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Fair and Efficient allocation of Mobility-on-Demand resources through a Karma Economy

Matteo Cederle, Saverio Bolognani, Gian Antonio Susto

TL;DR

The paper addresses fair and efficient allocation of Mobility-on-Demand resources under time-sensitive demand that evolves with system state. It extends the Karma economy to Dynamic Population Games by modeling each user as an ego agent with private urgency $u\in\mathcal{U}$ and karma $k$, and by introducing endogenous urgency transitions $\Phi[u^+|u,o]$ alongside a redistribution mechanism that preserves Karma. The authors prove the existence of a Stationary Nash Equilibrium under Karma-preservation and continuity assumptions and demonstrate, via a large-scale numerical study, that the decentralized Karma-based scheme achieves high system-wide reward with fairness close to an optimal centralized benchmark $MAX\_EFF$. The framework provides a principled approach to fair MoD resource allocation in the presence of realistic, state-dependent user time-sensitivity, with practical implications for reducing inequities in ride-hailing access. Future work includes handling heterogeneous user preferences and validating the model with real-world ride-hailing data.

Abstract

Mobility-on-demand systems like ride-hailing have transformed urban transportation, but they have also exacerbated socio-economic inequalities in access to these services, also due to surge pricing strategies. Although several fairness-aware frameworks have been proposed in smart mobility, they often overlook the temporal and situational variability of user urgency that shapes real-world transportation demands. This paper introduces a non-monetary, Karma-based mechanism that models endogenous urgency, allowing user time-sensitivity to evolve in response to system conditions as well as external factors. We develop a theoretical framework maintaining the efficiency and fairness guarantees of classical Karma economies, while accommodating this realistic user behavior modeling. Applied to a simulated mobility-on-demand scenario we show that our framework is able to achieve high levels of system efficiency, guaranteeing at the same time equitable resource allocation for the users.

Fair and Efficient allocation of Mobility-on-Demand resources through a Karma Economy

TL;DR

The paper addresses fair and efficient allocation of Mobility-on-Demand resources under time-sensitive demand that evolves with system state. It extends the Karma economy to Dynamic Population Games by modeling each user as an ego agent with private urgency and karma , and by introducing endogenous urgency transitions alongside a redistribution mechanism that preserves Karma. The authors prove the existence of a Stationary Nash Equilibrium under Karma-preservation and continuity assumptions and demonstrate, via a large-scale numerical study, that the decentralized Karma-based scheme achieves high system-wide reward with fairness close to an optimal centralized benchmark . The framework provides a principled approach to fair MoD resource allocation in the presence of realistic, state-dependent user time-sensitivity, with practical implications for reducing inequities in ride-hailing access. Future work includes handling heterogeneous user preferences and validating the model with real-world ride-hailing data.

Abstract

Mobility-on-demand systems like ride-hailing have transformed urban transportation, but they have also exacerbated socio-economic inequalities in access to these services, also due to surge pricing strategies. Although several fairness-aware frameworks have been proposed in smart mobility, they often overlook the temporal and situational variability of user urgency that shapes real-world transportation demands. This paper introduces a non-monetary, Karma-based mechanism that models endogenous urgency, allowing user time-sensitivity to evolve in response to system conditions as well as external factors. We develop a theoretical framework maintaining the efficiency and fairness guarantees of classical Karma economies, while accommodating this realistic user behavior modeling. Applied to a simulated mobility-on-demand scenario we show that our framework is able to achieve high levels of system efficiency, guaranteeing at the same time equitable resource allocation for the users.

Paper Structure

This paper contains 13 sections, 1 theorem, 20 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. Notation
  3. PROBLEM FORMULATION
  4. System Model
  5. Problem-specific characteristics
  6. AUGMENTED KARMA ECONOMIES FOR MOBILITY ON DEMAND
  7. A novel Karma economy for ride-hailing systems
  8. Existence of Stationary Nash Equilibrium
  9. NUMERICAL ANALYSIS
  10. Performance metrics and benchmarks
  11. Case studies
  12. Results and discussion
  13. CONCLUSIONS

Key Result

Theorem 1

Let Assumptions ass2 and ass hold. Then, for each $\bar{k}\in\mathbb{N}$, a Stationary Nash Equilibrium $(d^*,\pi^*)$ satisfying $\sum_{u,k}d^*[u,k]k=\bar{k}$ is guaranteed to exist in the extended Karma formulation with endogenous urgency processes.

Figures (3)

  • Figure 1: Graphical representation of $\Phi[u^+|u,o]$. The solid arrows represent the high probability transitions when $o=1$, while the dashed arrows represent the high probability transitions when $o=0$.
  • Figure 2: Stationary Nash Equilibrium policy with the urgency transition process in (\ref{['eq:phi1']})
  • Figure 3: Performance of the augmented Karma economy and the three benchmarks RANDOM, TURN, and MAX_EFF across the performance metrics introduced in Section \ref{['subsec:bench']}.

Theorems & Definitions (2)

  • Definition 1
  • Theorem 1