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Existence of simulationist programs achieving certain two-player strategy profiles

Determine whether, for every two-player normal-form game and every strategy profile that is both strictly Pareto optimal in the limit of small deviations and strictly individually rational, there exist simulationist programs (in the uncorrelated setting) that implement that profile as a program equilibrium.

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Background

The authors show that their necessary conditions for enforceability by simulationist programs do not rule out two-player strategy profiles that are strictly Pareto optimal in the limit of small deviations and strictly individually rational.

However, they do not establish that such profiles can always be implemented by simulationist programs. They explicitly identify this existence question as open and mention a potential scheme in Appendix A (Algorithm gen_simul) as a candidate direction.

References

It remains an open question whether there always exist simulationist programs (e.g., perhaps something like \Cref{app:gen_simul_idea}, \Cref{algorithm:gen_simul}) attaining such strategy profiles at equilibrium.

— Characterising Simulation-Based Program Equilibria (2412.14570 - Cooper et al., 19 Dec 2024) in Appendix, Further results on more general simulationist programs (following Theorem ‘noRuleOutPareto’)