# Dynamic Multicriteria Games with Finite Horizon

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## Abstract

**:**

## 1. Introduction

## 2. Multicriteria Games and Solution Concepts

**Definition**

**1.**

- 1.
- weak Pareto equilibrium if$\forall i\in N$$$\neg \exists {y}_{i}\in {X}_{i}:{u}_{i}({y}_{i},{x}_{-i})>{u}_{i}\left(x\right)\phantom{\rule{0.166667em}{0ex}},$$
- 2.
- strong Pareto equilibrium if$\forall i\in N$$$\neg \exists {y}_{i}\in {X}_{i}:{u}_{i}({y}_{i},{x}_{-i})\geqq {u}_{i}\left(x\right)\phantom{\rule{0.166667em}{0ex}}.$$

**Definition**

**2.**

## 3. Dynamic Multicriteria Model with Finite Horizon and Solution Concepts

#### 3.1. Multicriteria Nash Equilibrium

**Definition**

**3.**

#### 3.2. Multicriteria Cooperative Equilibrium

**Definition**

**4.**

## 4. Dynamic Multicriteria Model with Finite Harvesting Times

#### 4.1. Multicriteria Nash Equilibrium

**Theorem**

**1.**

**Proof.**

#### 4.2. Cooperative Equilibrium

**Theorem**

**2.**

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Rettieva, A. Dynamic Multicriteria Games with Finite Horizon. *Mathematics* **2018**, *6*, 156.
https://doi.org/10.3390/math6090156

**AMA Style**

Rettieva A. Dynamic Multicriteria Games with Finite Horizon. *Mathematics*. 2018; 6(9):156.
https://doi.org/10.3390/math6090156

**Chicago/Turabian Style**

Rettieva, Anna. 2018. "Dynamic Multicriteria Games with Finite Horizon" *Mathematics* 6, no. 9: 156.
https://doi.org/10.3390/math6090156