Abstract
We consider a differential game of fisheries in a fan-like control structure of the type “supervisor—several agents”. The dynamics of the controlled system is described by a non-linear differential equation model which is identified on the Azov Sea data. An averaging by two spatial coordinates is conducted. Different information structures of the game are generated by the control methods of compulsion (supervisor restricts the feasible strategies of agents) and impulsion (she exerts an impact to their payoff functionals). Both Stackerlberg and inverse Stackelberg games are considered. For the numerical investigation we use a discretization of the initial model and the method of qualitatively representative scenarios in simulation modeling.
Highlights
Introduction and Related WorkThe models of optimal exploitation of water biological resources have been investigated since the middle of the last century [1,2], in the frame of sustainability science [3,4] and viability theory [5].A comprehensive review of the game-theoretic applications to the fisheries is presented in [6].From the societal point of view, overfishing is dangerous for biological and economical reasons, but it still holds [1]
Game theoretic models can help in resolving these issues [7]
The hierarchical control mechanisms are presented as solutions of the Stackelberg games with phase constraints which reflect the requirements to the state of a controlled system
Summary
The models of optimal exploitation of water biological resources have been investigated since the middle of the last century [1,2], in the frame of sustainability science [3,4] and viability theory [5]. The authors’ approach to the modeling of fisheries is based on the concept of sustainable management [34,35,36] In this frame, the hierarchical control mechanisms (compulsion and impulsion methods) are presented as solutions of the Stackelberg games with phase constraints which reflect the requirements to the state of a controlled system (the conditions of sustainable development). Defined by a system of six partial differential equations in parabolic partial derivatives in the region G that represents a closed basin bounded by an undisturbed surface of the body of water, the bed, and cylindrical surface, for the time interval 0 ≤ t ≤ T [24,25,26,27,29] Extending this model, we construct a hierarchical differential game of two players with the leader (the supervisory body of the fishing service) and the follower (a fishing company). If the supervisor violates it a penalty is imposed with coefficient H
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
