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Variational optimization of probability measure spaces resolves the chain store paradox

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Author Info
Gagen, Michael
Nemoto, Kae

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Abstract

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 4778.

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Date of creation: 11 May 2006
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Handle: RePEc:pra:mprapa:4778

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Related research
Keywords: optimization; probability measure space; noncooperative game; chain store paradox;

Find related papers by JEL classification:
C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107 Elsevier. [Downloadable!] (restricted)
  2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March. [Downloadable!] (restricted)
  3. U. Witt, 2006. "Evolutionary Economics," Papers on Economics and Evolution 2006-05, Max Planck Institute of Economics, Evolutionary Economics Group.
  4. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation, Yale University. [Downloadable!]
  5. Wilson, Robert, 1992. "Strategic models of entry deterrence," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 10, pages 305-329 Elsevier. [Downloadable!] (restricted)
  6. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August. [Downloadable!] (restricted)
  7. Simon, Herbert A. & Schaeffer, Jonathan, 1992. "The game of chess," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 1, pages 1-17 Elsevier. [Downloadable!] (restricted)
  8. Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40 Elsevier. [Downloadable!] (restricted)
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