Two-Person Bargaining when the Disagreement Point is Private Information

TL;DR

This paper analyzes two-person bargaining with private disagreement payoffs, showing that under certain conditions, the bargaining outcome cannot depend on private information, impacting axiomatic bargaining and mechanism design.

Contribution

It establishes conditions under which private disagreement information does not influence bargaining outcomes, extending previous results to non-linear Pareto frontiers and specific informational settings.

Findings

Outcome independence when Pareto frontier is linear

Outcome independence with non-linear frontier under independence or limited types

Implications for axiomatic bargaining and surplus extraction

Abstract

We consider two-person bargaining problems in which (only) the disagreement outcome is private (and possibly correlated) information and it is common knowledge that disagreement is inefficient. We show that if the Pareto frontier is linear, the outcome of an ex post efficient mechanism cannot depend on the disagreement payoffs. If the frontier is non-linear, the result continues to hold when the disagreement payoffs are independent or there is a player with at most two types. We discuss implications of these results for axiomatic bargaining theory and for full surplus extraction in mechanism design.