Existence and indeterminacy of Markovian equilibria in dynamic bargaining games

Abstract

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.

Political Economy of Redistribution

“…Anesi and Seidmann (2015) assume that players are supportive of the proposal when they are indifferent, depending on the coalition formed on the equilibrium path. (Anesi and Duggan (2015) extend this construction to the spatial setting.) We assume that transitions unlock an arbitrarily small budget that may be 14 In models with information aggregation in voting (e.g., Feddersen and Pesendorfer (1998)), the supermajority requirement may have nonmonotone effects as it influences pivotal events that players condition upon.…”

“…When indifferences are present because of the nature of the model, most papers, including Kalandrakis (2004), Diermeier and Fong (2011), and Anesi and Duggan (2015), assume that a player supports the new proposal when he is indifferent. In contrast, Baron and Bowen (2015) argue that it is important to assume that players vote against the proposal when they are indifferent.…”

Bargaining over Taxes and Entitlements

“…In his environment, the focus is on private transfers, but there is no public good provision. Other papers that make contributions on legislative bargaining with unidimensional policies are Baron and Ferejohn (1989), Baron and Kalai (1993), Kalandrakis (2004), Battaglini et al (2012), Duggan and Kalandrakis (2012a), Dziuda and Loeper (2018), Dziuda and Loeper (2016), Anesi (2010), Anesi and Seidmann (2013), Anesi and Duggan (2018) Diermeier et al (2017), Richter (2014), Piguillem and Riboni (2011), Baron and Bowen (2015), Bowen et al (2017), Karakas (2017) and Grechyna (2017). Our main departure from these papers is that in our model government policies affect both, public and private goods.…”

Policy Experimentation, Redistribution and Voting Rules

“…Our framework extends the stationary dividethe-dollar framework studied in Kalandrakis (2004Kalandrakis ( , 2010, Battaglini and Palfrey (2012), Bowen and Zahran (2012), Baron and Bowen (2015), Nunnari (2014), Richter (2014), and Anesi and Seidmann (2015), by adding experimentation and taxation components to the choice space. To establish our efficiency result for non-collegial voting rules and limited redistribution (Proposition 2), we exploit the constructive techniques developed in Baron and Bowen (2015), Anesi and Seidmann (2015), and Anesi and Duggan (2018) but push this further to construct an efficient Markovian equilibrium in a non-stationary environment where: (i) the size of the benefits allocated in each period is endogenously determined by policy choices, and (ii) the committee members' policy preferences over an additional (non-redistributive) policy dimension evolve with their endogenous beliefs. Our characterization of non-stationary equilibria for collegial voting rules also extends the work of Nunnari (2014) who focuses on stationary Markov perfect equilibria in divide-the-dollar environments with veto players.…”