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See detailExistence and Indeterminacy of Markovian Equilibria in Dynamic Bargaining Games
Anesi, Vincent UL; Duggan, John

in Theoretical Economics (2018), 13

This paper studies stationary Markov perfect equilibria in multidimensional models of dynamic bargaining, in which the alternative chosen in one period determines the status quo for the next. We ... [more ▼]

This paper studies stationary Markov perfect equilibria in multidimensional models of dynamic bargaining, in which the alternative chosen in one period determines the status quo for the next. We generalize a sufficient condition for existence of equilibrium due to Anesi and Seidmann, 2015. We then use this existence result to show that if a weak gradient restriction holds at an alternative, then when players are sufficiently patient, there is a continuum of equilibria with absorbing sets arbitrarily close to that alternative. A sufficient condition for our gradient restriction is that the gradients of all players' utilities are linearly independent at that alternative. When the dimensionality of the set of alternatives is high, this linear independence condition holds at almost all alternatives, and equilibrium absorbing sets are dense in the set of alternatives. This implies that constructive techniques, which are common in the literature, fail to identify many plausible outcomes in dynamic bargaining games. [less ▲]

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See detailBargaining over an Endogenous Agenda
Anesi, Vincent UL; Seidmann, Daniel

in Theoretical Economics (2014), 9

We present a model of bargaining in which a committee searches over the pol-icy space, successively amending the default by voting over proposals. Bargaining ends when proposers are unable or unwilling to ... [more ▼]

We present a model of bargaining in which a committee searches over the pol-icy space, successively amending the default by voting over proposals. Bargaining ends when proposers are unable or unwilling to amend the existing default,which is then implemented. Our main goal is to study the policies that can be implemented from any initial default in a pure-strategy stationary Markov perfect equilibrium for an interesting class of environments including multidimensional and infinite policy spaces. It is convenient to start by characterizing the set of immovable policies that are implemented, once reached as default. These policies form a weakly stable set and, conversely, any weakly stable set is supported by some equilibrium. Using these results, we show that minimum-winning coalitions may not form and that a player who does not propose may nevertheless earn all of the surplus from agreement. We then consider how equilibrium outcomes change as we vary the order in which players propose, the identity of proposers,and the set of winning coalitions. First, if the policy space is well ordered, then the committee implements the ideal policy of the last proposer in a subset of a weakly stable set, but this result does not generalize to other cases. We also show, surprisingly, that a player may prefer not to be given the opportunity to propose and that the set of immovable policies may shrink as the quota increases. Finally, we derive conditions under which immovable policies in semi-Markovian equilibria form a consistent choice set. [less ▲]

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