Vincent Knight

I am a professor of Mathematics at Cardiff University. My interests are in teaching, research software, Game Theory and applied stochastic modelling.

Latest post

2026-05-26 — An Exact Cooperation Formula for Introspection Dynamics in the Heterogeneous Public Goods Game

Introspection dynamics is a nice population dynamic that was originally formulated in 2022. In this paper Harry, Sebastian and I describe how for some games (which we call "state independent") it can be decomposed allow for an explicit formula for the steady state probabilities.

Teaching

Computing for Mathematics (BSc. Year 1)
Game Theory (BSc. Year 3)
Writing with LaTeX (Any)
Introduction to Object Oriented Programming (MSc.)
Research Software Development (PhD)

Software

Axelrod: A research tool for the study of cooperation.
CoopGt: A library for the study of cooperative game theory.
dwys: A language agnostic doctesting library.
Nashpy: A python library for 2 player games.
nbchkr: A lightweight tool to grade notebook assignements.
Ludics: A Python library for modelling evolutionary processes as Markov chains.
Backstab: A python library for game-theoretic analysis and Monte Carlo simulation of social deduction games in the Traitors/Mafia/Werewolf family.
Sold: A library for the study of auctions.
Stet: Persistent memoization by parameter identity for experiment scripts

Publications (65)

Books

62 Articles

2026: The Vote-Left Equilibrium: A Deterministic Coordination Strategy for the Faithful in The Traitors. Vincent Knight. Preprint.
2026: An Exact Cooperation Formula for Introspection Dynamics in the Heterogeneous Public Goods Game. Harry Foster, Vincent Knight, Sebastian Krapohl. Preprint.
2025: Reviving, reproducing, and revisiting Axelrod's second tournament. Vincent Knight, Owen Campbell, Marc Harper, Tj Gaffney, Nikoleta Glynatsi. Preprint.
2025: Extortionist Trade Policies in a Multipolar World: The Rationale Behind the US Trade Policy Under Donald Trump. Submitted to the Journal of Theoretical Politics. Sebastian Krapohl, Vincent Knight.
2025: Modelling Spatio-Temporal Progression of Cyberattacks in Data Networks. IEEE BCCA-CERC Workshop 2025. Malik Shahzad Kaleem Awan, Vincent Knight, Omer Rana, Pete Burnap.
2025: On the Optimisation of Heterogeneous Ambulance Fleet Allocations. IMA Journal of Management Mathematics. Geraint Palmer, Mark Tuson, Vincent Knight, Paul Harper, Syaribah Noor Brice, Leanne Smith, Daniel Gartner.
2025: Queues Under Stochastic Priority Switching. Journal of the Operational Research Society. Geraint Palmer, Michalis Panayides, Vincent Knight, Elizabeth Williams.
2025: Optimizing healthcare queues: a case study on chronic respiratory illness. IMA Journal of Management Mathematics. Henry Wilde, Vincent Knight, Jon Gillard, Kendal Smith. Preprint.
2025: Transforming emergency and urgent care services with mathematical modelling. More UK Success Stories in Industrial Mathematics. Paul Harper, Daniel Gartner, Vincent Knight, Geraint Palmer, Mark Tuson.
2024: A Close-Up on Ambulance Service Estimation in Indonesia Using Monte Carlo Simulation. Interactive Journal of Medical Research. Syaribah Noor Brice, Justin Boutilier, Paul Harper, Geraint Palmer, Vincent Knight, Mark Tuson, Daniel Gartner.
2024: Properties of Winning Iterated Prisoner’s Dilemma Strategies. Plos Computational Biology. Nikoleta Glynatsi, Vincent Knight, Marc Harper. Preprint.
2024: Recognising and evaluating the effectiveness of extortion in the Iterated Prisoner's Dilemma. PLOS One. Vincent Knight, Marc Harper, Nikoleta Glynatsi, Jon Gillard. Preprint.
2023: A novel initialisation based on hospital-resident assignment for the k-modes algorithm. Accepted in Soft Computing (SOCO). Henry Wilde, Vincent Knight, Jon Gillard. Preprint.
2023: Optimising Heterogeneous Ambulance Fleet Allocations in Jakarta. European Journal of Operational Research. Geraint Palmer, Mark Tuson, Vincent Knight, Paul Harper, Syaribah Noor Brice, Leanne Smith, Daniel Gartner.
2022: A game theoretic model of the behavioural gaming that takes place at the EMS - ED interface. European Journal of Operational Research. Michalis Panayides, Vincent Knight, Paul Harper.
2022: Emergency services utilization in Jakarta (Indonesia): a cross-sectional study of patients attending hospital emergency departments. BMC Health Services Research. Syaribah Noor Brice, Justin Boutilier, Daniel Gartner, Paul Harper, Vincent Knight, Jen Lloyd, Aryono Djuned Pusponegoro, Asti Puspita Rini, Jonathan Turnbull Ross, Mark Tuson.
2021: A bibliometric study of research topics, collaboration and centrality in the Iterated Prisoner's Dilemma. Humanities and Social Sciences Communications. Nikoleta Glynatsi, Vincent Knight. Preprint.
2021: Game Theory and Python: An educational tutorial to game theory and repeated games using Python. Journal of Open Source Education. Vincent Knight, Nikoleta Glynatsi.
2021: Modelling changes in healthcare demand through geographic data extrapolation. Health Systems. Geraint Palmer, Paul Harper, Vincent Knight, Cathy Brooks.
2020: Evolutionary Dataset Optimisation: Learning algorithm quality through evolution. Applied Intelligence. Henry Wilde, Vincent Knight, Jon Gillard. Preprint.
2020: Matching: A Python library for solving matching games. Journal of Open Source Software. Henry Wilde, Vincent Knight, Jon Gillard.
2020: Using a theory of mind to find best responses to memory-one strategies. Accepted for publication in Scientific Reports. Nikoleta Glynatsi, Vincent Knight. Preprint.
2019: A conservative index heuristic for routing problems with multiple heterogeneous service facilities. Mathematical Methods of Operations Research. Rob Shone, Vincent Knight, Paul Harper.
2019: Memory depth of finite state machine strategies for the iterated prisoner's dilemma. Tj Gaffney, Marc Harper, Vincent Knight. Preprint.
2018: Determining patient outcomes from patient letters: A comparison of text analysis approaches. Journal of the Operational Research Society. Jennifer Morgan, Paul Harper, Vincent Knight, Andrew Nelson, Andreas Artemiou, Alex Carney.
2018: Evolution Reinforces Cooperation with the Emergence of Self-Recognition Mechanisms: an empirical study of the Moran process for the iterated Prisoner's dilemma . PLOS One. Vincent Knight, Marc Harper, Nikoleta Glynatsi, Owen Campbell. Preprint.
2018: Nashpy: a Python library for the computation of Nash equilibria. Journal of Open Source Software. Vincent Knight, James Campbell. Preprint.
2017: An Evolutionary Game Theoretic Model of Rhino Horn Devaluation. Ecological Modelling. Nikoleta Glynatsi, Vincent Knight, Tamsin Lee. Preprint.
2017: Ciw: An open source discrete event simulation library. Journal of Simulation. Geraint Palmer, Vincent Knight, Paul Harper, Asyl Hawa. Preprint.
2017: Modelling deadlock in open restricted queueing networks. European Journal of Operational Research. Geraint Palmer, Paul Harper, Vincent Knight.
2017: Predicting Adolescent Social Networks to Stop Smoking in Secondary Schools. European Journal of Operational Research. Angelico Fetta, Vincent Knight, Paul Harper, Janet Williams.
2017: Reinforcement Learning Produces Dominant Strategies for the Iterated Prisoner's Dilemma. PLOS One. Marc Harper, Vincent Knight, Martin Jones, Georgios Koutsovoulos, Nikoleta Glynatsi, Owen Campbell. Preprint.
2016: Ambulance Allocations for Maximising Survival within a Heterogeneous Population using a Heterogeneous Fleet. Submitted to the journal of the operational research society. Leanne Smith, Paul Harper, Vincent Knight.
2016: An Open Framework for the Reproducible Study of the Iterated Prisoner’s Dilemma. Journal of open research software. Vincent Knight, Owen Campbell, Marc Harper, Karol Langner, James Campbell, Thomas Campbell, Alex Carney, Martin Chorley, Cameron Davidson Pilon, Kristian Glass, Nikoleta Glynatsi, tomáš-ehrlich, Martin Jones, Georgios Koutsovoulos, Holly Tibble, jochen-müller, Geraint Palmer, Piotr Petunov, Paul Slavin, Timothy Standen, Luis Visintini, Karl Molden.. Preprint.
2016: Editorial: Health Systems ESI XXXI — OR applied to Health in a Modern World. Operations Research for Health Care, 5, 3. Roberto Aringhieri, Vincent Knight, Honora Smith.
2016: Editorial: Operations Research for Health Care ESI XXXI — OR applied to Health in a Modern World. Operations Research for Health Care, 8, 22–23. Roberto Aringhieri, Vincent Knight, Honora Smith.
2016: Measuring the Price of Anarchy in Critical Care Unit Interactions. The journal of the operational research society. Vincent Knight, Izabela Komenda, Jeff Griffiths.
2016: Time-dependent stochastic methods for managing and scheduling Emergency Medical Services. Operations Research for Health Care. Julie Vile, Jon Gillard, Paul Harper, Vincent Knight.
2015: Compliance with National Guidelines for Stroke in Radiology. Operations Research for Health Care. Izabela Komenda, Hannah Williams, Vincent Knight.
2015: Containment of socially optimal policies in multiple-facility Markovian queueing systems. Journal of the Operational Research Society. Rob Shone, Vincent Knight, Paul Harper, Janet Williams, John Minty.
2015: Modelling of psoriasis patient flows for the reconfiguration of secondary care services and treatments. Health Systems. Kayne Putman, Alex Anstey, Paul Harper, Vincent Knight.
2015: Playing games: a case study in active learning applied to Game Theory. Connections. Vincent Knight.
2015: Rostering staff at a mathematics support service using a finite-source queueing model. IMA Journal of Management Mathematics. 27 (2). Jon Gillard, Vincent Knight, Julie Vile, Rob Wilson.
2014: Mathematical modelling of patient flows to predict critical care capacity required following the merger of two district general hospitals into one. Anaesthesia. 70 (1). James Williams, Steve Dumont, Jack Parry Jones, Izabela Komenda, Jeff Griffiths, Vincent Knight.
2014: Operational research ambassadors in schools. Proceedings of the HEA STEM, Edinburgh 2014. Noel Ann Bradshaw, Paul Harper, Vincent Knight, Louise Orpin.
2014: Tweeting the Terror: Modelling the Social Media Reaction to the Woolwich Terrorist Attack. Social Network Analysis and Mining. Peter Burnap, Matthew Williams, Luke Sloan, Omer Rana, Will Housley, Adam Edwards, Vincent Knight, Rob Procter, Alex Voss.
2013: Comparisons between observable and unobservable M/M/1 queues with respect to optimal customer behavior. European Journal of Operational Research. Rob Shone, Vincent Knight, Janet Williams.
2013: Selfish routing in public services. European Journal of Operational Research. 230 (1) 122-132. Vincent Knight, Paul Harper.
2013: Using Singular Spectrum Analysis to Obtain Staffing Level Requirements in Healthcare. Journal of the Operational Research Society. Vincent Knight, Jon Gillard.
2012: Ambulance Allocation for Maximal Survival with Heterogeneous Outcome Measures. OMEGA - The International Journal of Management Science. 40 (6) 918--926. Vincent Knight, Paul Harper, Leanne Smith.
2012: Discrete Conditional Phase-Type Models Utilising Classification Trees: Application to Modelling Health Service Capacities. European Journal of Operational Research. 219 (3) 522--530. Paul Harper, Vincent Knight, Adele Marshall.
2012: How Efficient can an Emergency Unit be? A Perfect World Model. Emergency Medicine Journal. Kesh Baboolal, Jeff Griffiths, Vincent Knight, Andrew Nelson, Cheryl Voake, Janet Williams.
2012: Modelling Emergency Medical Services with Phase Type Distributions. Health Systems. 1 53-68. Vincent Knight, Paul Harper.
2012: Simulating Bed Capacity: Evaluating the Impact of Healthcare Service Transfers. IEEE UKSim 14th International Conference on Computer Modelling and Simulation. Robert Bares, Jeff Griffiths, Vincent Knight, Janet Williams, Kesh Baboolal, Andrew Nelson.
2011: Bed Management in a Critical Care Unit. IMA Journal of Management Mathematics. Jeff Griffiths, Vincent Knight, Izabela Komenda.
2011: Cost-Effective Workforce Planning: Optimising the Dental Team Skill-Mix for England. Journal of Enterprise Information Management. Paul Harper, E Kleinman, Jenny Gallagher, Vincent Knight.
2011: Forecasting Welsh Ambulance Demand using Singular Spectrum Analysis. In Journal of the Operational Research Society. Janet Williams, Jon Gillard, Paul Harper, Vincent Knight.
2011: Modelling Patient Choice in Healthcare Systems: Development and Application of a Discrete Event Simulation with Agent-Based Functionality. Journal of Simulation. Vincent Knight, Janet Williams, Iain Reynolds.
2011: On the Peter Principle: An Agent Based Investigation into the Consequential Effects of Social Networks and Behavioural Factors. Physica A: Statistical Mechanics and its Applications. Angelico Fetta, Paul Harper, Vincent Knight, Janet Williams, Israel Vieira.
2011: Operational Research Informing National Health Policy. Cardiff University. ISBN: 978-0-9569158-0-1. Paul Harper, Vincent Knight, Israel Vieira, Janet Williams.
2010: Forecasting Welsh Ambulance Demand using Singular Spectrum Analysis. In Proceedings of the XXXVI International ORAHS Conference. Janet Williams, Jon Gillard, Paul Harper, Vincent Knight.
2008: Higher Spin Alternating Sign Matrices. Electronic Journal of Combinatorics. 14(1): R83, 38pp. Roger Behrend, Vincent Knight. Preprint.