# The computational complexity of evolutionarily stable strategies

@article{Etessami2004TheCC, title={The computational complexity of evolutionarily stable strategies}, author={Kousha Etessami and Andreas Lochbihler}, journal={International Journal of Game Theory}, year={2004}, volume={37}, pages={93-113} }

The concept of evolutionarily stable strategies (ESS) has been central to applications of game theory in evolutionary biology, and it has also had an influence on the modern development of game theory. A regular ESS is an important refinement the ESS concept. Although there is a substantial literature on computing evolutionarily stable strategies, the precise computational complexity of determining the existence of an ESS in a symmetric two-player strategic form game has remained open, though…

## 32 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.

### The Exact Computational Complexity of Evolutionarily Stable Strategies

- Computer ScienceWINE
- 2013

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.

### Evolutionary equilibrium in Bayesian routing games: Specialization and niche formation

- EconomicsTheor. Comput. Sci.
- 2007

### Algorithmic Game Theory: Computational Evolutionary Game Theory

- Biology
- 2007

The classical model of evolutionary game theory is described and the computational complexity of its central equilibrium concept is analyzed, and an instance of an evolutionary game-theoretic concept providing an algorithm for finding an equilibrium is shown.

### The complexity of evolutionary games on graphs

- Mathematics
- 2015

Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study…

### Invitation games and the price of stability

- EconomicsITCS
- 2014

For a wide range of schedulers it is proved that there are only two types of basic games, those that are invitation resistant in which the price of stability of the invitation version is equal to that of the basic game, and Those that are asymptotically efficient in whichThe price of Stability tends to 0 as the number of rounds grows.

### On Evolutionarily Stable Strategy

- Economics, Mathematics2018 International Conference on Applied and Engineering Mathematics (ICAEM)
- 2018

This paper provides necessary and sufficient conditions along with an algorithm that can be used to find all ESS and result describing the equilibrium points for the game dynamics, which were not discussed before.

### 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.

### 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.

## References

SHOWING 1-10 OF 32 REFERENCES

### Detecting all evolutionarily stable strategies

- Economics
- 1992

In evolutionary game theory, the central solution concept is the evolutionarily stable state, which also can be interpreted as an evolutionarily stable population strategy (ESS). As such, this notion…

### Evolution and the Theory of Games

- EconomicsAmerican scientist
- 1976

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.

### A Note on the computational hardness of evolutionary stable strategies

- MathematicsElectron. 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.…

### Complexity Results about Nash Equilibria

- EconomicsIJCAI
- 2003

A single reduction demonstrates NP- hardness of determining whether Nash equilibria with certain natural properties exist, and demonstrates the NP-hardness of counting NashEquilibria (or connected sets of Nash Equilibria).

### A general technique for computing evolutionarily stable strategies based on errors in decision-making.

- EconomicsJournal of theoretical biology
- 1997

This work presents a general computational technique based on errors in decision making that works for a simple example (the Hawk-Dove game) where an analytic solution is known, and proves general results about the technique for more complex games.

### Evolutionary Games and Population Dynamics

- Psychology
- 1998

In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.

### Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points

- Economics
- 1973

Equilibrium points in mixed strategies seem to be unstable, because any player can deviate without penalty from his equilibrium strategy even if he expects all other players to stick to theirs. This…