory. In Anais do VII Workshop-Escola de Sistemas de Agentes, seus Ambientes e Aplicações (WESAAC). Sociedade Brasileira de Computação.
Fawcett, T. (2006). An introduction to roc analysis. Pattern Recognition Letters, 27(8):861–874.
Kosko, B. (1990). Fuzziness vs. probability. International Journal of General Systems, 17(2-3):211–240.
Leibo, J. Z., Zambaldi, V., Lanctot, M., Marecki, J., and Graepel, T. (2017). Multi-agent reinforcement learning in sequential social dilemmas. Proceedings of AAMAS.
Nielsen, M. A. and Chuang, I. L. (2010). Quantum computation and quantum information. Cambridge University Press.
Nowak, M. A. (2006). Evolutionary dynamics: exploring the equations of life. Harvard University Press.
Nowak, M. A. and Sigmund, K. (1992). Tit for tat in heterogeneous populations. Nature, 355:250–253.
Powers, D. M. W. (2011). Evaluation: From precision, recall and f-measure to roc, informedness, markedness and correlation. Journal of Machine Learning Technologies, 2(1):37–63.
Qiskit Development Team (2021). Qiskit: An open-source framework for quantum computing. [link].
Rodrigues, H. D. N., Dimuro, G. P., and Adamatti, D. F. (2017). Um modelo de reputação fuzzy de dimensão variável. In Anais do XI Workshop-Escola de Sistemas de Agentes, seus Ambientes e Aplicações, pages 113–124, São Paulo, SP, Brasil. Sociedade Brasileira de Computação.
Rojas, Y. E. L., Dimuro, G. P., and Adamatti, D. F. (2014). Trocas sociais em sistemas multiagentes: Transferência de confiança com base na reputação e na relação de dependência. In Anais do VIII Workshop-Escola de Sistemas de Agentes, seus Ambientes e Aplicações (WESAAC). Sociedade Brasileira de Computação.
Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20:53–65.
Sandholm, W. H. (2010). Population games and evolutionary dynamics. MIT Press.
Sutton, R. S. and Barto, A. G. (2018). Reinforcement learning: An introduction. MIT Press, 2 edition.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3):338–353.
Zadeh, L. A. (1996). Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems, 4(2):103–111.
Busemeyer, J. R. and Bruza, P. D. (2012). Quantum models of cognition and decision. Cambridge University Press.
Farias, G. P., Dimuro, G. P., Peter, G. D., and De Manuel Jerez, E. (2013). A bdi-fuzzy agent model for exchanges of non-economic services based on the social exchange theory. In Anais do VII Workshop-Escola de Sistemas de Agentes, seus Ambientes e Aplicações (WESAAC). Sociedade Brasileira de Computação.
Fawcett, T. (2006). An introduction to roc analysis. Pattern Recognition Letters, 27(8):861–874.
Kosko, B. (1990). Fuzziness vs. probability. International Journal of General Systems, 17(2-3):211–240.
Leibo, J. Z., Zambaldi, V., Lanctot, M., Marecki, J., and Graepel, T. (2017). Multi-agent reinforcement learning in sequential social dilemmas. Proceedings of AAMAS.
Nielsen, M. A. and Chuang, I. L. (2010). Quantum computation and quantum information. Cambridge University Press.
Nowak, M. A. (2006). Evolutionary dynamics: exploring the equations of life. Harvard University Press.
Nowak, M. A. and Sigmund, K. (1992). Tit for tat in heterogeneous populations. Nature, 355:250–253.
Powers, D. M. W. (2011). Evaluation: From precision, recall and f-measure to roc, informedness, markedness and correlation. Journal of Machine Learning Technologies, 2(1):37–63.
Qiskit Development Team (2021). Qiskit: An open-source framework for quantum computing. [link].
Rodrigues, H. D. N., Dimuro, G. P., and Adamatti, D. F. (2017). Um modelo de reputação fuzzy de dimensão variável. In Anais do XI Workshop-Escola de Sistemas de Agentes, seus Ambientes e Aplicações, pages 113–124, São Paulo, SP, Brasil. Sociedade Brasileira de Computação.
Rojas, Y. E. L., Dimuro, G. P., and Adamatti, D. F. (2014). Trocas sociais em sistemas multiagentes: Transferência de confiança com base na reputação e na relação de dependência. In Anais do VIII Workshop-Escola de Sistemas de Agentes, seus Ambientes e Aplicações (WESAAC). Sociedade Brasileira de Computação.
Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20:53–65.
Sandholm, W. H. (2010). Population games and evolutionary dynamics. MIT Press.
Sutton, R. S. and Barto, A. G. (2018). Reinforcement learning: An introduction. MIT Press, 2 edition.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3):338–353.
Zadeh, L. A. (1996). Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems, 4(2):103–111.
Publicado
19/07/2026
Como Citar
SALEM, Murilo; PONTES, Daniel; BÖHM, Luísa; REIS, Henrique dos; FERRUGEM, Anderson Priebe.
Quantum-Fuzzy Relational Dynamics in the Iterated Prisoner’s Dilemma: Competitive Prediction with Stronger Recovery, Coupling, and Resilience Effects. In: SIMPÓSIO BRASILEIRO DE COMPUTAÇÃO E COMUNICAÇÃO QUÂNTICAS (SBCCQ), 1. , 2026, Gramado/RS.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 143-154.
DOI: https://doi.org/10.5753/sbccq.2026.23434.
