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
Advised by Prof. Wenjun Mei.
Research theme
Modeling and Analysis of Multi-Agent Systems
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 mathematical modeling and dynamic analysis.
My research focuses on 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.
- How do individual agents influence each other's states and collective behaviors?
- How do fairness preferences shape coordination and system behavior?
- 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
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