Pareto-optimal Nash equilibrium: Sufficient conditions and existence in mixed strategies

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• 作者：V. I. Zhukovskiy ; K. N. Kudryavtsev
• 刊名：Automation and Remote Control
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：77
• 期：8
• 页码：1500-1510
• 全文大小：275 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Systems Theory and Control
  Automation and Robotics
  Mechanical Engineering
  Computer-Aided Engineering and Design
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1608-3032
• 卷排序：77

文摘

This paper considers the Nash equilibrium strategy profiles that are Pareto optimal with respect to the rest Nash equilibrium strategy profiles. The sufficient conditions for the existence of such pure strategy profiles are established. These conditions employ the Germeier convolutions of the payoff functions. For the non-cooperative games with compact strategy sets and continuous payoff functions, the existence of the Pareto optimal Nash equilibria in mixed strategies is proved.Original Russian Text © V.I. Zhukovskiy, K.N. Kudryavtsev, 2015, published in Matematicheskaya Teoriya Igr i Ee Priloszheniya, 2015, No. 1, pp. 74–91.