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.multi-issue bargaining, finiteness of alternatives, multiple equilibria, inefficiency and delay

A Fictitious-Play Model of Bargaining To Implement the Nash Solution

We present a fictitious-play model of bargaining, where two bargainers play the Nash demand game repeatedly. The bargainers make a deliberate decision on their demands in the initial period and then follow a fictitious play process subsequently. If the bargainers are patient, the set of epsilon -equilibria of the initial-demand game is in a neighborhood of the division corresponding to the Nash bargaining solution. As the bargainers make a more accurate comparison of payoffs and become more patient accordingly, the set of epsilon-equilibria shrinks and the only equilibrium left is the division of the Nash bargaining solution.fictitious play, Nash demand game, epsilon-equilibrium, Nash bargaining solution, Nash program.

On the Relevance of Alternatives in Bargaining: Average Alternative Solutions

We compare bargaining solutions in terms of the relevance of alternatives. We show that most well-known bargaining solutions do not use all the alternatives, but there are numerous bargaining solutions that do. We introduce a new class of bargaining solutions called ``average alternative solutions'', characterize them, and show that the Nash solution and the Kalai-Smorodinsky solution are limits of average alternative solutions. We also provide alternative characterizations for the Nash solution and the Kalai-Smorodinsky solution.bargaining, solutions, axioms, relevance of alternatives, average alternative solutions, monotonic bounds

Agenda Restrictions in Multi-Issue Bargaining (II): Unrestricted Agendas

We study a bilateral multi-issue bargaining procedure with complete information and endogenous unrestricted agenda, in which offers can be made in any subset of outstanding issues. We find necessary and sufficient conditions for this procedure to have a unique subgame perfect equilibrium agreement.multi-issue bargaining, complete information, agenda