scholarly journals Markov Perfect Equilibria in Multi-mode Differential Games with Endogenous Timing of Mode Transitions

2021 ◽  
Author(s):  
Herbert Dawid ◽  
Serhat Gezer
Keyword(s):  
Differential Games ◽  
Endogenous Timing ◽  
Markov Perfect ◽  
Mode Transitions ◽  
Perfect Equilibria ◽  
Multi Mode

scholarly journals Markov Perfect Equilibria in Multi-Mode Differential Games with Endogenous Timing of Mode Transitions

2021 ◽  
Author(s):  
Herbert Dawid ◽  
Serhat Gezer
Keyword(s):  
Differential Games ◽  
Initial Conditions ◽  
New Product ◽  
Mode Switch ◽  
Product Introduction ◽  
Wide Range ◽  
Markov Perfect ◽  
Mode Transitions ◽  
Perfect Equilibria ◽  
Multi Mode

AbstractWe study Markov perfect equilibria (MPE) of two-player multi-mode differential games with controlled state dynamics, where one player controls the transition between modes. Different types of MPE are characterized distinguishing between delay equilibria, inducing for some initial conditions mode switches after a positive finite delay, and now or never equilibria, under which, depending on the initial condition, a mode switch occurs immediately or never. These results are applied to analyze the MPE of a game capturing the dynamic interaction between two incumbent firms among which one has to decide when to extend its product range by introducing a new product. The market appeal of the new product can be influenced over time by both firms through costly investments. Under a wide range of market introduction costs a now or never equilibrium coexists with a continuum of delay equilibria, each of them inducing a different time of product introduction.

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

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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