Book excerpt: This note examines the structure of stationary bargaining equilibria in the nite framework of Anesi (2010). The main result establishes a tight connection between the set of equilibrium absorbing points and the von Neumann-Morgestern solutions: assuming that players are patient, that the voting rule is oligarchical, and that there is at least one veto player with positive recognition probability, a set of alternatives corresponds to the absorbing points of an equilibrium if and only if it is a von Neumann-Morgenstern solution. We also apply our analysis of ergodic properties of equilibria to the persistent agenda setter environment of Diermeier and Fong (2012). We show that all equilibria are essentially pure, and we extend their characterization of absorbing sets to allow an arbitrary voting rule and by removing the restriction to pure strategy equilibira.