Extension of TNBR safety and performance bounds to n-player games

Derive serviceable safety and performance bounds for Truncated Noisy Best-Response algorithms in general n-player submodular maximization games, extending the two-player bounds established for recurrent classes.

Background

The analytical results in the paper are established for two-player submodular maximization games. The authors note that a multi-player analogue of one structural lemma can be proved, but that the two-player proof techniques do not yield comparable safety bounds for recurrent classes when more than two agents are present.

The unresolved difficulty is linked to the fact that any two-player action profile can be reached from another through at most two unilateral deviations, whereas the corresponding deviation distance increases with the number of agents. A successful extension would require new mathematical techniques and would generalize the paper’s guarantees beyond the two-player setting.