scholarly journals Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games

2014 ◽  
Author(s):  
Fedor Iskhakov ◽  
John Rust ◽  
Bertel Schjerning
Keyword(s):  
Dynamic Games ◽  
Markov Perfect ◽  
Finite State ◽  
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 Robust Markov perfect equilibria

2014 ◽  
Vol 419 (2) ◽  
pp. 1322-1332 ◽  
Author(s):  
Anna Jaśkiewicz ◽  
Andrzej S. Nowak
Keyword(s):  
Markov Perfect ◽  
Perfect Equilibria

State-Feedback Zero-Sum Dynamic Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Discrete Time ◽  
Information Structure ◽  
Dynamic Games ◽  
State Feedback ◽  
Linear Quadratic ◽  
Feedback Information ◽  
Time Dynamic ◽  
Finite State ◽  
Solution Methods ◽  
Zero Sum

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum discrete time dynamic game in a state-feedback policy. It begins by considering solution methods for two-player zero sum dynamic games in discrete time, assuming a finite horizon stage-additive cost that Player 1 wants to minimize and Player 2 wants to maximize, and taking into account a state feedback information structure. The discussion then turns to discrete time dynamic programming, the use of MATLAB to solve zero-sum games with finite state spaces and finite action spaces, and discrete time linear quadratic dynamic games. The chapter concludes with a practice exercise that requires computing the cost-to-go for each state of the tic-tac-toe game, and the corresponding solution.

scholarly journals Markov decision processes with quasi-hyperbolic discounting

2020 ◽  
Author(s):  
Anna Jaśkiewicz ◽  
Andrzej S. Nowak
Keyword(s):  
Markov Decision Processes ◽  
Dynamic Game ◽  
Hyperbolic Discounting ◽  
Decision Processes ◽  
State Spaces ◽  
Long Run ◽  
Markov Perfect ◽  
Markov Decision ◽  
Time Inconsistent ◽  
Perfect Equilibria

AbstractWe study Markov decision processes with Borel state spaces under quasi-hyperbolic discounting. This type of discounting nicely models human behaviour, which is time-inconsistent in the long run. The decision maker has preferences changing in time. Therefore, the standard approach based on the Bellman optimality principle fails. Within a dynamic game-theoretic framework, we prove the existence of randomised stationary Markov perfect equilibria for a large class of Markov decision processes with transitions having a density function. We also show that randomisation can be restricted to two actions in every state of the process. Moreover, we prove that under some conditions, this equilibrium can be replaced by a deterministic one. For models with countable state spaces, we establish the existence of deterministic Markov perfect equilibria. Many examples are given to illustrate our results, including a portfolio selection model with quasi-hyperbolic discounting.

scholarly journals Existence of Stationary Markov Perfect Equilibria in Stochastic Altruistic Growth Economies

2014 ◽  
Vol 165 (1) ◽  
pp. 295-315 ◽  
Author(s):  
Łukasz Balbus ◽  
Anna Jaśkiewicz ◽  
Andrzej S. Nowak
Keyword(s):  
Markov Perfect ◽  
Perfect Equilibria
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