Pareto efficiency of infinite-horizon cooperative stochastic differential games with Markov jumps and Poisson jumps

Po Hu, Hongbin Ma, Xiaoguang Yang and Yifen Mu

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 480-494

Abstract: This paper investigates a wide class of infinite-horizon cooperative stochastic differential games with Markov jumps and Poisson jumps, which can model uncertainties of internal mode transition and characterize occasional sudden changes in the games, respectively. Firstly, the necessary conditions which guarantee the existence of Pareto solutions are obtained by utilizing the Lagrange multiplier method and the stochastic maximum principle with Markov jumps and Poisson jumps. Then the sufficient conditions which guarantee the existence of Pareto efficient strategies are derived. Secondly, the well-posedness of cooperative stochastic differential games (CSDG) with Markov jumps and Poisson jumps in infinite horizon is established when the solution of generalized algebraic Riccati equation (GARE) exists. Furthermore, we can obtain Pareto solutions by introducing the coupled algebraic Lyapunov equations (ALEs). Finally, the numerical examples verify the theoretical results.

Keywords: Stochastic differential games; Poisson jumps; Markov jumps; Pareto efficiency; Cooperative games (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475424001629
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:480-494

DOI: 10.1016/j.matcom.2024.04.036

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().