Problem
Research questions and friction points this paper is trying to address.
feasible stable equilibria
Lotka-Volterra systems
ecological interaction networks
replicator dynamics
symmetric Nash equilibria
Stable Coexistence in Ecologies and Games
🤖 AI Summary
研究通过扩展Lotka-Volterra模型解决生态系统中物种稳定共存问题，并探讨了高阶互动对实现稳定均衡的作用。
📝 Abstract
We study feasible stable equilibria of Lotka-Volterra systems and their higher-order extensions. We complete the classification of impossible ecological interaction networks with at most four species and extend several of these impossibility results to families with arbitrarily many species. We then show that these sign-pattern obstructions are specific to the pairwise Lotka-Volterra model: arbitrary prescribed growth rates and pairwise coefficients can be supplemented by higher-order interactions so as to admit a feasible asymptotically stable equilibrium. Through the correspondence with replicator dynamics, we interpret feasible equilibria of higher-order Lotka-Volterra systems as totally mixed symmetric Nash equilibria of symmetric multiplayer games, derive bounds on their number, and study their robustness under perturbations of the payoff tensors. We conclude by showing that every impossible ecology determines a nonempty open class of symmetric two-player games with no totally mixed evolutionarily stable strategy.
Innovation
Methods, ideas, or system contributions that make the work stand out.
feasible stable equilibria
higher-order Lotka-Volterra systems
totally mixed symmetric Nash equilibria
evolutionarily stable strategy
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