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Certainty equivalence principle in stochastic differential games: An inverse problem approach
Author(s) -
JosaFombellida Ricardo,
RincónZapatero Juan Pablo
Publication year - 2019
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2494
Subject(s) - mathematics , mathematical economics , stochastic game , equivalence (formal languages) , differential game , certainty , mathematical optimization , pure mathematics , geometry
Summary This paper aims to characterize a class of stochastic differential games, which satisfy the certainty equivalence principle beyond the cases with quadratic, linear, or logarithmic value functions. We focus on scalar games with linear dynamics in the players' strategies and with separable payoff functionals. Our results are based on the resolution of an inverse problem that determines strictly concave utility functions of the players so that the game satisfies the certainty equivalence principle. Besides establishing necessary and sufficient conditions, the results obtained in this paper are also a tool for discovering new closed‐form solutions, as we show in two specific applications: in a generalization of a dynamic advertising model and in a game of noncooperative exploitation of a productive asset.