A Note on Multi-Issue Bargaining with a Finite Set of Alternatives

We study two bilateral multi-issue bargaining procedures with complete information and endogenous agenda, where each issue is associated with a finite set of alternatives. In both procedures, when bargaining frictions are small, we find a large multiplicity of equilibrium agreements, including ones with arbitrarily long delays. Thus, this paper extends the previous results of van Damme et al. (1990) and Muthoo (1991) for the single-issue case to multi-issue cases. Furthermore, we show that in the first procedure (issue-by-issue bargaining), the stationary subgame perfect equilibria alone may support a large multiplicity of inefficient agreements. Confronting a recent study, this implies that it is not necessary to appeal to “strictly controversial” issues in a bargaining problem in order to find multiplicity and delay in agreements.