A one-period memory folk theorem for multilateral bargaining games

We study strategies with one-period recall in the context of a general class of multilateral bargaining games. A strategy has one-period recall if actions in a particular period are only conditioned on information in the previous and the current period. We show that if players are sufficiently patient, given any proposal in the space of possible agreements, there exists a subgame perfect equilibrium such that the given proposal is made and unanimously accepted in period zero. As a corollary we derive that also perpetual delay can be sustained as a subgame perfect equilibrium. Our strategies are pure and have one-period recall, and we do not make use of a public randomization device. The players' discount factors are allowed to be heterogeneous. We also construct a finite automata representation of our strategy profile.