• 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={13}
}
  • 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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18 Citations
Highly Influential Citations
1
Background Citations
10
Methods Citations
1
Results Citations
3

18 Citations

The Exact Computational Complexity of Evolutionarily Stable Strategies
TLDR
This paper proves that deciding the existence of an evolutionarily stable strategy is $\Sigma_2^P$ -complete, which means that the solution to the Nash equilibrium problem is known.
Computational Complexity of Multi-player Evolutionarily Stable Strategies
TLDR
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.
Existence of Evolutionarily Stable Strategies Remains Hard to Decide for a Wide Range of Payoff Values
TLDR
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.
Poising on Ariadne's thread: An algorithm for computing a maximum clique in polynomial time
TLDR
A polynomial-time algorithm for the maximum clique problem, which implies P = NP, is presented, based on a continuous game-theoretic representation of this problem and at its heart lies a discrete-time dynamical system.
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. Bulò, M. Pelillo
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 2013
TLDR
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
TLDR
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
TLDR
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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Appendix: Rationality of x and
  • Appendix: Rationality of x and
The computational complexity of evolutionary stable strategies
  • The computational complexity of evolutionary stable strategies
  • 2004