To “ a Theory of Disagreement in Repeated Games with Bargaining ”

THEOREM 9: For each i, let a be a pure action profile in the stage game. If aii is a best response to ai−i for both i and (π2 −π1) · (u(a2)− u(a1)) > 0, then the following two-state automaton strategy, with states 1 and 2, yields a BSG set for δ sufficiently high: • Disagreement: In state i, make no transfers and play a in the action phase. If player j = i deviates unilaterally, go to state j; otherwise stay in state i. • Agreement: Play arg maxa ∑ i ui(a) in the action phase and pay transfers that split the surplus with respect to disagreement play in the current state. If nobody deviates or both deviate, randomize between the two states with equal probabilities. If player i deviates unilaterally, go to state i. The continuation values in the two states are the endpoints of a BSG set contained in V (SCE).