Viable Nash Equilibria: Formation and Sustainability

To be viable, a Nash equilibrium should deter the defection of groups of players. For a newly proposed equilibrium to be viable, it should deter defections but also have a reasonable likelihood of formation. To assess the viability of equilibria, we study a defection-deterrence index D that describes the size of defection groups that an equilibrium is sure to deter, and a dual index of formation difficulty, F (= n - D), that describes the critical size of groups that guarantee equilibrium formation. These viability indices are compatible with observations in behavioral economics and with functioning social systems, and offer a tool for assessing the performance of proposed equilibria.