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Dynamic Games and Applications

Erschienen in:

10.05.2017

Stochastic Differential Games for Which the Open-Loop Equilibrium is Subgame Perfect

verfasst von: Ricardo Josa-Fombellida, Juan Pablo Rincón-Zapatero

Erschienen in: Dynamic Games and Applications | Ausgabe 2/2018

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Abstract

It is generally admitted that a correct forecasting of uncertain variables needs Markov decision rules. In a dynamic game environment, this belief is reinforced if one focuses on credible actions of the players. Usually, subgame perfectness requires equilibrium strategies to be constructed on Markov rules. It comes as a surprise that there are interesting classes of stochastic differential games where the equilibrium based on open-loop strategies is subgame perfect. This fact is well known for deterministic games. We explore here the stochastic case, not dealt with up to now, identifying different game structures leading to the subgame perfectness of the open-loop equilibrium.

Vorheriger Artikel Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints

Nächster Artikel Tauberian Theorem for Value Functions

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See Başar and Olsder [1], where the issue of information in dynamic games is thoroughly analyzed. Also, Fershtman [6] provides a clever analysis of the meaning of open-loop and closed-loop rules.

The results shown in the paper remain valid for a variable discount factor \(\mathrm{e}^{-\int _t^s \rho ^i(r) \mathrm{d}r}\), where \(\rho ^i(r)\ge 0\) is a continuous function. The changes in the equations shown in the paper are straightforward.

See Fleming and Rishel [7] or Dockner et al. [4] for details about the HJB equation.

If no bequest function is imposed, then the extraction rate equilibrium becomes unbounded at the terminal time. The model is similar to that studied in Reinganum and Stokey [14]. Uncertainty does not mitigate the problem.

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Titel: Stochastic Differential Games for Which the Open-Loop Equilibrium is Subgame Perfect
verfasst von: Ricardo Josa-Fombellida
Juan Pablo Rincón-Zapatero
Publikationsdatum: 10.05.2017
Verlag: Springer US
Erschienen in: Dynamic Games and Applications / Ausgabe 2/2018
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-017-0221-y

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