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5 - Game theory

from Part II - Techniques for design, analysis, and optimization of dynamic spectrum access and management

Published online by Cambridge University Press:  26 February 2010

Ekram Hossain
Affiliation:
University of Manitoba, Canada
Dusit Niyato
Affiliation:
Nanyang Technological University, Singapore
Zhu Han
Affiliation:
University of Houston
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Summary

The ideas underlying game theory have appeared throughout history, in the Bible, the Talmud, the works of Descartes and Sun Tzu, and the writings of Chales Darwin. Modern game theory, however, can be considered as an outgrowth of three seminal works:

  • Augustin Cournot's Research into the Mathematical Principles of the Theory of Wealth in 1838 gives an intuitive explanation of what would eventually be formalized as the Nash equilibrium, as well as provides an evolutionary, or dynamic notion of best-response to the actions of others.

  • Francis Ysidro Edgeworth's Mathematical Psychics demonstrated the notion of competitive equilibria in a two-person (as well as two-type) economy; Emile Borel, in “Algèbre et calcul des probabilités,” Comptes Rendus Académie des Sciences, vol. 184, 1927, provided the first insight into mixed strategies that randomization may support a stable outcome.

  • While many other contributors hold a place in the history of game theory, it is widely accepted that modern analysis began with John von Neumann and Oskar Morgenstern's book, Theory of Games and Economic Behavior. Then building on von Neumann and Morgenstern's results John Nash developed the modern framework for methodological analysis.

Depending on the nature of the different approaches, there are different possible applications of game theory. If the information is strictly limited to local information, the non-cooperative game might be the only choice for each individual to play. However, such a game might have a very low-efficiency outcome. To overcome this problem, pricing or referee approaches have been proposed. If the users care about long-term benefits, the repeated game can be employed to enforce cooperation by the threat of future punishment from others.

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Publisher: Cambridge University Press
Print publication year: 2009

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  • Game theory
  • Ekram Hossain, University of Manitoba, Canada, Dusit Niyato, Nanyang Technological University, Singapore, Zhu Han, University of Houston
  • Book: Dynamic Spectrum Access and Management in Cognitive Radio Networks
  • Online publication: 26 February 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511609909.006
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  • Game theory
  • Ekram Hossain, University of Manitoba, Canada, Dusit Niyato, Nanyang Technological University, Singapore, Zhu Han, University of Houston
  • Book: Dynamic Spectrum Access and Management in Cognitive Radio Networks
  • Online publication: 26 February 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511609909.006
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Game theory
  • Ekram Hossain, University of Manitoba, Canada, Dusit Niyato, Nanyang Technological University, Singapore, Zhu Han, University of Houston
  • Book: Dynamic Spectrum Access and Management in Cognitive Radio Networks
  • Online publication: 26 February 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511609909.006
Available formats
×