Constrained stochastic differential games with additive structure: Average and discount payoffs

Beatris Adriana Escobedo-Trujillo; Alejandro Alaffita-Hernández; Raquiel López-Martínez

doi:10.3934/jdg.2018008

Article Contents

2018, Volume 5, Issue 2: 109-141. Doi: 10.3934/jdg.2018008

This issue Previous Article Games with nested constraints given by a level structure Next Article A risk minimization problem for finite horizon semi-Markov decision processes with loss rates

Constrained stochastic differential games with additive structure: Average and discount payoffs

1.
Engineering Faculty. Universidad Veracruzana, Coatzacoalcos, Ver., México
2.
Mathematics Faculty, Universidad Veracruzana, Xalapa, Ver., México

* Corresponding author: Beatris Adriana Escobedo-Trujillo
* Corresponding author: Beatris Adriana Escobedo-Trujillo

Received: July 2017

Revised: December 2017

Published: March 2018

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Abstract

This paper deals with two-person nonzero-sum stochastic differential games (SDGs) with an additive structure, subject to constraints that are additive also. Our main objective is to give conditions for the existence of constrained Nash equilibria for the case of infinite-horizon discounted payoff. This is done by means of the Lagrange multipliers approach combined with dynamic programming arguments. Then, following the vanishing discount approach, the results in the discounted case are used to obtain constrained Nash equilibria in the case of long-run average payoff.

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Mathematics Subject Classification: Primary: 91A10, 91A15, 91A25.

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