Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
140 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Incentive Designs for Learning Agents to Stabilize Coupled Exogenous Systems (2403.18164v2)

Published 27 Mar 2024 in eess.SY, cs.SY, math.DS, and math.OC

Abstract: We consider a large population of learning agents noncooperatively selecting strategies from a common set, influencing the dynamics of an exogenous system (ES) we seek to stabilize at a desired equilibrium. Our approach is to design a dynamic payoff mechanism capable of shaping the population's strategy profile, thus affecting the ES's state, by offering incentives for specific strategies within budget limits. Employing system-theoretic passivity concepts, we establish conditions under which a payoff mechanism can be systematically constructed to ensure the global asymptotic stability of the ES's equilibrium. In comparison to previous approaches originally studied in the context of the so-called epidemic population games, the method proposed here allows for more realistic epidemic models and other types of ESs, such as predator-prey dynamics. The stability of the equilibrium is established with the support of a Lyapunov function, which provides useful bounds on the transient states.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (21)
  1. N. C. Martins, J. Certório, and R. J. La, “Epidemic population games and evolutionary dynamics,” Automatica, vol. 153, p. 111016, Jul. 2023. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109823001711
  2. J. Certório, N. C. Martins, and R. J. La, “Epidemic Population Games With Nonnegligible Disease Death Rate,” IEEE Control Systems Letters, vol. 6, pp. 3229–3234, 2022.
  3. J. Certório, R. J. La, and N. C. Martins, “Epidemic Population Games for Policy Design: Two Populations with Viral Reservoir Case Study,” in Proc. IEEE conf. decis. control (CDC), 2023, pp. 7667–7674. [Online]. Available: https://ieeexplore.ieee.org/document/10383665
  4. A. Korobeinikov, “A Lyapunov function for Leslie-Gower predator-prey models,” Appl. Math. Lett., vol. 14, no. 6, pp. 697–699, Aug. 2001. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S089396590180029X
  5. W. H. Sandholm, “Potential games with continuous player sets,” Journal of economic theory, vol. 97, pp. 81–108, 2001.
  6. J. Hofbauer and W. H. Sandholm, “Stable games and their dynamics,” Journal of Economic Theory, vol. 144, no. 4, pp. 1665–1693.e4, Jul. 2009.
  7. S. Kara, N. C. Martins, and M. Arcak, “Population games with erlang clocks: Convergence to nash equilibria for pairwise comparison dynamics,” in Proc. IEEE conf. decis. control (CDC), 2022, pp. 7688–7695.
  8. S. Kara and N. C. Martins, “Excess Payoff Evolutionary Dynamics With Strategy-Dependent Revision Rates: Convergence to Nash Equilibria for Potential Games,” IEEE Control Systems Letters, vol. 7, pp. 1009–1014, 2023.
  9. N. Quijano, C. Ocampo-Martinez, J. Barreiro-Gomez, G. Obando, A. Pantoja, and E. Mojica-Nava, “The Role of Population Games and Evolutionary Dynamics in Distributed Control Systems: The Advantages of Evolutionary Game Theory,” IEEE Control Syst., vol. 37, no. 1, pp. 70–97, 2017. [Online]. Available: https://ieeexplore.ieee.org/document/7823106/
  10. M. J. Fox and J. S. Shamma, “Population games, stable games, and passivity,” Games, vol. 4, pp. 561–583, 2013.
  11. S. Park, N. C. Martins, and J. S. Shamma, “Payoff dynamics model and evolutionary dynamics model: Feedback and convergence to equilibria,” 2020.
  12. M. Arcak and N. C. Martins, “Dissipativity Tools for Convergence to Nash Equilibria in Population Games,” IEEE Control Netw. Syst., vol. 8, no. 1, pp. 39–50, Mar. 2021.
  13. K. S. Schweidel and M. Arcak, “Compositional Analysis of Interconnected Systems Using Delta Dissipativity,” IEEE Control Systems Letters, vol. 6, pp. 662–667, 2022.
  14. M. A. Mabrok and J. S. Shamma, “Passivity analysis of higher order evolutionary dynamics and population games,” in Proc. IEEE conf. decis. control (CDC), 2016, pp. 6129–6134. [Online]. Available: https://ieeexplore.ieee.org/abstract/document/7799211
  15. S. Park, J. S. Shamma, and N. C. Martins, “Passivity and evolutionary game dynamics,” in Proc. IEEE conf. decis. control (CDC), 2018, pp. 3553–3560.
  16. J. Martinez-Piazuelo, N. Quijano, and C. Ocampo-Martinez, “A Payoff Dynamics Model for Equality-Constrained Population Games,” IEEE Control Systems Letters, vol. 6, pp. 530–535, 2022.
  17. J. Martinez-Piazuelo, C. Ocampo-Martinez, and N. Quijano, “On Distributed Nash Equilibrium Seeking in a Class of Contractive Population Games,” IEEE Control Systems Letters, pp. 1–1, 2022.
  18. G. Obando, A. Pantoja, and N. Quijano, “Building temperature control based on population dynamics,” IEEE transactions on Control Systems Technology, vol. 22, no. 1, pp. 404–412, Jan. 2014.
  19. S. Park, J. Certório, N. C. Martins, and R. J. La, “Epidemic population games and perturbed best response dynamics,” 2024.
  20. W. H. Sandholm, “Excess payoff dynamics and other well-behaved evolutionary dynamics,” Journal of Economic Theory, vol. 124, no. 2, pp. 149–170, Oct. 2005. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/S0022053105000554
  21. ——, “Pairwise comparison dynamics and evolutionary foundations for Nash equilibrium,” Games, vol. 1, no. 1, pp. 3–17, 2010.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now