# Evolutionary Stable Strategies in Multistage Games

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Definition of ESS for Two-Person Games

**Definition**

**1.**

**Definition**

**2.**

**Example**

**1.**

**Theorem**

**1.**

## 3. Definition of ESS for **n**-Person Games

**Definition**

**3.**

## 4. Existence of ESS in Multistage Repeated **n**-Person Games

**Theorem**

**2.**

## 5. ESS for Metagames

**Definition**

**4.**

**Theorem**

**3.**

**Proof.**

**Example**

**2.**

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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${\mathit{x}}_{21}^{\prime}$ | ${\mathit{x}}_{22}^{\prime}$ | ${\mathit{x}}_{23}^{\prime}$ | |
---|---|---|---|

1 | 2 | 3 | |

${x}_{11}^{\prime}$ 1 | (10, 10) | (0, 15) | (0, 0) |

${x}_{12}^{\prime}$ 2 | (15, 0) | (6, 6) | (0, 0) |

${x}_{13}^{\prime}$ 3 | (0, 0) | (0, 0) | (0, 0) |

${\mathit{x}}_{21}^{\u2033}$ | ${\mathit{x}}_{22}^{\u2033}$ | ${\mathit{x}}_{23}^{\u2033}$ | |
---|---|---|---|

1 | 2 | 3 | |

${x}_{11}^{\u2033}$ 1 | (11, 11) | (0, 15) | (2, 2) |

${x}_{12}^{\u2033}$ 2 | (15, 0) | (6, 6) | (2, 2) |

${x}_{13}^{\u2033}$ 3 | (2, 2) | (2, 2) | (2, 2) |

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**MDPI and ACS Style**

Petrosyan, L.A.; Liu, X.
Evolutionary Stable Strategies in Multistage Games. *Mathematics* **2023**, *11*, 2492.
https://doi.org/10.3390/math11112492

**AMA Style**

Petrosyan LA, Liu X.
Evolutionary Stable Strategies in Multistage Games. *Mathematics*. 2023; 11(11):2492.
https://doi.org/10.3390/math11112492

**Chicago/Turabian Style**

Petrosyan, Leon A., and Xiuxiu Liu.
2023. "Evolutionary Stable Strategies in Multistage Games" *Mathematics* 11, no. 11: 2492.
https://doi.org/10.3390/math11112492