Extension of CURB’s Formal Analysis to More Than Two Players

Extend the formal guarantees for CURB, the TV-distance reward-shaping framework for eliminating punishment-based collusion, from two-player repeated games to repeated games with more than two players.

Background

The paper’s formal guarantees concern two-player collusion in repeated games. CURB detects punishment-based collusion through differences in an agent’s conditional action distributions after cooperation and defection, measured by total variation distance, and uses reward shaping to eliminate non-trivial Simple Penal Code fixed points when the penalty is sufficiently large.

Although the algorithm includes a maximum-TV penalty intended to extend operationally to more than two agents and the experiments include a three-agent Bertrand setting, the authors explicitly state that the corresponding formal analysis for games with more than two players has not been established. The unresolved problem is therefore to generalize the theoretical guarantees, including the detection and fixed-point results, beyond the two-player case.