Stable coexistence patterns found in ecological and game systems
Stable Coexistence in Ecologies and Games
Computer Science and Game Theory
Summary
This paper looks at how groups of species or players interact in stable and balanced ways, focusing on models that describe these relationships. The authors figured out exactly which small groups of species cannot coexist stably, and showed that adding more complex interactions can allow stability even when the simpler models fail. They also showed how these ecological models relate to game theory, helping us understand stable strategies in games with many players. Finally, they connect impossible ecological scenarios to games where no universally stable strategy exists.
What this means in practice
- •For ecological modelers: Know which small species groups cannot reach stable coexistence and how to design models with stable equilibria including higher-order interactions.
- •For game theorists: Identify symmetric multiplayer games that lack totally mixed stable strategies and understand robustness of equilibria under perturbations.
A theory result. No direct application yet.
Authors
Türkü Özlüm Çelik, Vincenzo Antonio Isoldi, Irem Portakal, Giulio Zucal
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.