Learning and Verifying Complex Games with AI-Assisted Theorem Proving University of Bristol in United Kingdom

This PhD project at the University of Bristol explores the intersection of artificial intelligence, theorem proving, and algorithmic game theory. Recent advances in AI-assisted theorem proving—such as search empowered by large language models, auto-formalisation, and solver-produced certificates—have enabled machines to propose mathematical theory and generate verifiable proofs or counterexamples. These hybrid workflows excel at pattern recognition and are particularly effective in search domains where combinatorial complexity presents significant challenges.

The research will apply these advances to computational social choice and algorithmic game theory, fields concerned with collective and strategic decision making. Many theoretical aspects, such as preference encoding and inter-agent incentives, can be formalised in large but finite combinatorial spaces. These spaces may fail to satisfy certain properties (e.g., stable outcomes), with rare edge cases that are difficult to identify. Traditional computer-aided techniques often reach their limits in such scenarios.

Building on prior work involving linear programming for game construction, the project aims to systematise the human–machine loop, progressing from semi-automated to fully automated construction and certification of complex instances. The research objectives are threefold: (1) Discovery—designing a generator to search spaces of preference profiles or games, surfacing rare combinatorial phenomena using LLM-guided proposals and exact optimisation (LP/MIP) or SAT/SMT encodings; (2) Verification—developing a modular verifier that produces machine-checkable certificates; (3) Explanation—extracting structural patterns to predict similar circumstances in broader contexts.

Key areas of exploration include coalition formation, voting, and matching, with learning loops established between generator and verifier. Expected outcomes are: (1) proof of concept by reconstructing instances/games with properties similar to sophisticated human-created games; (2) tackling open problems with rich combinatorics; (3) deducing theoretical insights to understand the boundary between typical and rare behaviour in complex social decision problems.

The School of Engineering Mathematics and Technology provides a vibrant research environment, with access to interdisciplinary expertise and resources. Applicants should have a strong background in computer science, mathematics, or engineering, with analytical and programming skills. Experience in AI, machine learning, or formal methods is advantageous. The application deadline is May 31, 2026. Funding details are not specified; candidates are encouraged to check the project link for updates.

To apply, submit your application via the University of Bristol portal, including your CV, transcripts, and a personal statement. For informal inquiries, contact the supervisor. See the project link for further information.