03 Mar 2026
Recently, the paper entitled “A hybrid differential game in renewable resources with sliding models and crossing limit cycle” by Dr Anton Bondarev from International Business School Suzhou (IBSS) at Xi’an Jiaotong-Liverpool University (XJTLU) has published in the Journal of Economic Dynamics and Control. The research, which expands on existing resource management models, offers fresh insights for sustainable renewable resource exploitation in multi-actor settings.
The research builds upon single-agent optimal harvesting models with regime-switching—where resource stock growth rates change abruptly at a critical stock threshold—by extending the framework to a two-agent non-cooperative dynamic game. This expansion into a three-dimensional state-costate phase space uncovered unexpected complexities in strategic interactions between competing resource harvesters.
A key finding of the analysis is the emergence of two novel equilibrium outcomes: sliding regions and hybrid crossing limit cycles (HCLCs). These phenomena are unique to PWS systems and have not been observed in traditional smooth dynamical systems. Sliding behavior occurs when the system’s equilibrium settles exactly at the switching threshold between high and low growth regimes, balancing the two distinct growth states. HCLCs, meanwhile, represent a new class of dynamical cycles that have never been documented in resource management or optimization literature.
The study demonstrates that under specific parameter conditions, either sliding behavior or an HCLC can emerge as an open-loop Nash equilibrium (OLNE) in the two-player game. Notably, this contrasts with recent findings in optimally controlled planar systems, where such cycles were proven non-optimal. The research does not address Markov feedback Nash equilibria, as the theory of discontinuous Markov strategies remains underdeveloped.
Beyond theoretical contributions, the work paves a new path for sustainable harvesting of renewable resources involving multiple actors. It shows that an intermittent equilibrium—alternating between low growth/high catch and high growth/low catch states—can be achieved through cyclic harvesting regimes around the critical growth threshold, a mechanism not described in previous research.
This discovery challenges conventional understanding of resource harvesting dynamics and provides a new analytical tool for policymakers and resource managers. By accounting for the complex strategic interactions and novel equilibria identified, stakeholders can develop more effective and sustainable resource management strategies in multi-actor environments.
Dr Anton Bondarev is an Associate professor in Economics at IBSS. He acquired his PhD from Bielefeld University concentrating on dynamics of innovations and optimal management of RD. Prior to joining XJTLU he served as a Postdoc in different international projects, such as Climate Policy of Nations in Germany, Competence Center for Research in Energy, Society and Transition in Switzerland and others. Anton’s research is focused on endogenous growth, environment, promotion of innovations and optimal governance of large-scale technological transitions, be it renewable energy or modernization of the economy. He actively publishes in such journals as Automatica (IF=6.150), European Economic Review (ABDC: A*), Journal of Economic Dynamics and Control ( ABDC: A*), China Economic Review (ABDC: A), Energy Policy (ABDC: A), Macroeconomic Dynamics (ABDC: A), Journal of Evolutionary Economics (ABDC: A) and others.
The Journal of Economic Dynamics and Control is a peer-reviewed scholarly publication established in 1979, published monthly by Elsevier, focusing on computational economics, dynamic economic models, and macroeconomics. As a leading venue in its field, the journal provides an outlet for theoretical and empirical research on economic dynamics and control, alongside advancements in computational methods applied to economics and finance, including artificial intelligence, neural networks, and optimization algorithms.
03 Mar 2026