Direct method comparing efficient and nonefficient payoffs in differential games

In this note, we present a method that allows us to decide when a Markov-perfect Nash equilibrium is not Pareto optimum, without the explicit knowledge of the respective solutions. For that purpose, we establish a sufficient condition in terms of an algebraic inequality where the gradient of the val...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2003-11, Vol.119 (2), p.395-405
Main Authors: RINCON-ZAPATERO, J. P, MARTIN-HERRAN, G
Format: Article
Language:English
Subjects:
Applied sciences
Cooperation
Equilibrium
Exact sciences and technology
Explicit knowledge
Game theory
Games
Inequality
Mathematical programming
Operational research and scientific management
Operational research. Management science
Pareto optimum
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Summary:In this note, we present a method that allows us to decide when a Markov-perfect Nash equilibrium is not Pareto optimum, without the explicit knowledge of the respective solutions. For that purpose, we establish a sufficient condition in terms of an algebraic inequality where the gradient of the value functions of the cooperative and noncooperative games as well as the state and control variables are involved.
ISSN:0022-3239
1573-2878
DOI:10.1023/B:JOTA.0000005453.96575.2a