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.
Bargaining existence one-stage-deviation principle dynamic programming recursive equations Markov Decision Theory