Bargaining with Costly Delay

Players 1 and 2 bargain over one dollar. In round 1 player 1 proposes a split, which player 2 accepts or rejects. After a rejection, player 2 proposes in round 2, then player 1 in round 3, and so on forever, alternating, with no deadline. If agreement on a split $(x_1,x_2)$ is reached in round $t$, player $i$ gets payoff $x_i - c_i\,(t-1)$, where the per-round waiting costs are $c_1 = 3/10$ and $c_2 = 1/10$. Never agreeing is worse than any agreement for both, so play always ends. A player who is indifferent accepts. Look for the subgame-perfect equilibrium. What share of the dollar does player 1 obtain? Give a reduced fraction.

• induction
• nash equilibrium

Source: Rubinstein (1982), the model with fixed per-round bargaining costs rather than discounting. Statement written for AxiomIQ.