Abstract
We consider a multilateral bargaining game in which the agents can be classified into two groups according to their instantaneous preferences. In one of these groups there is one agent with a different discount factor. We analyze how this time-preference heterogeneity may generate multiplicity of equilibria. When such an agent is sufficiently more patient than the rest, there is an equilibrium in which her group-mates make the same proposal as the members of the other group. Thus, in heterogeneous groups the presence of more patient members may reduce the utility of its members.
Highlights
In this note we consider a non-cooperative multilateral bargaining game in which agents can be classified into two groups according to their instantaneous preferences over a one-dimensional policy
We show that heterogeneous time preferences in one of the groups may lead to multiple equilibrium expected outcomes
Show that this heterogeneity may induce the impatient members of the heterogeneous group to concede more than what is minimally required to obtain the acceptance of the agents in the opposite group
Summary
In this note we consider a non-cooperative multilateral bargaining game in which agents can be classified into two groups according to their instantaneous preferences over a one-dimensional policy. We show that heterogeneous time preferences in one of the groups may lead to multiple equilibrium expected outcomes We characterize these equilibria, and show that this heterogeneity may induce the impatient members of the heterogeneous group to concede more than what is minimally required to obtain the acceptance of the agents in the opposite group. In our setting with two groups, where unanimity is required and the single-period payoff space is one-dimensional, intuition would suggest that the bargaining would be determined by the most patient agents.2 This logic applies when negotiations yield a unique bargaining outcome, we highlight that heterogeneity of time preferences within a group is a source of multiplicity, and this may involve that in some equilibrium the utility of all its members is affected negatively by the presence of a more patient agent in their group..
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