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Topological essentiality in infinite games
1. | School of Mathematics and Computer Science, Guizhou Normal University, Guizhou, Guiyang 550001, China |
2. | Department of Mathematics, Guizhou Uniersity, Guizhou, Guiyang 550025, China |
3. | Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China |
References:
[1] |
N. Al-Najjar, Strategically stable equilibria in games with infinitely many pure strategies, Math. Soc. Sci., 29 (1995), 151-164.
doi: 10.1016/0165-4896(94)00765-Z. |
[2] |
P. Billingsley, "Convergence of Probability Measures," John Wiley & Sons, Inc., New York-London-Sydney, 1968. |
[3] |
K. Fan, Fixed-point and minimax theorems in locally convex linear spaces, Proc. Natl. Acad. Sci. USA, 38 (1952), 121-126.
doi: 10.1073/pnas.38.2.121. |
[4] |
D. Fudenberg and D. Levine, Subgame perfect equilibria of finite- and infinite-horizon games, J. Economic Theory, 31 (1983), 251-268. |
[5] |
D. Fudenberg and D. Levine, Limit games and limit equilibria, J. Economic Theory, 38 (1986), 261-279.
doi: 10.1016/0022-0531(86)90118-3. |
[6] |
I. Glicksberg, A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc., 3 (1952), 170-174. |
[7] |
S. Govindan and R. Wilson, Essential equilibria, Proc. Natl. Acad. Sci. USA, 102 (2005), 15706-15711.
doi: 10.1073/pnas.0506796102. |
[8] |
J. Hillas, On the definition of the strategic stability of equilibria, Econometrica, 58 (1990), 1365-1390.
doi: 10.2307/2938320. |
[9] |
J. Jiang, Essential equilibrium points of n-person non-cooperative games. II, Sci. Sinica, 12 (1963), 651-671. |
[10] |
J. Jiang, Essential component of the set of fixed points of the multivalued mappings and its application to the theory of games, Sci. Sinica, 12 (1963), 951-964. |
[11] |
E. Klein and A. Thompson, "Theory of Correspondences. Including Applications to Mathematical Economics," Canadian Mathematical Society Series of Monographs and Advanced Texts, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1984. |
[12] |
E. Kohlberg and J. Mertens, On the strategic stability of equilibria, Econometrica, 54 (1986), 1003-1037.
doi: 10.2307/1912320. |
[13] |
A. McLennan, Consistent conditional beliefs in noncooperative game theory, Int. J. of Game Theory, 18 (1989), 175-184.
doi: 10.1007/BF01268156. |
[14] |
J. F. Nash, Jr., Equilibrium points in $n$-person games, Proc. Natl. Acad. Sci. USA, 36 (1950) 48-49.
doi: 10.1073/pnas.36.1.48. |
[15] |
J. Nash, Non-cooperative games, Ann. Math. (2), 54 (1951), 286-295.
doi: 10.2307/1969529. |
[16] |
B. O'Neill, Essential sets and fixed points, Am. J. Math., 75 (1953), 497-509. |
[17] |
R. Selten, Reexamination of the perfectness concept for equilibrium points in extensive games, Int. J. of Game Theory, 4 (1975), 25-55.
doi: 10.1007/BF01766400. |
[18] |
L. Simon, Local perfection, J. Economic Theory, 43 (1987), 134-156.
doi: 10.1016/0022-0531(87)90118-9. |
[19] |
L. Simon and M. Stinchcombe, Equilibrium refinement for infinite normal-form games, Econometrica, 63 (1995), 1421-1443.
doi: 10.2307/2171776. |
[20] |
A. Tychonoff, Ein fixpunktsatz, Math. Ann., 111 (1935), 767-776. |
[21] |
E. van Damme, "Stability and Perfection of Nash Equilibria," Second edition, Springer-Verlag, New-York, 1991. |
[22] |
W. Wu and J. Jiang, Essential equilibrium points of n-person non-cooperative games, Sci. Sinica, 11 (1962), 1307-1322. |
[23] |
Y. Zhou, J. Yu and L. Wang, A new proof of existence of equilibria in infinite normal form games, Appl. Math. Lett., 24 (2011), 253-256.
doi: 10.1016/j.aml.2010.09.014. |
[24] |
Y. Zhou, J. Yu and S. Xiang, Essential stability in games with infinitely many pure strategies, Int. J. of Game Theory, 35 (2007), 493-503.
doi: 10.1007/s00182-006-0063-0. |
[25] |
Y. Zhou, J. Yu and S. Xiang, A metric on the space of finite measures with an application to fixed point theory, Appl. Math. Lett., 21 (2008), 489-495.
doi: 10.1016/j.aml.2007.05.015. |
show all references
References:
[1] |
N. Al-Najjar, Strategically stable equilibria in games with infinitely many pure strategies, Math. Soc. Sci., 29 (1995), 151-164.
doi: 10.1016/0165-4896(94)00765-Z. |
[2] |
P. Billingsley, "Convergence of Probability Measures," John Wiley & Sons, Inc., New York-London-Sydney, 1968. |
[3] |
K. Fan, Fixed-point and minimax theorems in locally convex linear spaces, Proc. Natl. Acad. Sci. USA, 38 (1952), 121-126.
doi: 10.1073/pnas.38.2.121. |
[4] |
D. Fudenberg and D. Levine, Subgame perfect equilibria of finite- and infinite-horizon games, J. Economic Theory, 31 (1983), 251-268. |
[5] |
D. Fudenberg and D. Levine, Limit games and limit equilibria, J. Economic Theory, 38 (1986), 261-279.
doi: 10.1016/0022-0531(86)90118-3. |
[6] |
I. Glicksberg, A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc., 3 (1952), 170-174. |
[7] |
S. Govindan and R. Wilson, Essential equilibria, Proc. Natl. Acad. Sci. USA, 102 (2005), 15706-15711.
doi: 10.1073/pnas.0506796102. |
[8] |
J. Hillas, On the definition of the strategic stability of equilibria, Econometrica, 58 (1990), 1365-1390.
doi: 10.2307/2938320. |
[9] |
J. Jiang, Essential equilibrium points of n-person non-cooperative games. II, Sci. Sinica, 12 (1963), 651-671. |
[10] |
J. Jiang, Essential component of the set of fixed points of the multivalued mappings and its application to the theory of games, Sci. Sinica, 12 (1963), 951-964. |
[11] |
E. Klein and A. Thompson, "Theory of Correspondences. Including Applications to Mathematical Economics," Canadian Mathematical Society Series of Monographs and Advanced Texts, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1984. |
[12] |
E. Kohlberg and J. Mertens, On the strategic stability of equilibria, Econometrica, 54 (1986), 1003-1037.
doi: 10.2307/1912320. |
[13] |
A. McLennan, Consistent conditional beliefs in noncooperative game theory, Int. J. of Game Theory, 18 (1989), 175-184.
doi: 10.1007/BF01268156. |
[14] |
J. F. Nash, Jr., Equilibrium points in $n$-person games, Proc. Natl. Acad. Sci. USA, 36 (1950) 48-49.
doi: 10.1073/pnas.36.1.48. |
[15] |
J. Nash, Non-cooperative games, Ann. Math. (2), 54 (1951), 286-295.
doi: 10.2307/1969529. |
[16] |
B. O'Neill, Essential sets and fixed points, Am. J. Math., 75 (1953), 497-509. |
[17] |
R. Selten, Reexamination of the perfectness concept for equilibrium points in extensive games, Int. J. of Game Theory, 4 (1975), 25-55.
doi: 10.1007/BF01766400. |
[18] |
L. Simon, Local perfection, J. Economic Theory, 43 (1987), 134-156.
doi: 10.1016/0022-0531(87)90118-9. |
[19] |
L. Simon and M. Stinchcombe, Equilibrium refinement for infinite normal-form games, Econometrica, 63 (1995), 1421-1443.
doi: 10.2307/2171776. |
[20] |
A. Tychonoff, Ein fixpunktsatz, Math. Ann., 111 (1935), 767-776. |
[21] |
E. van Damme, "Stability and Perfection of Nash Equilibria," Second edition, Springer-Verlag, New-York, 1991. |
[22] |
W. Wu and J. Jiang, Essential equilibrium points of n-person non-cooperative games, Sci. Sinica, 11 (1962), 1307-1322. |
[23] |
Y. Zhou, J. Yu and L. Wang, A new proof of existence of equilibria in infinite normal form games, Appl. Math. Lett., 24 (2011), 253-256.
doi: 10.1016/j.aml.2010.09.014. |
[24] |
Y. Zhou, J. Yu and S. Xiang, Essential stability in games with infinitely many pure strategies, Int. J. of Game Theory, 35 (2007), 493-503.
doi: 10.1007/s00182-006-0063-0. |
[25] |
Y. Zhou, J. Yu and S. Xiang, A metric on the space of finite measures with an application to fixed point theory, Appl. Math. Lett., 21 (2008), 489-495.
doi: 10.1016/j.aml.2007.05.015. |
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