Pre-bargaining Investment Implies a Pareto Ranking of Bargaining Solutions

n players choose investment levels that determine a bargaining problem. Investments model pre-bargaining preparations such as arming and hiring legal aid—costly actions that turn out to be beneficial only if the agents do not reach an agreement. In the bargaining problem, payoffs are distributed according to an exogenously given bargaining solution. Investment influences positively the investor’s disagreement payoff, but it also has a cost, which is modeled as a shrinkage of the feasible set. Two types of shrinkage are considered. Under either one, the investment is a waste from an ex-post point of view, because the agents end up reaching an agreement. The equilibrium level of wastefulness is increasing in the bargaining solution’s disagreement sensitivity. The Kalai-Smorodinsky solution is less disagreement sensitive than the Nash solution, and is therefore better.