Existence and indeterminacy of Markovian equilibria in dynamic bargaining games

Anesi, Vincent; Duggan, John

Abstract

The 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.

Citation

Anesi, V., & Duggan, J. (2018). Existence and indeterminacy of Markovian equilibria in dynamic bargaining games. Theoretical Economics, 13(2), 505-525. https://doi.org/10.3982/TE2215

• Journal Article Type: Article
• Acceptance Date: Oct 9, 2017
• Online Publication Date: May 29, 2018
• Publication Date: May 29, 2018
• Deposit Date: Oct 12, 2017
• Publicly Available Date: Aug 15, 2018
• Journal: Theoretical Economics
• Print ISSN: 1933-6837
• Electronic ISSN: 1555-7561
• Publisher: Econometric Society
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 2
• Pages: 505-525
• DOI: https://doi.org/10.3982/TE2215
• Public URL: https://nottingham-repository.worktribe.com/output/886746
• Publisher URL: https://onlinelibrary.wiley.com/doi/abs/10.3982/TE2215
• Contract Date: Oct 12, 2017