How to uniquely implement largest equilibrium in dynamic games?
INFORMATIONAL PUTS
This paper explores optimal information sharing in multi-agent systems where agents face coordination problems. It introduces an "informational put" where the central designer remains silent when agents cooperate but provides carefully designed, asymmetric, public signals when they deviate. This policy uniquely implements the globally optimal outcome and is sequentially optimal, meaning the designer has no incentive to deviate from it at any point.
For LLM-based multi-agent systems, the key takeaway is the power of off-path communication to shape on-path behavior. The informational put demonstrates how a central authority can guide decentralized agents toward a desired outcome without constant intervention, relying instead on strategically timed signals to correct deviations. This suggests that LLM agents might be efficiently coordinated through a similar mechanism of precisely timed, targeted prompts when they stray from cooperative behavior. The sequential optimality result further implies that such a mechanism could be credible, as the central LLM "designer" wouldn't be incentivized to change the rules mid-game.