Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Adaptive Incentive Design with Learning Agents

Chinmay Maheshwari, Kshitij Kulkarni, Manxi Wu, Shankar Sastry

TL;DR

This paper addresses incentive design in environments where agents learn and adapt their strategies over time. It introduces an externality-based adaptive incentive mechanism that updates incentives on a slower timescale than players' strategy updates, forming a two-timescale coupled system that is agnostic to the specific learning dynamics. The authors prove that fixed points of the coupled dynamics induce socially optimal outcomes, and they provide sufficient conditions for local and global convergence, applying the results to both atomic aggregative games and non-atomic routing games. The framework offers robust alignment of Nash equilibria with the social optimum without requiring convexity or non-singularity assumptions typical of gradient-based approaches, and it demonstrates practical convergence in two representative game classes with Lyapunov-based arguments.

Abstract

We propose an adaptive incentive mechanism that learns the optimal incentives in environments where players continuously update their strategies. Our mechanism updates incentives based on each player's externality, defined as the difference between the player's marginal cost and the operator's marginal cost at each time step. The proposed mechanism updates the incentives on a slower timescale compared to the players' learning dynamics, resulting in a two-timescale coupled dynamical system. Notably, this mechanism is agnostic to the specific learning dynamics used by players to update their strategies. We show that any fixed point of this adaptive incentive mechanism corresponds to the optimal incentive mechanism, ensuring that the Nash equilibrium coincides with the socially optimal strategy. Additionally, we provide sufficient conditions under which the adaptive mechanism converges to a fixed point. Our results apply to both atomic and non-atomic games. To demonstrate the effectiveness of our proposed mechanism, we verify the convergence conditions in two practically relevant classes of games: atomic aggregative games and non-atomic routing games.

Adaptive Incentive Design with Learning Agents

TL;DR

This paper addresses incentive design in environments where agents learn and adapt their strategies over time. It introduces an externality-based adaptive incentive mechanism that updates incentives on a slower timescale than players' strategy updates, forming a two-timescale coupled system that is agnostic to the specific learning dynamics. The authors prove that fixed points of the coupled dynamics induce socially optimal outcomes, and they provide sufficient conditions for local and global convergence, applying the results to both atomic aggregative games and non-atomic routing games. The framework offers robust alignment of Nash equilibria with the social optimum without requiring convexity or non-singularity assumptions typical of gradient-based approaches, and it demonstrates practical convergence in two representative game classes with Lyapunov-based arguments.

Abstract

We propose an adaptive incentive mechanism that learns the optimal incentives in environments where players continuously update their strategies. Our mechanism updates incentives based on each player's externality, defined as the difference between the player's marginal cost and the operator's marginal cost at each time step. The proposed mechanism updates the incentives on a slower timescale compared to the players' learning dynamics, resulting in a two-timescale coupled dynamical system. Notably, this mechanism is agnostic to the specific learning dynamics used by players to update their strategies. We show that any fixed point of this adaptive incentive mechanism corresponds to the optimal incentive mechanism, ensuring that the Nash equilibrium coincides with the socially optimal strategy. Additionally, we provide sufficient conditions under which the adaptive mechanism converges to a fixed point. Our results apply to both atomic and non-atomic games. To demonstrate the effectiveness of our proposed mechanism, we verify the convergence conditions in two practically relevant classes of games: atomic aggregative games and non-atomic routing games.
Paper Structure (23 sections, 13 theorems, 74 equations, 1 figure)

This paper contains 23 sections, 13 theorems, 74 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Works
  3. Model
  4. Static Games
  5. Atomic Games
  6. Non-atomic Games
  7. Coupled Strategy and Incentive Update
  8. General results
  9. Fixed point analysis
  10. Convergence to optimal incentive mechanism
  11. Applications
  12. Atomic Aggregative Games
  13. Non-atomic Traffic Routing on General Networks
  14. Concluding Remarks
  15. Counter-example.
  16. ...and 8 more sections

Key Result

Proposition 3.1

Let Assumptions assm: SocCostAtomic hold and the strategy set $X$ in an atomic game $G$ be compact. The set $P^{\dagger}$ is a non-empty singleton set. The unique $p^{\dagger} \in P^{\dagger}$ is socially optimal, i.e. $x^{\ast}_{}(p^{\dagger}) = {x}^{\dagger}$. Moreover, in a non-atomic game $\tild

Figures (1)

  • Figure 1: Two-link routing game.

Theorems & Definitions (20)

  • Proposition 3.1
  • Definition 3.2
  • Proposition 3.3
  • Proposition 4.1
  • Proposition 4.2
  • Proposition 4.3
  • Proposition 4.4
  • Remark 4.5
  • Proposition B.1
  • proof
  • ...and 10 more