Non-cooperative bargaining and the incomplete informational core

In an exchange economy with incomplete information, the signaling core is defined by the set of state-contingent allocations to which no coalitions object under informational leakage through proposals by informed agents. An objection underlying the signaling core is supported by a sequential equilibrium of an ultimatum bargaining game with an informed proposer. We prove that a stationary sequential equilibrium allocation in a Rubinstein-type sequential bargaining game with a restart rule belongs to the signaling core if the belief of players satisfies a self-selection property.