scholarly journals Markov perfect equilibria in a dynamic decision model with quasi-hyperbolic discounting

2018 ◽  
Vol 287 (2) ◽  
pp. 573-591 ◽  
Author(s):  
Łukasz Balbus ◽  
Anna Jaśkiewicz ◽  
Andrzej S. Nowak
Keyword(s):  
Decision Model ◽  
Hyperbolic Discounting ◽  
Markov Perfect ◽  
Perfect Equilibria ◽  
Dynamic Decision Model

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 Robust Markov perfect equilibria

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

Bayesian dynamic programming

1975 ◽  
Vol 7 (2) ◽  
pp. 330-348 ◽  
Author(s):  
Ulrich Rieder
Keyword(s):  
Dynamic Programming ◽  
Weak Convergence ◽  
Decision Model ◽  
Transition Probabilities ◽  
General State ◽  
Parameter Spaces ◽  
State Action ◽  
Total Rewards ◽  
Bayesian Dynamic Programming ◽  
Dynamic Decision Model

We consider a non-stationary Bayesian dynamic decision model with general state, action and parameter spaces. It is shown that this model can be reduced to a non-Markovian (resp. Markovian) decision model with completely known transition probabilities. Under rather weak convergence assumptions on the expected total rewards some general results are presented concerning the restriction on deterministic generalized Markov policies, the criteria of optimality and the existence of Bayes policies. These facts are based on the above transformations and on results of Hindererand Schäl.

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