Equilibrium, evolutionary stability and gradient dynamics. (English) Zbl 1049.91004
Summary: Considered here are equilibria, notably those that solve noncooperative games. Focus is on connections between evolutionary stability, concavity and monotonicity. It is shown that evolutionary stable points are local attractors under gradient dynamics. Such dynamics, while reflecting search for individual improvement, can incorporate myopia, imperfect knowledge and bounded rationality/competence.
MSC:
| 91A10 | Noncooperative games |
References:
| [1] | DOI: 10.1137/S0363012993253534 · Zbl 0841.62072 · doi:10.1137/S0363012993253534 |
| [2] | DOI: 10.1007/BF02192244 · Zbl 0903.49006 · doi:10.1007/BF02192244 |
| [3] | Blum E., Mathematics Student 63 pp 123– (1994) |
| [4] | DOI: 10.1006/tpbi.1996.0011 · Zbl 0865.92012 · doi:10.1006/tpbi.1996.0011 |
| [5] | Ermoliev Yu. M., (in Russian), Kibernetika 3 pp 85– (1982) |
| [6] | DOI: 10.1007/BF02614504 · Zbl 0890.90150 · doi:10.1007/BF02614504 |
| [7] | DOI: 10.1023/A:1018987409039 · Zbl 0910.90281 · doi:10.1023/A:1018987409039 |
| [8] | DOI: 10.1016/S0165-1889(97)00103-6 · Zbl 0905.90188 · doi:10.1016/S0165-1889(97)00103-6 |
| [9] | DOI: 10.1023/A:1008709129421 · Zbl 0952.91002 · doi:10.1023/A:1008709129421 |
| [10] | DOI: 10.1080/02331930008844472 · Zbl 0963.91067 · doi:10.1080/02331930008844472 |
| [11] | DOI: 10.2307/2938222 · Zbl 0745.90012 · doi:10.2307/2938222 |
| [12] | DOI: 10.1016/0022-5193(79)90058-4 · doi:10.1016/0022-5193(79)90058-4 |
| [13] | DOI: 10.1016/0893-9659(90)90051-C · Zbl 0709.92015 · doi:10.1016/0893-9659(90)90051-C |
| [14] | DOI: 10.1006/game.1998.0647 · Zbl 0915.90284 · doi:10.1006/game.1998.0647 |
| [15] | DOI: 10.1023/A:1004665830923 · Zbl 1016.90066 · doi:10.1023/A:1004665830923 |
| [16] | DOI: 10.1038/246015a0 · Zbl 1369.92134 · doi:10.1038/246015a0 |
| [17] | DOI: 10.2307/1969530 · Zbl 0045.08203 · doi:10.2307/1969530 |
| [18] | DOI: 10.2307/1911749 · Zbl 0142.17603 · doi:10.2307/1911749 |
| [19] | DOI: 10.2307/3213376 · Zbl 0398.90120 · doi:10.2307/3213376 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
