Approximation theorem and general convergence of population games. (Chinese. English summary) Zbl 1516.91011
Summary: In this paper, we study whether the approximate solution of bounded rationality converges to the exact solution of complete rationality, which provides a theoretical support for the algorithm of population games. Firstly, under certain assumptions, the approximation theorem of population games under bounded rationality is proved. Then, by using the method of set-valued analysis and in the sense of Baire classification, we obtain the result that the solution of population games with perturbations on the objective function has generic convergence.
MSC:
| 91A22 | Evolutionary games |
References:
| [1] | Nash J . Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 1950, 36 (1): 48- 49 · Zbl 0036.01104 · doi:10.1073/pnas.36.1.48 |
| [2] | Smith M . Evolution and the Theory of Games. Cambridge: Cambridge University Press, 1982 · Zbl 0526.90102 |
| [3] | Sandholm W H . Population Games and Evolutionary Dynamics. Massachusetts: MIT Press, 2011 · Zbl 1208.91003 |
| [4] | Yang G H , Yang H . Stability of weakly Pareto-Nash equilibria and Pareto-Nash equilibria for multiobjective population games. Set-Valued and Variational Analysis, 2017, 25 (2): 427- 439 · Zbl 1366.91039 · doi:10.1007/s11228-016-0391-6 |
| [5] | Yang G H , Yang H , Song Q Q . Stability of weighted Nash equilibrium for multiobjective population games. The Journal of Nonlinear Sciences and Applications, 2016, 9 (6): 4167- 4176 · Zbl 1346.90758 · doi:10.22436/jnsa.009.06.59 |
| [6] | Yang G H , Yang H . Stability of group game Nash equilibrium under finite rationality. Journal of Guizhou University(Natural Science), 2019, 36 (5): 14- 16 |
| [7] | Simon H A. The Cornerstone of Modern Decision Theory. Translated by Yang L, et al. Beijing: Beijing Institute of Economics Press, 1989 |
| [8] | Simon H A . Administrative Behavior: A Study of Decision-Making Processces in Administrative Organizations. Beijing: Mechanical Industry Press, 2013 |
| [9] | Yu J . Bounded Rationality and the Stability of Equilibrium Point Set in Game Theory. Beijing: Science Press, 2017 |
| [10] | Chen B , Liu Q Y , Huang N J . Connectedness of approximate solutions set for vector equilibrium problems in Hausdorff topological vector spaces. Fixed Point Theory Appl., 2011, 36, 1- 11 · Zbl 1315.47055 |
| [11] | Han Y , Huang N J . Some characterizations of the approximate solutions to generalized vector equilibrium problems. J Ind Manag Optim, 2016, 12, 1135- 1151 · Zbl 1328.90147 |
| [12] | Qiu X L , Jia W S , Pe ng , D T . An approximation theorem and generic convergence for equilibrium problems. Journal of Inequalities and Applications, 2018, 30, 1- 12 · Zbl 1395.46057 |
| [13] | Yang Z , Zhang H Q . Essential stability of cooperative equilibria for population games. Optimization Letters, 2019, 13 (7): 1573- 1582 · Zbl 1432.91016 · doi:10.1007/s11590-018-1303-5 |
| [14] | Qiu X L , Jia W S . Approximation theorem of variational inequality under bounded rationality. Journal of Mathematical Physics, 2019, 39 (4): 730- 737 · Zbl 1449.49014 · doi:10.3969/j.issn.1003-3998.2019.04.004 |
| [15] | Jia W S , Qiu X L , Peng D T . An approximation theorem for vector equilibrium problems under bounded rationality. Mathematics, 2020, 45, 1- 9 |
| [16] | Yu J . Game Theory and Nonlinear Analysis (Continued). Beijing: Science Press, 2011 |
| [17] | Yu J . Game Theory and Nonlinear Analysis. Beijing: Science Press, 2008 |
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