Academic profile
Yi Han
Ph.D. Candidate in Control Science and Systems Engineering
Peking University
- Multi-Agent Systems
- Network Dynamics
- Game Theory
- Fairness-aware Optimization
- Mechanism Design
I am a Ph.D. candidate in Control Science and Systems Engineering at Peking University, advised by Prof. Wenjun Mei.
Research theme
Modeling and Analysis of Multi-Agent Systems
My research focuses on mathematical modeling and analysis of multi-agent systems, with particular interests in how autonomous agents interact, learn, compete, and coordinate in complex networks. I develop theoretical frameworks combining dynamical systems, optimization, and game theory to study collective behaviors, resource allocation, fairness-efficiency trade-offs, and strategic decision-making among interacting agents.
Modern systems increasingly consist of multiple autonomous decision-makers whose behaviors are coupled through social interactions, resource constraints, and strategic incentives.
My research aims to understand the underlying mechanisms governing such systems through rigorous mathematical modeling and analysis.
- How do individual agents influence each other's states and collective behaviors?
- How should limited resources be allocated among competing objectives and agents?
- How can appropriate mechanisms and incentives promote desirable long-term outcomes?
Current work
Research Areas
Multi-Agent Interaction and Network Dynamics
Modeling and Analysis of Continuous-Time Weighted-Median Opinion Dynamics
This work studies nonlinear state evolution in social influence networks. We propose a continuous-time weighted-median interaction model, extending discrete weighted-median updating mechanisms into a nonlinear ordinary differential equation framework.
The model captures compromise behavior among interacting agents, where individual states continuously evolve toward the weighted median of neighboring states.
Focus of the analysis
- Existence and uniqueness of system trajectories
- Equilibrium structures and Lyapunov stability
- Global convergence from arbitrary initial conditions
- Graph-theoretic conditions for consensus and disagreement
The analysis combines nonlinear dynamical systems, invariant set theory, and graph-based characterization.
- Multi-agent systems
- Social influence networks
- Consensus dynamics
- Nonlinear dynamical systems
- Graph theory
Fairness-Aware Resource Allocation
The Cost α-Fairness Model: A Unified Framework for Fairness in Cost Allocation
Fairness is a fundamental consideration in resource allocation problems where efficiency and equality must be balanced. This work develops a cost-side α-fairness framework that introduces a unified parameterized objective for cost allocation.
The proposed model continuously interpolates between utilitarian allocation minimizing total cost, inverse proportional fairness, and Min-Max fairness protecting the most disadvantaged agents.
Focus of the analysis
- Theoretical characterization of fairness-efficiency trade-offs
- Interpretation of the α = 1 midpoint
- Price of Fairness and Price of Efficiency analysis
- Worst-case bounds for objective selection
The framework provides a quantitative approach to understanding how different allocation principles affect collective outcomes.
- Fair optimization
- Resource allocation
- Convex optimization
- Efficiency-equality trade-off
- Worst-case analysis
Dynamic Games and Strategic Resource Management
Balancing Sustainability and Output in Renewable-Resource Differential Games via a Fairness-Competition Lever
This work investigates strategic resource exploitation among self-interested agents sharing renewable common-pool resources.
We formulate a two-player differential game where a redistribution parameter controls the incentive structure between fairness-oriented sharing and competition-driven rewards. The study focuses on stationary feedback Nash equilibria and develops a theoretical framework based on Hamilton-Jacobi-Bellman equations, auxiliary dynamical systems, and stable manifold analysis.
Focus of the analysis
- Existence and uniqueness of globally defined continuous feedback Nash equilibria
- Structural characterization of active and inactive regimes
- Comparative statics revealing the trade-off between long-term sustainability and short-term incentives
- Differential games
- Feedback Nash equilibrium
- HJB equations
- Dynamic optimization
- Sustainability
- Mechanism design
Measuring Fairness Preferences
How to Build a “Straight Ruler” That Measures Allocation Fairness?
This work studies how fairness preferences can be quantitatively measured in allocation problems. Instead of treating fairness as a fixed principle, we introduce a γ-fairness framework that characterizes allocations according to their position on the efficiency-equality trade-off frontier.
Focus of the analysis
- A parameterized fairness measurement model
- γ-fair frontier analysis
- Allocation preference identification methods
We further conducted behavioral experiments using allocation scenarios to estimate individual fairness preferences and examine the stability of efficiency-equality attitudes across contexts.
- Fairness measurement
- Behavioral experiments
- Decision theory
- Preference learning
- Optimization
Applied work
Projects
Complex Relationship Networks: Resource Allocation Games and Dynamic Evolution
This project studies resource allocation and dynamic decision-making in complex relationship networks. We constructed signed interaction networks from real-world event data and developed models combining network science, dynamical systems, and game theory.
Contributions
- Developing node state and security-index measurement methods
- Modeling dynamic resource evolution
- Analyzing how network topology and centrality influence system evolution
- Conducting simulations and prediction experiments based on time-varying relationship networks
- Complex networks
- Signed networks
- Dynamic games
- Network evolution
- Data-driven modeling
momoai: Agent Service Marketplace and Evaluation Platform
momoai is an early-stage AI application startup project aiming to build a marketplace for AI agent services. The project explores how agent capabilities can be standardized, evaluated, and exchanged through a trusted service ecosystem.
Contributions
- Product architecture and business model design
- Writing the initial business plan
- Designing workflows for agent service discovery, matching, evaluation, delivery, and feedback
- Developing an evaluation benchmark framework for agent capabilities
Benchmark dimensions
- Performance and stability
- Output consistency
- Cost efficiency
- Reproducibility and version tracking
The platform has completed early-stage transaction validation and accumulated more than 200 active users.
- AI agents
- Benchmarking
- AI product design
- Evaluation systems
- Marketplace mechanisms
Research output
Selected Publications & Presentations
-
Modeling and Analysis of Continuous-Time Weighted-Median Opinion Dynamics
Submitted to IEEE Transactions on Automatic Control.
-
The Cost α-Fairness Model: A Unified Framework for Fairness in Cost Allocation
Submitted to Operations Research Letters.
-
Balancing Sustainability and Output in Renewable-Resource Differential Games via a Fairness-Competition Lever
To be presented at the 23rd IFAC World Congress, Busan, Republic of Korea, 2026.
-
How to Build a “Straight Ruler” That Measures Allocation Fairness?
Workshop Presentation, IEEE CDC 2025, Rio de Janeiro, Brazil.
Methods
Skills
Mathematical Methods
- Multi-Agent Systems
- Nonlinear Dynamical Systems
- Consensus and Network Dynamics
- Game Theory
- Differential Games
- Optimization Theory
- Convex Analysis
- Mechanism Design
Technical Tools
- Python
- MATLAB
- LaTeX
- Numerical Simulation
- Network Analysis
- Data-driven Modeling
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