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Token Economy for Fair and Efficient Dynamic Resource Allocation in Congestion Games

Leonardo Pedroso, Andrea Agazzi, W. P. M. H. Heemels, Mauro Salazar

Abstract

Self-interested behavior in sharing economies often leads to inefficient aggregate outcomes compared to a centrally coordinated allocation, ultimately harming users. Yet, centralized coordination removes individual decision power. This issue can be addressed by designing rules that align individual preferences with system-level objectives. Unfortunately, rules based on conventional monetary mechanisms introduce unfairness by discriminating among users based on their wealth. To solve this problem, in this paper, we propose a token-based mechanism for congestion games that achieves efficient and fair dynamic resource allocation. Specifically, we model the token economy as a continuous-time dynamic game with finitely many boundedly rational agents, explicitly capturing their evolutionary policy-revision dynamics. We derive a mean-field approximation of the finite-population game and establish strong approximation guarantees between the mean-field and the finite-population games. This approximation enables the design of integer tolls in closed form that provably steer the aggregate dynamics toward an optimal efficient and fair allocation from any initial condition.

Token Economy for Fair and Efficient Dynamic Resource Allocation in Congestion Games

Abstract

Self-interested behavior in sharing economies often leads to inefficient aggregate outcomes compared to a centrally coordinated allocation, ultimately harming users. Yet, centralized coordination removes individual decision power. This issue can be addressed by designing rules that align individual preferences with system-level objectives. Unfortunately, rules based on conventional monetary mechanisms introduce unfairness by discriminating among users based on their wealth. To solve this problem, in this paper, we propose a token-based mechanism for congestion games that achieves efficient and fair dynamic resource allocation. Specifically, we model the token economy as a continuous-time dynamic game with finitely many boundedly rational agents, explicitly capturing their evolutionary policy-revision dynamics. We derive a mean-field approximation of the finite-population game and establish strong approximation guarantees between the mean-field and the finite-population games. This approximation enables the design of integer tolls in closed form that provably steer the aggregate dynamics toward an optimal efficient and fair allocation from any initial condition.
Paper Structure (29 sections, 13 theorems, 30 equations, 2 figures)

This paper contains 29 sections, 13 theorems, 30 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Statement of Contributions
  3. Notation
  4. Token Economy Model
  5. Finite-Population Dynamic Congestion Game Model
  6. Information Structure
  7. Regularity Assumptions
  8. Evolutionary Decision Model
  9. Problem Statement
  10. Efficiency
  11. Fairness
  12. Design Problem
  13. Descriptive Analysis
  14. Mean Field Token Economy Model
  15. Equilibria
  16. ...and 14 more sections

Key Result

Lemma 1

Under Assumption ass:noise, the continuous-time Markov chain of the amount of tokens of an agent $i\in \mathcal{C}_c$ that uses a policy $u\in \mathcal{U}^c_D$, whose jump chain is defined in eq:equiv_jump_chain_noise, admits a unique stationary distribution denoted by $\eta^{c,u} \in \mathcal{P}(\m

Figures (2)

  • Figure 1: Illustrative token transition chains: Nodes represent the token amounts, edges represent the transition after taking an action and are labeled with the corresponding toll value.
  • Figure 2: Simulation of the token economy for the illustrative traffic network.

Theorems & Definitions (31)

  • Definition 1
  • Lemma 1
  • proof
  • Example 1
  • Definition 2: Imitative via comparison revision protocol Sandholm2010
  • Definition 3: Pairwise comparison revision protocol Sandholm2010
  • Remark 1
  • Example 2
  • Example 3
  • Lemma 2
  • ...and 21 more