PhD in Mathematics

Agentic AI is rapidly affecting diverse aspects of our life, including social, technological and financial interactions. They may seem like human agents, yet their "thinking" and "reasoning" is not the same. The aim of this project is to study, understand and design the strategic interaction between LLM agents. As Agentic AI is rapidly moving from research labs into the real world, we expect it to affect many aspects of our social, technological, and financial world. A large number of interactions will be mediated via AI systems giving rise to complex multi-human-multi-AI systems. Traditionally, multi-agent interactions are studied through the lenses of Game Theory -- which aims to study the effects of self-interested behaviour, -- and mechanism design -- which aims to align the personal with the collective incentives. Classical game theory offers powerful tools for analysing strategic behaviour, yet assumes fully rational, utility-maximising agents operating in well-defined games. In contrast, large language model (LLM) agents reason via learned heuristics, finite context windows, prompts, and training data rather than explicit utility optimisation. As a result, classical notions of negotiation, belief formation, and best-response strategies break down when applied to LLM agents. The aim of this project is to study the emergent strategies and stable points as we shift from rational agents to foundation-model-based agents, opening the path to more robust, strategic, and socially aligned Agentic AI. The scope of this project is wide by design, with details to be refined collaboratively with the prospective PhD applicant. Potential applications include market negotiations, collaborative resource allocation, and AI governance simulations. For example, consider the case of Autonomous Supply Chain Negotiation. Multiple LLM agents, each representing different companies or suppliers, could negotiate delivery schedules, prices, and production priorities. These agents can learn and update their beliefs, strategically adjust offers, form coalitions, and negotiate. The School of Electronics & Computer Science is committed to promoting equality, diversity inclusivity as demonstrated by our Athena SWAN award. We welcome all applicants regardless of their gender, ethnicity, disability, sexual orientation or age, and will give full consideration to applicants seeking flexible working patterns and those who have taken a career break. The University has a generous maternity policy, onsite childcare facilities, and offers a range of benefits to help ensure employees’ well-being and work-life balance. The University of Southampton is committed to sustainability and has been awarded the Platinum EcoAward.