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Stationary Markov equilibria for K-class discounted stochastic games

Page, Frank (2015) Stationary Markov equilibria for K-class discounted stochastic games. SRC Discussion Paper, No 44. Systemic Risk Centre, The London School of Economics and Political Science, London, UK.

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Abstract

For a discounted stochastic game with an uncountable state space and compact metric action spaces, we show that if the measurable-selection-valued, Nash payoff selection correspondence of the underlying one-shot game contains a sub-correspondence having the K-limit property (i.e., if the Nash payoff selection sub-correspondence contains its K-limits and therefore is a K correspondence), then the discounted stochastic game has a stationary Markov equilibrium. Our key result is a new fixed point theorem for measurable-selection-valued correspondences having the K-limit property. We also show that if the discounted stochastic game is noisy (Duggan, 2012), or if the underlying probability space satisfies the G-nonatomic condition of Rokhlin (1949) and Dynkin and Evstigneev (1976) (and therefore satisfies the coaser transition kernel condition of He and Sun, 2014), then the Nash payoff selection correspondence contains a sub-correspondence having the K-limit property.

Item Type: Monograph (Discussion Paper)
Official URL: http://www.systemicrisk.ac.uk/
Additional Information: © 2015 The Authors
Divisions: Systemic Risk Centre
Subjects: H Social Sciences > HB Economic Theory
JEL classification: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory
Sets: Research centres and groups > Systemic Risk Centre
Date Deposited: 21 Jan 2016 15:16
Last Modified: 12 Dec 2017 08:26
Projects: ES/K002309/1
Funders: ESRC
URI: http://eprints.lse.ac.uk/id/eprint/65103

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