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Dynamic Games and Applications
Published in: Dynamic Games and Applications 2/2018

03-04-2017

Potential Differential Games

Authors: Alejandra Fonseca-Morales, Onésimo Hernández-Lerma

Published in: Dynamic Games and Applications | Issue 2/2018

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Abstract

This paper introduces the notion of a potential differential game (PDG), which roughly put is a noncooperative differential game to which we can associate an optimal control problem (OCP) whose solutions are Nash equilibria for the original game. If this is the case, there are two immediate consequences. Firstly, finding Nash equilibria for the game is greatly simplified, because it is a lot easier to deal with an OCP than with the original game itself. Secondly, the Nash equilibria obtained from the associated OCP are automatically “pure” (or deterministic) rather than “mixed” (or randomized). We restrict ourselves to open-loop differential games. We propose two different approaches to identify a PDG and to construct a corresponding OCP. As an application, we consider a PDG with a certain turnpike property that is obtained from results for the associated OCP. We illustrate our results with a variety of examples.
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Metadata
Title
Potential Differential Games
Authors
Alejandra Fonseca-Morales
Onésimo Hernández-Lerma
Publication date
03-04-2017
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 2/2018
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-017-0218-6

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