But Some Neutrally Stable Strategies are More Neutrally Stable than Others

For games in which there is no evolutionarily stable strategy, it can be useful to look for neutrally stable ones. In extensive form games for instance there is typically no evolutionary stable strategy, while there may very well be a neutrally stable one. Such strategies can however still be relatively stable or unstable, depending on whether or not the neutral mutants it allows for - which by definition do not have a selective advantage themselves - can open doors for other mutants, that do have a selective advantage. This paper defines robustness against indirect invasions in order to be able to discern between those two very different situations. Robustness against indirect invasions turns out to come with a very natural setwise generalisation of evolutionary stability; we prove that if a strategy is robust against indirect invasions, then this strategy and its (indirect) neutral mutants form a set that is asymptotically stable in the replicator dynamics.