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

@article{Melissourgos2017ExistenceOE,
  title={Existence of Evolutionarily Stable Strategies Remains Hard to Decide for a Wide Range of Payoff Values},
  author={Themistoklis Melissourgos and Paul G. Spirakis},
  journal={ArXiv},
  year={2017},
  volume={abs/1701.08108}
}
The concept of an evolutionarily stable strategy (ESS), introduced by Smith and Price [4], is a refinement of Nash equilibrium in 2-player symmetric games in order to explain counter-intuitive natural phenomena, whose existence is not guaranteed in every game. The problem of deciding whether a game possesses an ESS has been shown to be \(\varSigma _{2}^{P}\)-complete by Conitzer [1] using the preceding important work by Etessami and Lochbihler [2]. The latter, among other results, proved that… 

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.

Multi-agent systems for computational economics and finance

In this article we survey the main research topics of our group at the University of Essex. Our research interests lie at the intersection of theoretical computer science, artificial intelligence,

References

SHOWING 1-10 OF 13 REFERENCES

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.

Evolutionarily Stable Strategies of Random Games, and the Vertices of Random Polygons

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

Evolutionarily stable strategies for a finite population and a variable contest size.

  • M. Schaffer
  • Economics, Mathematics
    Journal of theoretical biology
  • 1988

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.

Evolution and the Theory of Games

TLDR
It is beginning to become clear that a range of problems in evolution theory can most appropriately be attacked by a modification of the theory of games, a branch of mathematics first formulated by Von Neumann and Morgenstern in 1944 for the analysis of human conflicts.

The theory of games and the evolution of animal conflicts.

  • J. M. Smith
  • Psychology
    Journal of theoretical biology
  • 1974

A Note on the computational hardness of evolutionary stable strategies

  • N. Nisan
  • Mathematics
    Electron. Colloquium Comput. Complex.
  • 2006
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.

Non-cooperative games

TLDR
Non-cooperative game models are described and game theoretic solution concepts are discussed, as well as refinements and relaxations of rationalizability and correlated equilibria.

Maxima for Graphs and a New Proof of a Theorem of Turán

Maximum of a square-free quadratic form on a simplex. The following question was suggested by a problem of J. E. MacDonald Jr. (1): Given a graph G with vertices 1, 2, . . . , n. Let S be the simplex

The complexity of facets (and some facets of complexity)

Many important combinatorial optimization problems, including the traveling salesman problem (TSP), the clique problem and many others, call for the optimization of a linear functional over some