We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective preferences, which may be inconsistent with the material payoff function giving them the actual fitness values. In each of the two settings, $n$-player games are played, and we provide necessary and sufficient conditions for multi-mutation stability. These results definitely reveal the connection between the order of stability and the level of efficiency.

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