Open AccessExistence and indeterminacy of Markovian equilibria in dynamic bargaining games
Author(s) -
Anesi Vincent,
Duggan John
Publication year - 2018
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2215
Subject(s) - mathematical economics , indeterminacy (philosophy) , constructive , markov perfect equilibrium , mathematics , set (abstract data type) , economics , curse of dimensionality , markov chain , equilibrium selection , mathematical optimization , nash equilibrium , repeated game , computer science , game theory , statistics , physics , process (computing) , quantum mechanics , programming language , operating system
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.