Existence and indeterminacy of markovian equilibria in dynamic bargaining games

We show that dynamic bargaining games are characterized by a continuum of stationary Markov perfect equilibria, when the set of alternatives is multidimensional and players are patient. In fact, we show that there is a continuum of equilibria close to any alternative satisfying a simple linear independence condition on the players' gradients. The approach extends the construction of simple solutions from Anesi and Seidmann (2015) to the spatial setting. The implication is that constructive techniques, which involve an explicit specification of a particular equilibrium and are common in the literature, implicitly rely on a restrictive selection of equilibria.