Cooperation behavior of L"ob-Safe agents in the Prisoner's Dilemma

Determine whether game-theoretic agents whose epistemic-doxastic reasoning is modeled by the proposed L"ob-Safe logics—Reasonable L"ob-Safe Epistemic Doxastic logic (LSED) and Supported L"ob-Safe Epistemic Doxastic logic (LSED)—would cooperate or defect in the Prisoner's Dilemma, in contrast to agents based on G"odel-L"ob provability logic that have been shown to achieve cooperation.

Background

The paper introduces two multimodal logics aimed at modeling human-like reflective agents that avoid the derivation of L"ob's Theorem, which can cause inconsistency in standard epistemic and doxastic logics. These are called Reasonable L"ob-Safe Epistemic Doxastic logic (LSED) and Supported L"ob-Safe Epistemic Doxastic logic (also denoted LSED).

In contrast, prior work using provability logic (GL) leveraged L"ob's Theorem to enable robust cooperation among program-agents in the Prisoner's Dilemma. The authors suggest their L"ob-Safe logics may provide an alternative foundation for agents, but they do not analyze the strategic outcomes.

The authors explicitly state that the question of whether agents grounded in their L"ob-Safe logics would cooperate or defect remains for future research, indicating an unresolved problem concerning the game-theoretic implications of these logics.