Stackelberg Mean-Field-Type Games with Polynomial Cost
| Autor: | Zahrate El Oula Frihi, Boualem Djehiche, Julian Barreiro-Gomez, Hamidou Tembine, Salah Eddine Choutri |
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| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Class (set theory) Mathematical optimization Polynomial Computer science 020208 electrical & electronic engineering Structure (category theory) 02 engineering and technology Function (mathematics) Set (abstract data type) symbols.namesake Range (mathematics) 020901 industrial engineering & automation Control and Systems Engineering Nash equilibrium 0202 electrical engineering electronic engineering information engineering symbols Stackelberg competition |
| Zdroj: | IFAC-PapersOnLine. 53:16920-16925 |
| ISSN: | 2405-8963 |
| DOI: | 10.1016/j.ifacol.2020.12.1234 |
| Popis: | This article presents a class of Stackelberg mean-field-type games with multiple leaders and multiple followers. The decision-makers act in sequential order with informational differences. The state dynamics is driven by jump-diffusion processes and the cost function is non-quadratic and has a polynomial structure. The structures of Stackelberg strategies and costs of the leaders and followers are given in a semi-explicit way in state-and- mean-field-type feedback form. A sufficiency condition is provided using an infinite dimensional partial integro-differential system. The methodology is extended to multi-level hierarchical systems. It is shown that not only the set of decision-makers per level matters but also the number of hierarchical levels plays a key role in the global performance of the system. We also identify specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play. |
| Databáze: | OpenAIRE |
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