Stable Coexistence in Ecologies and Games
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.
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BibTeX
@misc{celik2026stable,
title = {{Stable Coexistence in Ecologies and Games}},
author = {Türkü Özlüm Çelik and Vincenzo Antonio Isoldi and Irem Portakal and Giulio Zucal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09286},
eprint = {2609.09286},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09286},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stable Coexistence in Ecologies and Games
AU - Türkü Özlüm Çelik
AU - Vincenzo Antonio Isoldi
AU - Irem Portakal
AU - Giulio Zucal
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09286
UR - https://arxiv.org/abs/2609.09286
AB - 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.
ER -