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As an equilibrium refinement of the Nash equilibrium, evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory and has attracted growing interest. An ESS can be either a pure strategy or a mixed strategy. Even…

Computer Science and Game Theory · Computer Science 2014-06-09 Xinyang Deng , Zhen Wang , Qi Liu , Yong Deng , Sankaran Mahadevan

We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to…

Computer Science and Game Theory · Computer Science 2025-12-15 Sam Ganzfried

Evolutionarily stable strategy (ESS) is the defining concept of evolutionary game theory. It has a fairly unanimously accepted definition for the case of symmetric games which are played in a homogeneous population where all individuals are…

Populations and Evolution · Quantitative Biology 2025-11-26 Vikash Kumar Dubey , Suman Chakraborty , Arunava Patra , Sagar Chakraborty

An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (``mutant'') strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the…

Probability · Mathematics 2022-09-22 Sergiu Hart , Yosef Rinott , Benjamin Weiss

In evolutionary game theory an Evolutionarily Stable Strategy (ESS) is a refinement of the Nash equilibrium concept that is sometimes also recognized as evolutionary stability. It is a game-theoretic model, well known to mathematical…

Quantum Physics · Physics 2016-12-21 Azhar Iqbal , Taksu Cheon

The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many…

Physics and Society · Physics 2022-04-06 Natalia L. Kontorovsky , Juan Pablo Pinasco , Federico Vazquez

Evolutionarily Stable Strategy (ESS) in classical game theory is a refinement of Nash equilibrium concept. We investigate the consequences when a small group of mutants using quantum strategies try to invade a classical ESS in a population…

Quantum Physics · Physics 2009-11-06 A. Iqbal , A. H. Toor

The concept of an evolutionarily stable strategy (ESS), introduced by Smith and Price, is a refinement of Nash equilibrium in 2-player symmetric games in order to explain counter-intuitive natural phenomena, whose existence is not…

Computational Complexity · Computer Science 2017-01-30 Themistoklis Melissourgos , Paul Spirakis

Evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory. ESS provides an evolutionary stability criterion for biological, social and economical behaviors. In this paper, we develop a new approach to evaluate ESS in…

Computer Science and Game Theory · Computer Science 2020-06-18 Haozhen Situ

In this paper we study the computational complexity of computing an evolutionary stable strategy (ESS) in multi-player symmetric games. For two-player games, deciding existence of an ESS is complete for {\Sigma} 2 , the second level of the…

Computational Complexity · Computer Science 2022-03-16 Manon Blanc , Kristoffer Arnsfelt Hansen

We quantized the Hawk-Dove game by using the most general form of a pure initial state to investigate the existence of pure and mixed Evolutionarily Stable Strategies (ESS). An example is considered to draw a comparison between classical…

Quantum Physics · Physics 2010-12-23 Ahmad Nawaz , A. H. Toor

The idea of evolutionarily stable state (ESS) of a population is a cornerstone of evolutionary game theory; moreover, it coincides with the game-theoretic concept of Nash equilibrium. Such a state corresponds to a strategy adopted by the…

Adaptation and Self-Organizing Systems · Physics 2026-01-06 Suman Chakraborty , Vikash Kumar Dubey , Vaibhav Madhok , Sagar Chakraborty

An evolutionarily stable strategy (ESS) was originally defined as a static concept but later given a dynamic characterization. A well known theorem in evolutionary game theory says that an ESS is an attractor of replicator dynamics but not…

Quantum Physics · Physics 2007-05-23 Azhar Iqbal , A. H. Toor

We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader…

Computer Science and Game Theory · Computer Science 2026-03-26 Sam Ganzfried

Evolution Strategies (ESs) have recently become popular for training deep neural networks, in particular on reinforcement learning tasks, a special form of controller design. Compared to classic problems in continuous direct search, deep…

Neural and Evolutionary Computing · Computer Science 2018-07-03 Nils Müller , Tobias Glasmachers

Evolutionary Strategies (ES) are a popular family of black-box zeroth-order optimization algorithms which rely on search distributions to efficiently optimize a large variety of objective functions. This paper investigates the potential…

Neural and Evolutionary Computing · Computer Science 2019-02-01 Louis Faury , Clement Calauzenes , Olivier Fercoq , Syrine Krichen

Evolution strategies (ESs) are zeroth-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are…

Numerical Analysis · Mathematics 2022-02-09 Youhei Akimoto , Anne Auger , Tobias Glasmachers , Daiki Morinaga

Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…

Neural and Evolutionary Computing · Computer Science 2022-02-23 Youssef Diouane , Aurelien Lucchi , Vihang Patil

Evolutionary algorithms (EAs) are general-purpose problem solvers that usually perform an unbiased search. This is reasonable and desirable in a black-box scenario. For combinatorial optimization problems, often more knowledge about the…

Neural and Evolutionary Computing · Computer Science 2020-04-23 Vahid Roostapour , Jakob Bossek , Frank Neumann

We explore the use of Evolution Strategies (ES), a class of black box optimization algorithms, as an alternative to popular MDP-based RL techniques such as Q-learning and Policy Gradients. Experiments on MuJoCo and Atari show that ES is a…

Machine Learning · Statistics 2017-09-11 Tim Salimans , Jonathan Ho , Xi Chen , Szymon Sidor , Ilya Sutskever
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