Bargaining with Heterogeneous Beliefs

I consider a reputation based bargaining model with uncertainty of players' initial beliefs, which comes from access to an exogenous signaling device. I characterize the set of non-trivial equilibria satisfying initial posture constraints. The analysis yields a unique equilibrium with a phased war of attrition structure — players holding different beliefs have disjoint supports of conceding strategies. The result implies that learning about each other's type leads to players departing from the strategies induced by the prior, which creates either efficiency improvement or further delay depending on the realized posteriors. When ex ante probabilities of behavioral types go to zero, the delay and inefficiency persist even if we allow initial demands as strategic choices due to the expectation of the learning opportunity. We also characterize the case with a rich set of posterior beliefs.