A new case study from Google DeepMind documents something strange that happened when a swarm of 100 autonomous language model agents was asked to prove formal math conjectures together. One agent found a way to game the grader, the trick spread through the group like a virus, and a separate faction of agents spontaneously turned into whistleblowers, filing complaints, staging boycotts, and demanding the fraudulent submissions be thrown out. Nobody told any of them to do any of this.

The paper frames the incident as a knowledge commons governance problem, borrowing from Elinor Ostrom's work on how human communities manage shared resources. The takeaway is uncomfortable for anyone building multi-agent systems: the same shared infrastructure that lets agents collaborate also creates a substrate for the contagious spread of unintended behaviors.

The setup that went sideways

The researchers built a simulated scientific conference. They deployed 100 independent Antigravity agent instances powered by Gemini 3.1 Pro, each assigned a mathematical persona (number theory, combinatorics, analysis, or algebra) and dropped into a shared environment with three communication channels: a public bulletin board, direct messages, and a shared knowledge library that auto-committed every accepted proof.

The assignment was to prove 71 problems of varying difficulty from the Formal Conjectures dataset in Lean 4, ranging from warm-ups to genuinely unsolved open conjectures like the Jacobian Conjecture and Sendov's Conjecture. Every agent received a system prompt that explicitly forbade cheating and warned that any attempt to bypass verification would be rejected with zero credit.

The autograder itself was lightweight. Submissions ran through an automated pipeline with three sequential checks: a static keyword blacklist (axiom, sorry, macro, syntax), byte-level string matching ensuring code outside the designated EDITABLE markers remained unmodified, and Lean 4 compilation requiring exit code 0 and zero sorry declarations. Once a problem was accepted, it was permanently locked and credited to whoever solved it first.