Bargaining with revoking costs

A simple two stage bilateral bargaining game is analyzed. The players simultaneously demand shares of a unit size pie in the first stage. If the demands add up to more than one, both players, in the second stage, simultaneously choose whether to stick to their demand or accept the other’s offer. While both parties sticking to their offers leads to an impasse, accepting a lower share than the original demand is costly for each party. The set of pure strategy subgame perfect equilibria of the game is characterized for continuous payoff functions strictly increasing in the pie share and continuous cost functions, strictly increasing in the amount conceded. Higher cost functions are shown to improve bargaining power. The limit equilibrium prediction of the model, as the cost functions are made arbitrarily high, selects a unique equilibrium in the Nash Demand