A Stochastic Nash Equilibrium Problem for Crisis Rescue
This paper proposes a two-stage stochastic non-cooperative game model to solve relief supplies procurement and distribution optimization of multiple rescue organizations in crisis rescue. Rescue organizations with limited budgets minimize rescue costs through relief supply procurement, storage, and...
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MDPI AG
2025-06-01
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| author | Cunlin Li Yiyan Li |
| author_facet | Cunlin Li Yiyan Li |
| author_sort | Cunlin Li |
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| description | This paper proposes a two-stage stochastic non-cooperative game model to solve relief supplies procurement and distribution optimization of multiple rescue organizations in crisis rescue. Rescue organizations with limited budgets minimize rescue costs through relief supply procurement, storage, and transportation in an uncertain environment. Under a mild assumption, we establish the existence and uniqueness of the equilibrium point and derive the optimality conditions by using the duality theory, characterizing the saddle point in the Lagrange framework. The problem is further reformulated as a constraint system governed by Lagrange multipliers, and its optimality is characterized by the Karush–Kuhn–Tucker condition. The economic interpretation of the multipliers as shadow prices is elucidated. Numerical experiments verify the effectiveness of the model in cost optimization in crisis rescue scenarios. |
| format | Article |
| id | doaj-art-b9ff9bd8608349bcb6f9bca1b6abc29e |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-b9ff9bd8608349bcb6f9bca1b6abc29e2025-08-20T03:32:31ZengMDPI AGAxioms2075-16802025-06-0114645610.3390/axioms14060456A Stochastic Nash Equilibrium Problem for Crisis RescueCunlin Li0Yiyan Li1Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Wenchang Street, Yinchuan 750021, ChinaSchool of Mathematics and Information Science, North Minzu University, Wenchang Street, Yinchuan 750021, ChinaThis paper proposes a two-stage stochastic non-cooperative game model to solve relief supplies procurement and distribution optimization of multiple rescue organizations in crisis rescue. Rescue organizations with limited budgets minimize rescue costs through relief supply procurement, storage, and transportation in an uncertain environment. Under a mild assumption, we establish the existence and uniqueness of the equilibrium point and derive the optimality conditions by using the duality theory, characterizing the saddle point in the Lagrange framework. The problem is further reformulated as a constraint system governed by Lagrange multipliers, and its optimality is characterized by the Karush–Kuhn–Tucker condition. The economic interpretation of the multipliers as shadow prices is elucidated. Numerical experiments verify the effectiveness of the model in cost optimization in crisis rescue scenarios.https://www.mdpi.com/2075-1680/14/6/456crisis reliefstochastic nash equilibriumlagrange variablesstochastic variational inequalities |
| spellingShingle | Cunlin Li Yiyan Li A Stochastic Nash Equilibrium Problem for Crisis Rescue Axioms crisis relief stochastic nash equilibrium lagrange variables stochastic variational inequalities |
| title | A Stochastic Nash Equilibrium Problem for Crisis Rescue |
| title_full | A Stochastic Nash Equilibrium Problem for Crisis Rescue |
| title_fullStr | A Stochastic Nash Equilibrium Problem for Crisis Rescue |
| title_full_unstemmed | A Stochastic Nash Equilibrium Problem for Crisis Rescue |
| title_short | A Stochastic Nash Equilibrium Problem for Crisis Rescue |
| title_sort | stochastic nash equilibrium problem for crisis rescue |
| topic | crisis relief stochastic nash equilibrium lagrange variables stochastic variational inequalities |
| url | https://www.mdpi.com/2075-1680/14/6/456 |
| work_keys_str_mv | AT cunlinli astochasticnashequilibriumproblemforcrisisrescue AT yiyanli astochasticnashequilibriumproblemforcrisisrescue AT cunlinli stochasticnashequilibriumproblemforcrisisrescue AT yiyanli stochasticnashequilibriumproblemforcrisisrescue |