Generalized replicator dynamics based on mean-field pairwise comparison dynamic
Gespeichert in:
| Titel: | Generalized replicator dynamics based on mean-field pairwise comparison dynamic |
|---|---|
| Autoren: | Hidekazu Yoshioka |
| Quelle: | Mathematics and Computers in Simulation. 236:200-220 |
| Publication Status: | Preprint |
| Verlagsinformationen: | Elsevier BV, 2025. |
| Publikationsjahr: | 2025 |
| Schlagwörter: | Optimization and Control (math.OC), FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Mathematics - Optimization and Control |
| Beschreibung: | The pairwise comparison dynamic is a forward ordinary differential equation in a Banach space whose solution is a time-dependent probability measure to maximize utility based on a nonlinear and nonlocal protocol. It contains a wide class of evolutionary game models, such as replicator dynamics and its generalization. We present an inverse control approach to obtain a replicator-type pairwise comparison dynamic from the large discount limit of a mean field game (MFG) as a coupled forward-backward system. This methodology provides a new interpretation of replicator-type dynamics as a myopic perception limit of the dynamic programming. The cost function in the MFG is explicitly obtained to derive the generalized replicator dynamics. We present a finite difference method to compute these models such that the conservation and nonnegativity of the probability density and bounds of the value function can be numerically satisfied. We conduct a computational convergence study of a large discount limit, focusing on potential games and an energy management problem under several conditions. A preprint of some submitted manuscript |
| Publikationsart: | Article |
| Sprache: | English |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2025.04.010 |
| DOI: | 10.48550/arxiv.2407.20751 |
| Zugangs-URL: | http://arxiv.org/abs/2407.20751 |
| Rights: | CC BY arXiv Non-Exclusive Distribution |
| Dokumentencode: | edsair.doi.dedup.....3e33b09d4f5fa5796671e9dd70a7ee2e |
| Datenbank: | OpenAIRE |
Full Text Finder 
Nájsť tento článok vo Web of Science | Abstract: | The pairwise comparison dynamic is a forward ordinary differential equation in a Banach space whose solution is a time-dependent probability measure to maximize utility based on a nonlinear and nonlocal protocol. It contains a wide class of evolutionary game models, such as replicator dynamics and its generalization. We present an inverse control approach to obtain a replicator-type pairwise comparison dynamic from the large discount limit of a mean field game (MFG) as a coupled forward-backward system. This methodology provides a new interpretation of replicator-type dynamics as a myopic perception limit of the dynamic programming. The cost function in the MFG is explicitly obtained to derive the generalized replicator dynamics. We present a finite difference method to compute these models such that the conservation and nonnegativity of the probability density and bounds of the value function can be numerically satisfied. We conduct a computational convergence study of a large discount limit, focusing on potential games and an energy management problem under several conditions.<br />A preprint of some submitted manuscript |
|---|---|
| ISSN: | 03784754 |
| DOI: | 10.1016/j.matcom.2025.04.010 |