Bargaining Under Liquidity Constraints : Nash vs. Kalai in the Laboratory

We report on an experiment in which buyers and sellers engage in semi-structured bargaining in two dimensions: how much of a good the seller will produce and how much money the buyer will offer the seller in exchange. Our aim is to evaluate the empirical relevance of two axiomatic bargaining solutions, the generalized Nash bargaining solution and Kalai's proportional bargaining solution. These bargaining solutions predict different outcomes when buyers are constrained in their money holdings. We first use the case when the buyer is not liquidity constrained to estimate the bargaining power parameter, which we find to be equal to 1/2. Then, imposing liquidity constraints on buyers, we find strong evidence in support of the Kalai proportional solution and against the generalized Nash solution. Our findings have policy implications, e.g., for the welfare cost of inflation in search-theoretic models of money