# The Exact Computational Complexity of Evolutionarily Stable Strategies

@inproceedings{Conitzer2013TheEC, title={The Exact Computational Complexity of Evolutionarily Stable Strategies}, author={Vincent Conitzer}, booktitle={WINE}, year={2013} }

While the computational complexity of many game-theoretic solution concepts, notably Nash equilibrium, has now been settled, the question of determining the exact complexity of computing an evolutionarily stable strategy has resisted solution since attention was drawn to it in 2004. In this paper, I settle this question by proving that deciding the existence of an evolutionarily stable strategy is $\Sigma_2^P$ -complete.

## 17 Citations

Existence of Evolutionarily Stable Strategies Remains Hard to Decide for a Wide Range of Payoff Values

- EconomicsCIAC
- 2017

A reduction robustness notion is introduced and it is shown that deciding the existence of an ESS remains coNP-hard for a wide range of games even if the authors arbitrarily perturb within some intervals the payoff values of the game under consideration.

Settling Some Open Problems on 2-Player Symmetric Nash Equilibria

- EconomicsSAGT
- 2015

It is shown that this problem of finding a non-symmetric Nash equilibrium (NE) in a symmetric game is NP-complete and the problem of counting the number of non-Symmetric NE in a symmetry game is #P-complete.

Computational Complexity of Multi-player Evolutionarily Stable Strategies

- Mathematics, Computer ScienceCSR
- 2021

It is shown that deciding existence of an ESS of a multiplayer game is closely connected to the second level of the real polynomial time hierarchy, and as a special case that deciding whether a given strategy is an LSS is complete for ∀R.

Algorithms and complexity of problems arising from strategic settings

- Computer Science, Mathematics
- 2019

This thesis deals with an evolutionary setting where it is shown that for a wide range of symmetric bimatrix games, deciding ESS existence is intractable, and presents a general framework for constructing approximation schemes for problems that can be written as an Existential Theory of the Reals formula with variables constrained in a bounded convex set.

A Case Study of Agent-Based Models for Evolutionary Game Theory

- MathematicsArXiv
- 2021

This short paper presents a game with complex interactions and examines how an agent-based model may be used as a heuristic technique to find evolutionarily stable states.

Algorithm for Evolutionarily Stable Strategies Against Pure Mutations

- Computer ScienceArXiv
- 2018

This work presents an algorithm for the case where mutations are restricted to pure strategies, and presents experiments on several game classes including random and a recently-proposed cancer model based on the first general optimization formulation for this problem.

Computing Nash Equilibria for District-based Nominations

- EconomicsAAMAS
- 2022

We study political parties that strategically place their candidates in districts so to maximise the number of their nominees that get elected. In each district, voters rank the nominated candidates…

alpha-Rank: Multi-Agent Evaluation by Evolution

- Economics
- 2019

Proofs are introduced that not only provide a unifying perspective of existing continuous- and discrete-time evolutionary evaluation models, but also reveal the formal underpinnings of the $\alpha$-Rank methodology.

Evolutionary stability implies asymptotic stability under multiplicative weights

- Economics, MathematicsArXiv
- 2016

It is shown that evolutionarily stable states in general (nonlinear) population games are asymptotically stable under a multiplicative weights dynamic (under appropriate choices of a parameter called the learning rate or step size, which is demonstrated to be crucial to achieve convergence, as otherwise even chaotic behavior is possible to manifest).

α-Rank: Multi-Agent Evaluation by Evolution

- EconomicsScientific Reports
- 2019

We introduce α-Rank, a principled evolutionary dynamics methodology, for the evaluation and ranking of agents in large-scale multi-agent interactions, grounded in a novel dynamical game-theoretic…

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