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Incentive Designs for Learning Agents to Stabilize Coupled Exogenous Systems

Jair Certório, Nuno C. Martins, Richard J. La, Murat Arcak

TL;DR

The 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, which allows for more realistic epidemic models and other types of ESs, such as predator-prey dynamics.

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.

Incentive Designs for Learning Agents to Stabilize Coupled Exogenous Systems

TL;DR

The 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, which allows for more realistic epidemic models and other types of ESs, such as predator-prey dynamics.

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.
Paper Structure (11 sections, 2 theorems, 45 equations, 3 figures)

This paper contains 11 sections, 2 theorems, 45 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Works
  4. Population Games and Learning Rules
  5. Main Result
  6. Bounds
  7. Examples
  8. Leslie-Gower predator-prey model
  9. Epidemic Population Games (EPG)
  10. Designing an Intervention Policy for Epidemics with Nonlinear Infection Rate
  11. Conclusion

Key Result

Lemma 1

For any fixed $q \in \mathbb{R}^n$ and $\bar{x} \in \mathscr{M}\left(q\right)$, the only vector $x \in \mathbb{X}$ that satisfies is $x = \bar{x}$.

Figures (3)

  • Figure 1: Bound $I_\text{max}(k_1,k_2)$, for the conditions in Example \ref{['example1']}, when varying $k_1$ and $k_2$.
  • Figure 2: Simulation of Example \ref{['example1']}, for many different learning rules, using $k_1=2,k_2=0.022,k_3=1$.
  • Figure 3: Simulation of Example \ref{['example1']}, for many different learning rules, using $k_1=k_2=k_3=1$.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Definition 3
  • Example 1
  • Example 2
  • Lemma 1
  • Theorem 1
  • Example 3