An Event-Triggered Distributed Generalized Nash Equilibrium Seeking Algorithm

Deployment of multiple radio access technologies (RATs) at the same cell site enables the system to flexibly support different types of devices and services. Such multi-RAT systems call for an efficient utilization of the system resources as well as simplified management. In this paper, we take a user-centric approach and let each individual user equipment decide its own access strategy in a multi-RAT system with regulated interference constraints. The formulated problem is a generalized Nash equilibrium (GNE) problem. We show that there always exists a GNE but its uniqueness is not guaranteed. A closed form solution is provided to characterize a special class of the GNEs. We then propose a primal-dual algorithm with detailed convergence analysis for computing a GNE. The proposed algorithm may have practical implications in the design of multi-RAT systems.

In this paper, we study the generalized Nash equilibrium (GNE) seeking problem for an N-coalition game with inequality constraints. First, using full decision information, a finite-time average consensus-based approach is proposed. It is demonstrated that the algorithm converges to a GNE (specifically, a variational equilibrium) of the game. Then, using the finite-time consensus tracking technique, we propose a distributed algorithm that only requires neighboring action information for each agent. The solution by using partial decision information covers the distributed GNE seeking solutions of generalized non-cooperative games as a special case.

In generalized Nash equilibrium (GNE) seeking problems over physical networks such as power grids, the enforcement of network constraints and time-varying environment may bring high computational costs. Developing online algorithms is recognized as a promising method to cope with this challenge, where the task of computing system states is replaced by directly using measured values from the physical network. In this paper, we propose an online distributed algorithm via measurement feedback to track the GNE in a time-varying networked resource sharing market. Regarding that some system states are not measurable and measurement noise always exists, a dynamic state estimator is incorporated based on a Kalman filter, rendering a closed-loop dynamics of measurement-feedback driven online algorithm. We prove that, with a fixed step size, this online algorithm converges to a neighborhood of the GNE in expectation. Numerical simulations validate the theoretical results.

With the development of cloud computing, heterogeneous service providers can publish services in the cloud market under the multi-cloud environment. As the cloud market expands, the relationship between service providers and users is changing. Users as rational individuals are no longer limited to choosing a single service provider, but observe the dynamic changes of services in the multi-cloud service market and choose services with better utilities; service providers need to consider the service selected situation in the market, and adjust service providing strategies to win the market share competition. It has been a great challenge for multi-cloud service providers to develop an effective service provisioning strategy according to the service changing utilities, user's service choice behavior, etc. This paper uses a non-cooperative game theory to study this service provisioning problem in multi-cloud competitions. The contributions are: (1) referring to the market economic theory, the changes of the service quality are added to the user choice model and described the influence to the multi-cloud competitions; (2) using the game theory, the problem is transformed into the GNEP (Generalized Nash Equilibrium Problem); (3) The existence of the GNE (Generalized Nash Equilibrium) solution is proved and an algorithm is proposed for providers to obtain the best market share and make the provisioning strategy. At last, we conduct simulation experiments on Matlab. The results show that the GNE method can improve the cloud service market share of providers and help providers propose effective service provisioning strategies.

We propose a new solution concept for generalized Nash equilibrium problems. This concept leads, under suitable assumptions, to unique solutions, which are generalized Nash equilibria and the result of a mathematical procedure modeling the process of finding a compromise. We first compute the favorite strategy for each player, if he could dictate the game, and use the best response on the others’ favorite strategies as starting point. Then, we perform a tracing procedure, where we solve parametrized generalized Nash equilibrium problems, in which the players reduce the weight on the best possible and increase the weight on the current strategies of the others. Finally, we define the limiting points of this tracing procedure as solutions. Under our assumptions, the new concept selects one reasonable out of typically infinitely many generalized Nash equilibria.

Generalized Nash equilibrium seeking algorithm design for distributed constrained noncooperative games with second-order players

Device-to-device (D2D)-enabled mobile edge computing (MEC) is an emerging technology which has been widely investigated in terrestrial networks. Different from most existing relevant work, where the network is base station-assisted and offloadings are made on homogeneous channels, this paper focuses on an unmanned aerial vehicle (UAV) swarm, where both the decentralized character and the heterogeneous data computation demands are considered. To fully utilize the limited time, spectrum and computation resources, the joint computation offloading and variable-width channel access problem is investigated. The problem is solved by a game-theoretic based solution. Specifically, the problem is first formulated into a game model which is proved to be an exact constrained potential game (ECPG). The game has at least one pure strategy generalized Nash equilibrium (GNE) and the best GNE is the global optimum of the problem. After that, to enable the UAV swarm reach the GNE autonomously, a distributed collective best response (COBR) algorithm is then proposed. The algorithm can converge to a GNE of the game, which is the local or global optimum of the proposed problem. Simulation results show that the proposed method can save about 10% energy than offloading on homogeneous channels.

We address the generalized Nash equilibrium seeking problem for a population of noncooperative agents playing potential games with linear coupling constraints over a communication network. We consider a class of generalized potential games where the coupling in the cost functions of the agents is linear, i.e., $J_{i}(x_{i}, x_{-i}): =f_{i}(x_{i})+\ell_{i}(x_{-i})^{\top}x_{i}$ where $\ell_{i}$ is linear. By exploiting this special structure, we design a distributed algorithm with convergence guarantee under mild assumptions, i.e., (non-strict) monotonicity of the pseudo-subdifferential mapping. The potential of the proposed algorithm is shown via numerical simulations on a networked Nash Cournot game, where we observe faster convergence with respect to standard projected pseudo-gradient algorithms.

The problem of seeking Nash equilibrium (NE) based on aggregative games under quantization constraints is full of challenges. Although the NE seeking algorithm in continuous-time systems has been studied, this problem in discrete-time systems still needs to be solved urgently. To address this problem, three distributed algorithms are first proposed under three quantization cases, adaptive, random, and time-varying quantizations, based on doubly stochastic communication topology networks. Then, the actions of players would eventually converge to NE under the conditions of vanishing step size and strong monotonicity are proved. Moreover, the convergence rate of the three quantization cases are analyzed, respectively. Finally, numerical experiments are implemented on plug-in hybrid electric vehicles (PHEVs) to validate the effectiveness of the proposed distributed algorithms. Comparing the convergence rates of the three proposed algorithms, the convergence effect of the adaptive quantization is better than that of the other two quantization cases.

We address the Nash equilibrium problem in a partial-decision information scenario, where each agent can only observe the actions of some neighbors, while its cost possibly depends on the strategies of other agents. Our main contribution is the design of a fully-distributed, single-layer, fixed-step algorithm, based on a proximal best-response augmented with consensus terms. To derive our algorithm, we follow an operator-theoretic approach. First, we recast the Nash equilibrium problem as that of finding a zero of a monotone operator. Then, we demonstrate that the resulting inclusion can be solved in a fully-distributed way via a proximal-point method, thanks to the use of a novel preconditioning matrix. Under strong monotonicity and Lipschitz continuity of the game mapping, we prove linear convergence of our algorithm to a Nash equilibrium. Furthermore, we show that our method outperforms the fastest known gradient-based schemes, both in terms of guaranteed convergence rate, via theoretical analysis, and in practice, via numerical simulations.

In major cities, with the rapid urbanization and population growth, sustainable development has become a pressing global concern, leading to increasing traffic congestion, energy consumption, and environmental pollution. The transportation sector, responsible for nearly a quarter of global energy-related emissions, plays a vital role in addressing these issues. In response, numerous international frameworks have emphasized the need for cleaner, more efficient mobility solutions. In this context, shared mobility has emerged as a promising solution, bridging private car ownership and public transit to reduce emissions and promote efficiency. This thesis investigates two representative forms of shared mobility: electric vehicle carsharing (EVCS) and collaborative passenger-parcel ridesharing (CPPR), with a focus on operational optimization to support sustainable and economically viable urban mobility. The first two works in this thesis examine EVCS. The first study addresses station-based EVCS in a competitive market. A Generalized Nash Equilibrium (GNE) framework is formulated, where companies compete for limited infrastructure and user demand while jointly optimizing facility deployment, vehicle allocation, relocation, and vehicle-trip assignment. In addition, the study incorporates the role of government by proposing a bi-level model: the upper level represents the government's objective to maximize social welfare through infrastructure planning, while the lower level captures operator competition via the GNE framework. A surrogate optimization approach is adopted to solve the bi-level model, with an ADMM-based algorithm embedded at the lower level for efficient GNE computation. To further enhance carsharing flexibility, the second study focuses on free-floating EV carsharing systems with battery swapping (FEVCS-BS). Unlike the station-based mode, free-floating allows users to pick up and return vehicles at any location within the service area, offering greater convenience. However, this flexibility introduces operational challenges. The absence of fixed returning charging stations and the limited driving range of EVs makes vehicle relocation unavoidable for both vehicle recharging and rebalancing. To address this, two relocation strategies are considered: user-based relocation, driven by pricing incentives, and staff-based relocation, carried out by operational personnel. A mixed-integer nonlinear programming (MINLP) model is developed to capture users’ price-incentivized behavior and to jointly optimize hybrid relocation, fleet size, vehicle allocation, and trip assignment for profit maximization. An outer-inner approximation method with range reduction is applied to solve the nonconvex model and obtain a global optimum. Building on this foundation, the next two studies shift focus to another key form of shared mobility—ridesharing, where individual travelers with similar routes share a vehicle and split travel costs. However, conventional ridesharing often overlooks unused trunk space, missing the opportunity to fully utilize vehicle capacity. To address this inefficiency, we explore an innovative mode: collaborative passenger-parcel ridesharing (CPPR), which enables the joint transportation of passengers and parcels in the same vehicle. The third study explores the routing problem in CPPR while incorporating compensation affected passenger behavior. In this innovative mode, some passengers may be hesitant to share rides with parcels due to perceived inconvenience. Therefore, an effective compensation mechanism is essential to encourage participation. This study embeds compensation-related behavior into a routing framework and formulates the problem as a Compensation Scheme Design in a Split Delivery Vehicle Routing Problem with Time Windows for CPPR (C-SDVRPTW-CPPR). To solve it efficiently, a Surrogate-based Adaptive Large Neighborhood Search (SOT-ALNS) algorithm is developed to generate near-optimal routing plans. The fourth study extends the CRRP problem into a dynamic demand setting, where travel and delivery requests fluctuate throughout the day. Such an environment requires real-time decision-making while also ensuring long-term profitability. To tackle this, we formulate the Dynamic Vehicle Routing Problem with Time Windows for CPPR (DVRPTW-CPPR) and propose a Deep Reinforcement Learning (DRL) framework with a dynamic encoder-decoder architecture to learn optimal routing policies. In conclusion, this thesis explores the different shared mobility modes, including carsharing and ridesharing, to address critical challenges in operations. Through the proposed models and solution methods, operators can effectively manage operations, thereby supporting sustainability goals, and ensuring profitability of shared mobility services.

This paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of other players. The goal is to find a decision vector that minimizes the cost for each player. Unlike most of the existing algorithms for GNEP, which require full information exchange among all players, this paper considers a more realistic scenario where players can only communicate with a subset of players through a connectivity graph. The proposed algorithm enables each player to estimate the decisions of other players and update their own and others’ estimates through local communication with their neighbors. By introducing a network Lagrangian function and applying the Douglas-Rachford splitting method (DR), the GNEP is reformulated as a zero-finding problem. It is shown that the DR method can find the generalized Nash equilibrium (GNE) of the original problem under some mild conditions.

Privacy impact on generalized Nash equilibrium in peer-to-peer electricity market

Mobile Network Operators (MNO) can reduce their Capital and Operational Expenditure (CAPEX) and (OPEX) with the help of tower sharing approach by utilizing the physical infrastructure equipped by a third party tower provider to expand their network coverage. Moreover, Computing Resource Providers (CRP) are also setting up their micro-datacenters at tower stations to provide the Multi-access Edge Computing (MEC) services by cooperating with tower providers. Since both the communication and computing services contribute to the task offloading in MEC, the resource allocation has become a challenging problem. In this paper, we formulate the joint uplink, downlink, and computing resources allocation problem in which the objectives of both MNOs and CRP are to minimize their OPEX. The task offloading is modeled as a network of queues where the end-to-end latency is calculated based on the performance of the queue network. Then, the formulated problem is transformed into a Generalized Nash Equilibrium Problem (GNEP) to capture the conflicting interests in the resource allocation among MNOs and CRP. To solve the formulated GNEP efficiently, two decentralized algorithms are proposed by introducing the penalty parameters to the coupling constraints. In addition, the convergence and performance of the algorithms on different parameters are analyzed.

The equilibrium selection problem in the variational Generalized Nash Equilibrium Problem (v-GNEP) has been reported as an optimization problem defined over the solution set of v-GNEP, called in this paper the lower-level v-GNEP. However, to make such a selection fair for every player, we have to rely on an unrealistic assumption, that is, the availability of a trusted center that does not induce any bias among players. In this paper, to ensure fairness for every player even in the process of equilibrium selection, we propose a new equilibrium selection problem, named the upper-level v-GNEP. The proposed upper-level v-GNEP is formulated as a v-GNEP defined over the solution set of the lower-level v-GNEP. We also present an iterative algorithm, of guaranteed convergence to a solution of the upper-level v-GNEP, as an application of the hybrid steepest descent method to a fixed point set characterization of the solution of the lower-level v-GNEP. Numerical experiments illustrate the proposed equilibrium selection and algorithm.