A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models†

Alejandra Fonseca-Morales; Onésimo Hernández-Lerma

doi:10.3934/jdg.2017012

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2017, Volume 4, Issue 3: 195-203. Doi: 10.3934/jdg.2017012

This issue Previous Article On Zermelo's theorem Next Article Game theory and dynamic programming in alternate games

A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models^†

Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México City, 07000, México

* Corresponding author
* Corresponding author

Received: February 28, 2017

Revised: March 31, 2017

Published: September 2017

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Abstract

Pareto optimality and Nash equilibrium are two standard solution concepts for cooperative and non-cooperative games, respectively. At the outset, these concepts are incompatible-see, for instance, [7] or [10]. But, on the other hand, there are particular games in which Nash equilibria turn out to be Pareto-optimal [1], [4], [6], [18], [20]. A class of these games has been identified in the context of discrete-time potential games [13]. In this paper we introduce several classes of deterministic and stochastic potential differential games [12] in which open-loop Nash equilibria are also Pareto optimal.

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Mathematics Subject Classification: Primary: 91A23, 49N70, 91A10; Secondary: 91A12, 91A25.

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