Benedict Russell

The Dynamics of Policy Gradient in Social Dilemmas with Partner Selection (ArXiv)

Paolo Turrini & Chin-wing Leung

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.

Learning partner selection in optional social dilemmas without prior information (AAMAS 2026)

Paolo Turrini & Chin-wing Leung

We study repeated Prisoner’s Dilemma interactions where self-interested agents can opt out and be randomly rematched, but lack information about non-partners’ 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 “hazing period,” 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.

Collective Dynamics of Bounded ABPs

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

We present two models for “weaselball” 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

• BMC-BAMC | 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 Warwick, April, 2024 | Poster on Collective Dynamics
• SPAAM Seminar | University of Warwick, Dec 5th 2024 | Talk on 'Multi-Agent Manipulation of STV Elections'

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

• MathSys Retreat | University of Warwick, May, 2026 | Poster on mean-field imitation

Teaching Experience

Senior Graduate Teaching Assistant for

• • MA3K1 Mathematics of Machine Learning (2025)
  • CS404 Agent-Based Systems (2025)
  • CS130 Mathematics for Computer Science (2024)
  • MA146, MA139, MA145 (Marking)

Education

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

Other Activities

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

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