DOI QR코드

DOI QR Code

NEW EXISTENCE OF SOCIAL EQUILIBRIA IN GENERALIZED NASH GAMES WITH INSATIABILITY

  • Kim, Won Kyu (Department of Mathematics Education Chungbuk National University)
  • Received : 2010.07.12
  • Accepted : 2010.11.09
  • Published : 2010.12.30

Abstract

In this paper, we first introduce a new model of strategic Nash game with insatiability, and next give two social equilibrium existence theorems for general strategic games which are comparable with the previous results due to Arrow and Debreu, Debreu, and Chang in several aspects.

Keywords

References

  1. K. J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica 22 (1954), 265-290. https://doi.org/10.2307/1907353
  2. A. Borglin and H. Keiding, Existence of equilibrium actions and of equilibrium: A note on the 'new' existence theorem, J. Math. Econom. 3 (1976), 313-316. https://doi.org/10.1016/0304-4068(76)90016-1
  3. S.-Y. Chang, Noncompact qualitative games with applications to equilibria, Nonlinear Anal. 65 (2006), 593-600. https://doi.org/10.1016/j.na.2005.09.041
  4. G. Debreu, A social equilibrium theorem, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 386-393.
  5. X. P. Ding, W. K. Kim and K.-K.Tan, Equilibria of non-compact generalized games with $L^{*}$-majorized preferences, J. Math. Anal. Appl. 164 (1992), 508-517. https://doi.org/10.1016/0022-247X(92)90130-6
  6. D. Gale and A. Mas-Colell, An equilibrium existence for a general model without ordered preferences, J. Math. Econom. 2 (1975), 9-15. https://doi.org/10.1016/0304-4068(75)90009-9
  7. W. K. Kim and G.X.-Z. Yuan, Existence of equilibria for generalized games and generalized social systems with coordination, Nonlinear Anal. 45 (2001), 169-188. https://doi.org/10.1016/S0362-546X(99)00336-3
  8. J. Nash, Non-cooperative games, Ann. Math. 54 (1951), 286-295. https://doi.org/10.2307/1969529
  9. S. Park, Acyclic versions of the von Neumann and Nash equilibrium theorems, J. Comp. Appl. Math. 113 (2000), 83-91. https://doi.org/10.1016/S0377-0427(99)00246-0
  10. W. Shafer and H. Sonnenschein, Equilibrium in abstract economies without ordered preferences, J. Math. Econom. 2 (1975), 345-348. https://doi.org/10.1016/0304-4068(75)90002-6