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Data-driven Dynamic Intervention Design in Network Games

Xiupeng Chen, Nima Monshizadeh

TL;DR

The paper tackles steering actions in network games toward a target profile $x^*$ when the regulator lacks priors on private utilities and network structure. It recasts intervention design as a direct data-driven control problem, introducing a PI policy with gains $K_x,K_z$ computed from historical action–intervention data via LMIs, ensuring convergence to $x^*$. To address practical constraints, it also develops a budget-aware version using saturation and a generalized sector condition to guarantee stability and provide a region of attraction. The main contributions are (i) a single-time-scale data-driven controller with convergence guarantees, (ii) an LMI-based procedure that avoids system identification, and (iii) a budget-constrained extension validated on a Cournot competition example. This work enables regulators to influence large-scale, privacy-sensitive networked systems under information constraints with concrete stability guarantees.

Abstract

Targeted interventions in games present a challenging problem due to the asymmetric information available to the regulator and the agents. This note addresses the problem of steering the actions of self-interested agents in quadratic network games towards a target action profile. A common starting point in the literature assumes prior knowledge of utility functions and/or network parameters. The goal of the results presented here is to remove this assumption and address scenarios where such a priori knowledge is unavailable. To this end, we design a data-driven dynamic intervention mechanism that relies solely on historical observations of agent actions and interventions. Additionally, we modify this mechanism to limit the amount of interventions, thereby considering budget constraints. Analytical convergence guarantees are provided for both mechanisms, and a numerical case study further demonstrates their effectiveness.

Data-driven Dynamic Intervention Design in Network Games

TL;DR

The paper tackles steering actions in network games toward a target profile when the regulator lacks priors on private utilities and network structure. It recasts intervention design as a direct data-driven control problem, introducing a PI policy with gains computed from historical action–intervention data via LMIs, ensuring convergence to . To address practical constraints, it also develops a budget-aware version using saturation and a generalized sector condition to guarantee stability and provide a region of attraction. The main contributions are (i) a single-time-scale data-driven controller with convergence guarantees, (ii) an LMI-based procedure that avoids system identification, and (iii) a budget-constrained extension validated on a Cournot competition example. This work enables regulators to influence large-scale, privacy-sensitive networked systems under information constraints with concrete stability guarantees.

Abstract

Targeted interventions in games present a challenging problem due to the asymmetric information available to the regulator and the agents. This note addresses the problem of steering the actions of self-interested agents in quadratic network games towards a target action profile. A common starting point in the literature assumes prior knowledge of utility functions and/or network parameters. The goal of the results presented here is to remove this assumption and address scenarios where such a priori knowledge is unavailable. To this end, we design a data-driven dynamic intervention mechanism that relies solely on historical observations of agent actions and interventions. Additionally, we modify this mechanism to limit the amount of interventions, thereby considering budget constraints. Analytical convergence guarantees are provided for both mechanisms, and a numerical case study further demonstrates their effectiveness.
Paper Structure (9 sections, 4 theorems, 58 equations, 3 figures)

This paper contains 9 sections, 4 theorems, 58 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Network games
  4. Best response dynamics
  5. Target action profile
  6. Intervention protocol
  7. Intervention with budget constraints
  8. Case study
  9. Conclusion

Key Result

Theorem 1

Suppose $\Theta\in\mathbb{R}^{(T-1)\times 2N}$ satisfies the matrix inequality Then, the intervention protocol PI with renders the equilibrium of eq_closedloop asymptotically stable. Consequently, the action profile asymptotically converges to the target profile $x^*$.

Figures (3)

  • Figure 1: The direct graph illustrating asymmetrical product substitutability
  • Figure 2: Agent action profile and intervention without budget constraints
  • Figure 3: Agent action profile and intervention with budget constraints

Theorems & Definitions (11)

  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Lemma 1
  • Theorem 2
  • proof
  • Lemma 2
  • proof
  • Remark 3
  • ...and 1 more