충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권2호
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  • Pages.213-219
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  • 2011
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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EXISTENCE OF NASH EQUILIBRIUM IN A NON-COMPACT ACYCLIC STRATEGIC GAME WITH INFINITE PLAYERS

  • Kim, Won Kyu (Department of Mathematics Education, Chungbuk National University)
  • 투고 : 2011.02.07
  • 심사 : 2011.05.13
  • 발행 : 2011.06.30
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초록

In this paper, we will prove an equilibrium existence theorem of a non-compact acyclic strategic game with affine constraint correspondences which is comparable with equilibrium existence theorems due to Debreu, Nash, Kim-Kum, and Lu in several aspects.

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참고문헌

  1. J. G. Becker and D. S. Damianov, On the existence of symmetric mixed strategy equilibria, Econom. Letters 90 (2006), 84-87. https://doi.org/10.1016/j.econlet.2005.07.005
  2. E. G. Begle, A fixed point theorem, Ann. Math. 51 (1950), 544-550. https://doi.org/10.2307/1969367
  3. G. Debreu, A social equilibrium existence theorem, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 386-393.
  4. W. K. Kim and K. H. Lee, Nash equilibrium and minimax theorem with C- concavity, J. Math. Anal. Appl. 328 (2007), 1206-1216. https://doi.org/10.1016/j.jmaa.2006.06.038
  5. W. K. Kim and S. Kum, Existence of Nash equilibrium in a compact acyclic strategic game, J. Chungcheong Math. Soc. 23 (2010), 29-35.
  6. H. Lu, On the existence of pure strategy Nash equilibrium, Econom. Letters 94 (2007), 459-462. https://doi.org/10.1016/j.econlet.2006.09.006
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  8. H. Nikaido and K. Isoda, Note on non-cooperative convex games, Pacific J. Math. 5 (1955), 807-815. https://doi.org/10.2140/pjm.1955.5.807