Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games
AbstractFor a class of n-player (n ? 2) sequential bargaining games with probabilistic recognition and general agreement rules, we characterize pure strategy Stationary Subgame Perfect (PSSP) equilibria via a finite number of equalities and inequalities. We use this characterization and the degree theory of Shannon, 1994, to show that when utility over agreements has negative definite second (contingent) derivative, there is a finite number of PSSP equilibrium points for almost all discount factors. If in addition the space of agreements is one-dimensional, the theorem applies for all SSP equilibria. And for oligarchic voting rules (which include unanimity) with agreement spaces of arbitrary finite dimension, the number of SSP equilibria is odd and the equilibrium correspondence is lower-hemicontinuous for almost all discount factors. Finally, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.
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Bibliographic InfoPaper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP37.
Length: 25 pages
Date of creation: Apr 2004
Date of revision:
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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.
Local Uniqueness of Equilibrium; Regularity; Sequential Bargaining.;
Other versions of this item:
- Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer, vol. 28(2), pages 309-329, 06.
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