# 15-010/II (2015-01-22)

Author(s)
P. Jean-Jacques Herings, Maastricht University, the Netherlands; Harold Houba, VU University Amsterdam, the Netherlands
Keywords:
Bargaining, existence, one-stage-deviation principle, dynamic programming, recursive equations, Markov Decision Theory
JEL codes:
C72, C73, C78

We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions are necessary for SSPE but insufficient because these equations can be singular. Strategy profiles excluding perpetual disagreement guarantee non-singularity. The necessary and sufficient conditions for existence of stationary best responses additionally require either an equalizing condition or a minimality condition. Quasi SSPE only satisfy the recursive equations and optimality conditions. These always exist and are SSPE if either all equalizing conditions or all minimality conditions hold.