Page, Frank (2016) On K-Class discounted stochastic games. Systemic Risk Centre Discussion Papers (61). 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: | © 2016 The Author |
| Divisions: | Finance Systemic Risk Centre |
| Subjects: | Q Science > QA Mathematics H Social Sciences > HC Economic History and Conditions H Social Sciences > HG Finance |
| JEL classification: | C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory |
| Date Deposited: | 20 Sep 2016 15:35 |
| Last Modified: | 15 Sep 2023 23:39 |
| Projects: | ES/K002309/1 |
| Funders: | Economic and Social Research Council |
| URI: | http://eprints.lse.ac.uk/id/eprint/67809 |
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