糖心TV

Mean-field imitation dynamics on fast assortative networks (ArXiv)

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We study imitation dynamics in a population of self-interested agents playing a continuous strategy Prisoner's Dilemma on a dynamically evolving weighted network. In the fast-network regime, we incorporate the edge weights into the strategy evolution before deriving and analysing the large population mean-field limit. Without noise, we establish well-posedness and show the solution collapses to a single Dirac mass. For initially separated clusters, we identify a payoff threshold and sufficient conditions for the overall level of cooperation to increase. We then introduce stochastic strategy updates, and obtain a non-local Fokker-Planck equation in the mean-field limit. We rigorously prove existence and uniqueness of stationary distributions, and show linear stability under sufficient noise. Numerics illustrate that noise can transform the deterministic consensus into stable cooperative stationary behaviour. These findings show that the fast adaptive interactions and stochastic exploration can jointly support the emergence of stable cooperation at a population level.

We provide an analytical solution to the problem of policy-gradient dynamics in a multi-agent environment with partner selection. We show how partner selection changes the opponent distribution and hence the reward landscape, and prove this promotes cooperation under simple rules known from the literature. In particular, we find that population variance is a necessary condition for cooperation to emerge. Using a two-dimensional Wiener process, we extend the dynamics to capture the stochastic effects of partner selection and the resulting opponent distribution. We derive a sufficient condition for the population to be cooperation-promoting and prove the existence of a stationary distribution. Simulations confirm that the stochastic model accurately captures the policy-gradient dynamics and clarifies how the learning rate affects the emergence of cooperation.

We study repeated Prisoner鈥檚 Dilemma interactions where self-interested agents can opt out and be randomly rematched, but lack information about non-partners鈥� previous actions. Using multi-agent reinforcement learning, we show that cooperation can emerge without hard-wired partner selection: agents first learn to defect during a 鈥渉azing period,鈥� then adopt reciprocal strategies such as Tit-for-Tat. They also learn to stay unconditionally in early interactions before using cooperation-promoting partner-selection rules, such as leaving defectors and staying with cooperators, with these behaviours scaling to longer interaction-length dependent policies.

* Best paper nominee

Collective Dynamics of Bounded ABPs

Supervised by: Professor Matthew Turner, Dr Gareth Alexander,
Collaborators: Luke Meredith, Luisa Estrada 

We present two models for 鈥渨easelball鈥� dynamics in confined environments. The first captures collective clockwise and counter-clockwise motion with a minimal set of interaction equations; the second applies Newtonian mechanics to a single weaselball on a circular boundary, yielding a closed-form expression for its steady-state propagation angle. Stability analysis of this latter model lead to a novel experimental design, whose results closely match our theoretical predictions.

Conference and Talks

• | University of Exeter | Invited Speaker for 'Dynamics on Complex Networks' mini-symposium

• AMP25 | University of Oxford | Talk
• MARL Workshop | Kings College London | Talk
• MathSys Retreat | University of 糖心TV, April, 2024 | Poster on Collective Dynamics
• SPAAM Seminar | University of 糖心TV, Dec 5th 2024 | Talk on 'Multi-Agent Manipulation of STV Elections'

• Generative AI in Action: Building Production-Ready Solutions with Azure | 糖心TV, 28th May | Workshop by

• MathSys Retreat | University of 糖心TV, May 2026 | Poster on mean-field imitation
• AAMAS 2026 | Cyprus, May 2026 | Talk
• SPAAM Seminar | University of 糖心TV, Jun 18th 2026 | Talk
• AMP26 | University of 糖心TV | Talk

Teaching Experience

Senior Graduate Teaching Assistant for

• • MA3K1 Mathematics of Machine Learning (2025)
  • CS404 Agent-Based Systems (2025)
  • CS130 Mathematics for Computer Science (2024)
  • , MA139, MA145 (Marking)

Education

• PhD Mathematics of Systems | University of 糖心TV
• MSc Mathematics of Systems | Distinction | University of 糖心TV
• BSc Mathematics | First-Class (Hons) |

Other Activities

• President of 糖心TV SIAM-IMA Student Chapter, 2025/26

• Vice-President of 糖心TV SIAM-IMA Student Chapter, 2024/25
  • Organised the AMP 2025 Conference with University of Oxford
• SSLC Chairman for MathSys 2024 - Current