scholarly journals A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification

2008 ◽  
Author(s):  
Ulrich Doraszelski ◽  
Juan F. Escobar
Keyword(s):  
Stochastic Games ◽  
Markov Perfect ◽  
Dynamic Stochastic ◽  
Perfect Equilibria

scholarly journals Protocol invariance and the timing of decisions in dynamic games

2019 ◽  
Vol 14 (2) ◽  
pp. 597-646
Author(s):  
Ulrich Doraszelski ◽  
Juan F. Escobar
Keyword(s):  
Research And Development ◽  
Repeated Games ◽  
Dynamic Games ◽  
Stochastic Games ◽  
Industry Dynamics ◽  
Extant Literature ◽  
Markov Perfect ◽  
Dynamic Stochastic ◽  
Perfect Equilibria

We characterize a class of dynamic stochastic games that we call separable dynamic games with noisy transitions and establish that these widely used models are protocol invariant provided that periods are sufficiently short. Protocol invariance means that the set of Markov perfect equilibria is nearly the same irrespective of the order in which players are assumed to move within a period. Protocol invariance can facilitate applied work, and renders the implications and predictions of a model more robust. Our class of dynamic stochastic games includes investment games, research and development races, models of industry dynamics, dynamic public contribution games, asynchronously repeated games, and many other models from the extant literature.

scholarly journals K-Correspondences, USCOs, and fixed point problems arising in discounted stochastic games

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Frank H. Page ◽  
Jing Fu
Keyword(s):  
Game Theory ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Probability Space ◽  
Stochastic Games ◽  
Measurable Selection ◽  
Markov Perfect ◽  
Open Question ◽  
Perfect Equilibria

Abstract We establish a fixed point theorem for the composition of nonconvex, measurable selection valued correspondences with Banach space valued selections. We show that if the underlying probability space of states is nonatomic and if the selection correspondences in the composition are K-correspondences (meaning correspondences having graphs that contain their Komlos limits), then the induced measurable selection valued composition correspondence takes contractible values and therefore has fixed points. As an application we use our fixed point result to show that all nonatomic uncountable-compact discounted stochastic games have stationary Markov perfect equilibria – thus resolving a long-standing open question in game theory.

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