# Personalized incentives as feedback design in generalized Nash equilibrium problems

arXiv: https://arxiv.org/abs/2203.12948 · HTML: https://mlsanity.com/paper/2203.12948/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 69 references that are in the map.
- First posted on arXiv 24 Mar 2022.

## Builds on (most cited first, 27 of 27)

- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Online Optimization : Competing with Dynamic Comparators](https://mlsanity.com/paper/1501.06225/) (2015)
- [Learning in games with continuous action sets and unknown payoff functions](https://mlsanity.com/paper/1608.07310/) (2016)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Distributed Online Optimization in Dynamic Environments Using Mirror Descent](https://mlsanity.com/paper/1609.02845/) (2016)
- [Convergence of a Stochastic Gradient Method with Momentum for Non-Smooth Non-Convex Optimization](https://mlsanity.com/paper/2002.05466/) (2020)
- [Online Optimization with Predictions and Switching Costs: Fast Algorithms and the Fundamental Limit](https://mlsanity.com/paper/1801.07780/) (2018)
- [Online Learning with Inexact Proximal Online Gradient Descent Algorithms](https://mlsanity.com/paper/1806.00202/) (2018)
- [Multi-agent online learning in time-varying games](https://mlsanity.com/paper/1809.03066/) (2018)
- [Optimization and Learning with Information Streams: Time-varying Algorithms and Applications](https://mlsanity.com/paper/1910.08123/) (2019)
- [Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications](https://mlsanity.com/paper/1601.04059/) (2016)
- [Distributed Nash Equilibrium Seeking by A Consensus Based Approach](https://mlsanity.com/paper/1602.00771/) (2016)
- [Distributed Personalized Gradient Tracking with Convex Parametric Models](https://mlsanity.com/paper/2008.04363/) (2020)
- [An Existence Result for Hierarchical Stackelberg v/s Stackelberg Games](https://mlsanity.com/paper/1401.0186/) (2013)
- [Asynchronous Schemes for Stochastic and Misspecified Potential Games and Nonconvex Optimization](https://mlsanity.com/paper/1711.03963/) (2017)
- [Personalized Optimization with User's Feedback](https://mlsanity.com/paper/1905.00775/) (2019)
- [Charging plug-in electric vehicles as a mixed-integer aggregative game](https://mlsanity.com/paper/1910.10272/) (2019)
- [Time-Varying Optimization of Networked Systems with Human Preferences](https://mlsanity.com/paper/2103.13470/) (2021)
- [Distributed Nash Equilibrium Seeking under Partial-Decision Information via the Alternating Direction Method of Multipliers](https://mlsanity.com/paper/1707.01965/) (2017)
- [Local Stackelberg equilibrium seeking in generalized aggregative games](https://mlsanity.com/paper/2006.03916/) (2020)
- [Solving non-monotone equilibrium problems via a DIRECT-type approach](https://mlsanity.com/paper/2002.12198/) (2020)
- [Personalized Demand Response via Shape-Constrained Online Learning](https://mlsanity.com/paper/2006.06932/) (2020)
- [On the exact convergence to Nash equilibrium in hypomonotone regimes under full and partial-information](https://mlsanity.com/paper/2104.11096/) (2021)
- [Learning equilibria with personalized incentives in a class of nonmonotone games](https://mlsanity.com/paper/2111.03854/) (2021)
- [On the needs for MaaS platforms to handle competition in ridesharing mobility](https://mlsanity.com/paper/1906.07567/) (2019)
- [Coordinated Online Learning for Multi-Agent Systems with Coupled Constraints and Perturbed Utility Observations](https://mlsanity.com/paper/2010.10878/) (2020)

## Built on by (most cited first, 1 of 1)

- [An active learning method for solving competitive multi-agent decision-making and control problems](https://mlsanity.com/paper/2212.12561/) (2022)

## Abstract (arXiv)

We investigate both stationary and time-varying, nonmonotone generalized Nash equilibrium problems that exhibit symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, however, we envision a scenario in which the formal expression of the underlying potential function is not available, and we design a semi-decentralized Nash equilibrium seeking algorithm. In the proposed two-layer scheme, a coordinator iteratively integrates the (possibly noisy and sporadic) agents' feedback to learn the pseudo-gradients of the agents, and then design personalized incentives for them. On their side, the agents receive those personalized incentives, compute a solution to an extended game, and then return feedback measurements to the coordinator. In the stationary setting, our algorithm returns a Nash equilibrium in case the coordinator is endowed with standard learning policies, while it returns a Nash equilibrium up to a constant, yet adjustable, error in the time-varying case. As a motivating application, we consider the ridehailing service provided by several companies with mobility as a service orchestration, necessary to both handle competition among firms and avoid traffic congestion, which is also adopted to run numerical experiments verifying our results.