Optimal substructure of set-valued solutions of normal-form games and coordination

A number of solution concepts of normal-form games have been proposed in the literature on subspaces of action profiles that have Nash type stability. While the literature mainly focuses on the minimal of such stable subspaces, this paper argues that non-minimal stable subspaces represent well the multi-agent situations to which neither Nash equilibrium nor rationalizability may be applied with satisfaction. As a theoretical support, the authors prove the optimal substructure of stable subspaces regarding the restriction of a game. It is further argued that the optimal substructure characterizes hierarchical diversity of coordination and interim phases in learning.