Beyond dominance and Nash: Ranking equilibria by critical mass

Strategic interactions pose central issues that are not adequately explained by the traditional concepts of dominant strategy equilibrium (DSE), Nash equilibrium (NE), and their refinements. A comprehensive analysis of equilibrium concepts within the von Neumann-Nash framework of n-person optimization reveals a decreasing hierarchy of n nested concepts ranging from DSE to NE. These concepts are defined by the “critical mass,” the number of players needed to adopt and sustain the play of a strategy profile as an equilibrium. In games with n>2 players, the n−2 intermediate concepts explain strategic issues in large social systems, implementation, decentralization, as well as replication studied in economics, operations management, and political games.