Characterize equilibria attainable by simulation-based programs without shared randomness

Characterize exactly which equilibrium outcomes (or payoff profiles) can be implemented as program equilibria by simulationist (simulation-based) programs in uncorrelated program games, i.e., when players do not have access to a shared random source. Establish necessary and sufficient conditions describing the full attainable set beyond the shown impossibility that the full Tennenholtz folk theorem cannot be achieved without shared randomness.

Background

The paper introduces simulation-based program equilibria and develops correlated and uncorrelated epsilon-Grounded π-Bots. With shared randomness, a folk theorem is achieved; without shared randomness, the authors prove negative results showing that simulation-based programs cannot generally attain the full folk theorem.

They then consider broader simulationist programs (programs that determine actions by simulating opponents). While they show additional equilibria are achievable beyond ε-Grounded π-Bots, they also prove that, absent shared randomness, the full folk theorem is unattainable. Precisely which equilibria remain attainable in the uncorrelated setting is left unresolved.