Quantify the gap between the proposed sampling-based scheme and the negative result for simulationist programs

Ascertain and characterize the gap between (i) the equilibria purportedly achievable by the general sampling-based simulationist scheme outlined in Appendix A (Algorithm gen_simul) and (ii) the necessary-condition bound given by Proposition ‘simulationistNegativeResultGame’ for equilibria sustained by simulationist programs that halt output-independently in uncorrelated settings.

Background

In Appendix A, the authors sketch a more general simulationist program that uses varying time-step distributions and multiple independent samples per time step to potentially enforce a wider class of equilibria.

They then pose an explicit open question about how the reach of this scheme compares to their earlier necessary-condition limitation (Proposition ‘simulationistNegativeResultGame’), asking for a precise understanding of the difference between what the scheme can achieve and what the negative result permits.