• Corpus ID: 13344088

A Note on the computational hardness of evolutionary stable strategies

@article{Nisan2006ANO,
  title={A Note on the computational hardness of evolutionary stable strategies},
  author={Noam Nisan},
  journal={Electron. Colloquium Comput. Complex.},
  year={2006},
  volume={TR06}
}
  • N. Nisan
  • Published 2006
  • Mathematics
  • Electron. Colloquium Comput. Complex.
We present a very simple reduction that when given a graph G and an integer k produces a game that has an evolutionary stable strategy if and only if the maximum clique size of G is not exactly k. Formally this shows that existence of evolutionary stable strategies is hard for a complexity class called co − D, slightly strengthening (and greatly simplifying) the known NP-hardness and co-NP-hardness. En route we show that even recognizing an evolutionary stable strategy is co-NP complete. 
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19 Citations
Highly Influential Citations
1
Background Citations
10
Methods Citations
1
Results Citations
2

19 Citations

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This paper shows that recognizing an ESS even in doubly symmetric bimatrix games is also coNP-complete, which implies that recognizing asymptotically stable equilibria of the replicator dynamic in this class of games isAlso a co NP-complete problem.

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

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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.

The computational complexity of evolutionarily stable strategies

TLDR
It is shown that determining the existence of an ESS is both hard and hard and coNP-hard, and that the problem is contained in $$\Sigma_{2}^{\rm p}$$ , the second level of the polynomial time hierarchy.

Algorithms and complexity of problems arising from strategic settings

TLDR
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.

NP = coNP

It is well-known that the problem of recognizing an ESS in a symmetric bimatrix game is coNP-complete. In this paper, we show that recognizing an ESS even in doubly symmetric bimatrix games is also…

A Game-Theoretic Approach to Hypergraph Clustering

  • S. R. BulòM. Pelillo
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 2013
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It is proved that the problem of finding the equilibria of the clustering game is equivalent to locally optimizing a polynomial function over the standard simplex, and a discrete-time high-order replicator dynamics to perform this optimization, based on the Baum-Eagon inequality is provided.

Evolutionary stability implies asymptotic stability under multiplicative weights

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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).

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

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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.

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The computational complexity of evolutionary stable strategies

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  • 2004

Appendix: Rationality of x and

  • Appendix: Rationality of x and