Bargaining Under Two-Sided Incomplete Information: The Unrestricted Offers Case

Abstract

Chatterjee and Samuelson (Chatterjee, K., L. Samuelson. 1987. Bargaining with two-sided incomplete information: An infinite horizon model with alternating offers. Rev. Econ. Stud. 54 175–192.) recently examined a noncooperative game-theoretic bargaining model with two-sided incomplete information and an infinite horizon. Results were obtained from the model with the help of restrictions on agents' strategies. This paper examines the model without these restrictions. By doing so, we will gain some insight into whether these results are robust, in the sense that they do not depend upon the special structure of the model, and hence, might provide useful theoretical foundations for applied work. We find that the basic results generalize. As with the restricted model, we find an equilibrium in which bargaining will proceed for a finite but endogeneously determined number of stages. A terminal condition on the equilibrium sequence of agents' beliefs determines the properties of the equilibrium and allows comparative static results to be obtained. These include the finding that agents are more likely to capture a large share of the potential gains from bargaining if they exhibit characteristics that can be readily interpreted as giving them more bargaining power. Unlike the restricted model, this equilibrium is not unique, though we argue that it is plausible.