Perfect equilibria in simultaneous-offers bargaining

A generalization of the Nash demand game is examined. Agents make simultaneous offers in each period as to how a pie is to be divided. Incompatible offers send the game to the next period, while compatible offers end the game with a split-the-difference trade. The set of perfect equilibria of this game includes any individually rational outcome, including inefficient outcomes and even including the outcome of perpetual disagreement. We suggest a stronger equilibrium concept of universal perfection, which requires robustness against every rather than just one sequence of perturbed games. The set of universally perfect equilibria also includes all individually rational outcomes. The results provide useful insights into both simultaneous-offers bargaining and the nature of the perfect equilibrium and similar concepts (such as stability and hyperstability) in infinite games.