# Game of Thrones: Accommodating Monetary Policies in a Monetary Union

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of the Dynamic Game Problem

## 3. The MUMOD2 Model

## 4. Results

- ‒
- sc1: the non-cooperative Nash game with four independent players,
- ‒
- sc2: a coalition of core and central bank (CB) versus a coalition of periphery countries, which results in a Nash game with two players: (1) central bank and core; (2) periphery,
- ‒
- sc3: a coalition of fiscal stability-oriented countries (Countries 1 and 2) with the central bank, which results in a Nash game with two players: (1) central bank + core + Country 2; (2) Country 3,
- ‒
- sc4: a coalition of Country 3 with central bank versus a coalition of Countries 1 and 2, which results in a Nash game with two players: (1) central bank and Country 3, (2) Countries 1 + 2, and
- ‒
- sc5: the cooperative Pareto solution where all players act in coordination as one player.

## 5. Sensitivity Analysis

## 6. Conclusions and Outlook

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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1. | The weights correspond to the respective shares in Euro Area real GDP (in 2007). |

${\mathit{\alpha}}_{\mathit{yi}},{\mathit{\alpha}}_{\mathit{gi}}$ | ${\mathit{\alpha}}_{\mathit{\pi}\mathit{E}}$ | ${\mathit{\alpha}}_{\mathit{yE}},{\mathit{\alpha}}_{\mathit{\pi}\mathit{i}}$ | ${\mathit{\alpha}}_{\mathit{D}1},{\mathit{\alpha}}_{\mathit{D}2}$ | ${\mathit{\alpha}}_{\mathit{D}3}$ | ${\mathit{\alpha}}_{\mathit{RE}}$ | ${\mathit{\mu}}_{\mathit{i}},{\mathit{\mu}}_{\mathit{E}}$ |
---|---|---|---|---|---|---|

1 | 2 | 0.5 | 0.01 | 0.0002 | 8 | 0.25 |

T | $\mathit{\theta}$ | ${\mathit{\omega}}_{1}$ | ${\mathit{\omega}}_{2},{\mathit{\omega}}_{3}$ | ${\mathit{\delta}}_{\mathit{i}},{\mathit{\eta}}_{\mathit{i}},{\mathit{\epsilon}}_{\mathit{i}}$ | ${\mathit{\rho}}_{21},{\mathit{\rho}}_{31}$ | ${\mathit{\rho}}_{23},{\mathit{\rho}}_{32},{\mathit{\beta}}_{\mathit{i}},{\mathit{\gamma}}_{\mathit{i}},{\mathit{\kappa}}_{\mathit{i}},{\mathit{\lambda}}_{\mathit{i}}$ | ${\mathit{\rho}}_{12},{\mathit{\rho}}_{13}$ | ${\mathit{\xi}}_{\mathit{i}}$ | ${\mathit{\chi}}_{\mathit{i}}$ |
---|---|---|---|---|---|---|---|---|---|

30 | 3 | 0.6 | 0.2 | 0.5 | 0.375 | 0.25 | 0.125 | 0.1 | 0.0125 |

${\mathit{y}}_{\mathit{i}}$ | ${\mathit{\pi}}_{\mathit{i}}$ | ${\mathit{\pi}}_{\mathit{i}}^{\mathit{e}}$ | ${\mathit{I}}_{\mathit{i}}$ | ${\mathit{D}}_{1}$ | ${\mathit{D}}_{2},{\mathit{D}}_{3}$ | ${\mathit{R}}_{\mathit{E}}$ | ${\mathit{g}}_{1}$ | ${\mathit{g}}_{2},{\mathit{g}}_{3}$ |
---|---|---|---|---|---|---|---|---|

0 | 2.5 | 2.5 | 3 | 60 | 80 | 3 | −2 | −4 |

${\tilde{\mathit{D}}}_{1\mathit{t}}$ | ${\tilde{\mathit{D}}}_{2\mathit{t}},{\tilde{\mathit{D}}}_{3\mathit{t}}$ | ${\tilde{\mathit{\pi}}}_{\mathit{it}}$ | ${\tilde{\mathit{\pi}}}_{\mathit{Et}}$ | ${\tilde{\mathit{y}}}_{\mathit{it}}$ | ${\tilde{\mathit{y}}}_{\mathit{Et}}$ | ${\tilde{\mathit{g}}}_{\mathit{it}}$ | ${\tilde{\mathit{R}}}_{\mathit{Et}}$ |
---|---|---|---|---|---|---|---|

60 | 80↘60 | 2 | 2 | 0 | 0 | 0 | 3 |

t | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... |
---|---|---|---|---|---|---|---|---|---|---|

$z{d}_{1t}$ | −1 | −6 | −1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$z{d}_{2t}$ | −1 | −6 | −1 | −3 | −4 | −3 | −1 | 0 | 0 | 0 |

$z{d}_{3t}$ | −1 | −6 | −1 | −3 | −4 | −3 | −1 | 0 | 0 | 0 |

Scenario | Game Strategy | |
---|---|---|

1 | everyone for themselves | Nash FB with 4 players: CB/C1/C2/C3 |

2 | core + CB vs. periphery: | Nash FB with 2 players: CB + C1/C2 + C3 |

3 | thrifty + CB vs. thriftless: | Nash FB with 2 players: CB + C1 + C2/C3 |

4 | thriftless + CB vs. thrifty: | Nash FB with 2 players: CB + C3/C1 + C2 |

5 | fiscal and monetary union | Pareto solution |

sc | CB | C1 | C2 | C3 | CB + C1 + C2 + C3 |
---|---|---|---|---|---|

sc1 | 183.42 | 113.20 | 319.46 | 233.02 | 849.10 |

sc2 | 140.21 | 81.93 | 216.86 | 184.28 | 623.28 |

sc3 | 228.26 | 77.98 | 140.55 | 94.88 | 541.67 |

sc4 | 150.34 | 85.26 | 192.03 | 161.43 | 589.06 |

sc5 | 203.03 | 66.96 | 102.64 | 120.17 | 492.81 |

CB | C1 | C2 | C3 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

sc | ${\mathit{y}}_{\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{E}}$ | ${\mathit{RE}}_{\mathit{E}}$ | ${\mathit{y}}_{1}$ | ${\mathit{\pi}}_{1}$ | ${\mathit{D}}_{1}$ | ${\mathit{g}}_{1}$ | ${\mathit{y}}_{2}$ | ${\mathit{\pi}}_{2}$ | ${\mathit{D}}_{2}$ | ${\mathit{g}}_{2}$ | ${\mathit{y}}_{3}$ | ${\mathit{\pi}}_{3}$ | ${\mathit{D}}_{3}$ | ${\mathit{g}}_{3}$ |

sc1 | 83 | 54 | 47 | 78 | 14 | 13 | 8 | 199 | 42 | 36 | 42 | 140 | 25 | 31 | 37 |

sc2 | 30 | 35 | 75 | 43 | 6 | 25 | 9 | 124 | 22 | 37 | 33 | 76 | 10 | 29 | 69 |

sc3 | 18 | 13 | 197 | 22 | 1 | 33 | 22 | 79 | 10 | 31 | 20 | 65 | 6 | 6 | 18 |

sc4 | 27 | 30 | 93 | 38 | 5 | 28 | 15 | 116 | 20 | 30 | 26 | 72 | 9 | 24 | 56 |

sc5 | 4 | 10 | 190 | 13 | 0.4 | 27 | 27 | 51 | 5 | 26 | 20 | 28 | 1 | 14 | 77 |

Experiment | Factor | Changed Weights |
---|---|---|

‘exp1’ | $\pi $− 0.5 | ${\tilde{\pi}}_{it}=0.25$, ${\tilde{\pi}}_{Et}=1$, |

‘exp2’ | $\pi $− 2 | ${\tilde{\pi}}_{it}=1$, ${\tilde{\pi}}_{Et}=4$ |

‘exp3’ | y− 0.5 | ${\tilde{y}}_{it}=0.5$, ${\tilde{y}}_{Et}=0.25$ |

‘exp4’ | y− 2 | ${\tilde{y}}_{it}=2$, ${\tilde{y}}_{Et}=1$ |

‘exp5’ | D− 0 | ${\tilde{D}}_{it}=0$ |

CB | C1 | C2 | C3 | ∑ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

sc | ${\mathit{y}}_{\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{E}}$ | ${\mathit{RE}}_{\mathit{E}}$ | ${\mathit{y}}_{1}$ | ${\mathit{\pi}}_{1}$ | ${\mathit{D}}_{1}$ | ${\mathit{g}}_{1}$ | ${\mathit{y}}_{2}$ | ${\mathit{\pi}}_{2}$ | ${\mathit{D}}_{2}$ | ${\mathit{g}}_{2}$ | ${\mathit{y}}_{3}$ | ${\mathit{\pi}}_{3}$ | ${\mathit{D}}_{3}$ | ${\mathit{g}}_{3}$ | |

sc1 | 65 | 55 | 27 | 94 | 9 | 15 | 10 | 234 | 27 | 36 | 51 | 166 | 17 | 38 | 34 | 878 |

sc2 | 35 | 23 | 59 | 52 | 4 | 20 | 9 | 141 | 14 | 39 | 38 | 86 | 6 | 35 | 71 | 632 |

sc3 | 20 | 9 | 181 | 25 | 1 | 30 | 21 | 89 | 6 | 29 | 22 | 71 | 4 | 7 | 18 | 534 |

sc4 | 32 | 20 | 79 | 44 | 3 | 31 | 16 | 131 | 12 | 32 | 30 | 85 | 6 | 24 | 47 | 592 |

sc5 | 11 | 3 | 183 | 15 | 0.3 | 26 | 26 | 55 | 3 | 25 | 21 | 31 | 1 | 15 | 73 | 487 |

CB | C1 | C2 | C3 | ∑ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

sc | ${\mathit{y}}_{\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{E}}$ | ${\mathit{RE}}_{\mathit{E}}$ | ${\mathit{y}}_{1}$ | ${\mathit{\pi}}_{1}$ | ${\mathit{D}}_{1}$ | ${\mathit{g}}_{1}$ | ${\mathit{y}}_{2}$ | ${\mathit{\pi}}_{2}$ | ${\mathit{D}}_{2}$ | ${\mathit{g}}_{2}$ | ${\mathit{y}}_{3}$ | ${\mathit{\pi}}_{3}$ | ${\mathit{D}}_{3}$ | ${\mathit{g}}_{3}$ | |

sc1 | 42 | 108 | 79 | 60 | 18 | 12 | 6 | 160 | 59 | 36 | 32 | 112 | 33 | 24 | 40 | 821 |

sc2 | 25 | 44 | 99 | 34 | 6 | 31 | 9 | 105 | 32 | 36 | 28 | 64 | 13 | 24 | 67 | 616 |

sc3 | 15 | 15 | 219 | 17 | 1 | 37 | 24 | 68 | 14 | 34 | 18 | 57 | 8 | 5 | 19 | 553 |

sc4 | 22 | 38 | 112 | 30 | 6 | 25 | 14 | 98 | 28 | 29 | 22 | 58 | 10 | 24 | 69 | 588 |

sc5 | 9 | 4 | 199 | 12 | 1 | 28 | 27 | 47 | 7 | 28 | 19 | 25 | 1 | 14 | 81 | 501 |

CB | C1 | C2 | C3 | ∑ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

sc | ${\mathit{y}}_{\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{E}}$ | ${\mathit{RE}}_{\mathit{E}}$ | ${\mathit{y}}_{1}$ | ${\mathit{\pi}}_{1}$ | ${\mathit{D}}_{1}$ | ${\mathit{g}}_{1}$ | ${\mathit{y}}_{2}$ | ${\mathit{\pi}}_{2}$ | ${\mathit{D}}_{2}$ | ${\mathit{g}}_{2}$ | ${\mathit{y}}_{3}$ | ${\mathit{\pi}}_{3}$ | ${\mathit{D}}_{3}$ | ${\mathit{g}}_{3}$ | |

sc1 | 35 | 107 | 49 | 49 | 18 | 9 | 7 | 125 | 52 | 26 | 42 | 95 | 35 | 25 | 15 | 688 |

sc2 | 22 | 55 | 71 | 31 | 9 | 22 | 5 | 86 | 31 | 27 | 31 | 60 | 17 | 25 | 36 | 528 |

sc3 | 14 | 26 | 172 | 18 | 3 | 28 | 12 | 60 | 17 | 27 | 17 | 51 | 11 | 6 | 8 | 471 |

sc4 | 20 | 48 | 85 | 28 | 8 | 18 | 8 | 80 | 28 | 23 | 27 | 55 | 14 | 24 | 38 | 502 |

sc5 | 9 | 9 | 167 | 11 | 1 | 24 | 16 | 41 | 9 | 23 | 16 | 26 | 3 | 15 | 57 | 426 |

CB | C1 | C2 | C3 | ∑ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

sc | ${\mathit{y}}_{\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{E}}$ | ${\mathit{RE}}_{\mathit{E}}$ | ${\mathit{y}}_{1}$ | ${\mathit{\pi}}_{1}$ | ${\mathit{D}}_{1}$ | ${\mathit{g}}_{1}$ | ${\mathit{y}}_{2}$ | ${\mathit{\pi}}_{2}$ | ${\mathit{D}}_{2}$ | ${\mathit{g}}_{2}$ | ${\mathit{y}}_{3}$ | ${\mathit{\pi}}_{3}$ | ${\mathit{D}}_{3}$ | ${\mathit{g}}_{3}$ | |

sc1 | 73 | 53 | 44 | 107 | 9 | 22 | 12 | 282 | 30 | 58 | 46 | 172 | 14 | 40 | 79 | 1042 |

sc2 | 35 | 17 | 80 | 51 | 3 | 28 | 17 | 156 | 13 | 54 | 41 | 76 | 4 | 34 | 120 | 728 |

sc3 | 17 | 4 | 229 | 20 | 0.4 | 37 | 37 | 90 | 5 | 37 | 28 | 68 | 2 | 6 | 35 | 615 |

sc4 | 31 | 15 | 101 | 42 | 2 | 46 | 28 | 146 | 12 | 45 | 30 | 79 | 4 | 24 | 83 | 687 |

sc5 | 9 | 1 | 216 | 12 | 0.3 | 30 | 40 | 56 | 2 | 31 | 29 | 25 | 0.2 | 14 | 99 | 565 |

CB | C1 | C2 | C3 | ∑ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

sc | ${\mathit{y}}_{\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{E}}$ | ${\mathit{RE}}_{\mathit{E}}$ | ${\mathit{y}}_{1}$ | ${\mathit{\pi}}_{1}$ | ${\mathit{D}}_{1}$ | ${\mathit{g}}_{1}$ | ${\mathit{y}}_{2}$ | ${\mathit{\pi}}_{2}$ | ${\mathit{D}}_{2}$ | ${\mathit{g}}_{2}$ | ${\mathit{y}}_{3}$ | ${\mathit{\pi}}_{3}$ | ${\mathit{D}}_{3}$ | ${\mathit{g}}_{3}$ | |

sc1 | 26 | 18 | 4 | 37 | 3 | - | 13 | 87 | 9 | - | 35 | 87 | 9 | - | 35 | 363 |

sc2 | 17 | 7 | 6 | 23 | 1 | - | 27 | 59 | 4 | - | 47 | 59 | 4 | - | 47 | 301 |

sc3 | 13 | 4 | 18 | 15 | 0.3 | - | 51 | 52 | 3 | - | 41 | 59 | 4 | - | 21 | 281 |

sc4 | 16 | 7 | 13 | 21 | 1 | - | 32 | 63 | 5 | - | 32 | 61 | 5 | - | 38 | 293 |

sc5 | 8 | 1 | 25 | 10 | 0.2 | - | 59 | 35 | 1 | - | 45 | 35 | 1 | - | 45 | 265 |

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**MDPI and ACS Style**

Blueschke, D.; Neck, R. Game of Thrones: Accommodating Monetary Policies in a Monetary Union. *Games* **2018**, *9*, 9.
https://doi.org/10.3390/g9010009

**AMA Style**

Blueschke D, Neck R. Game of Thrones: Accommodating Monetary Policies in a Monetary Union. *Games*. 2018; 9(1):9.
https://doi.org/10.3390/g9010009

**Chicago/Turabian Style**

Blueschke, Dmitri, and Reinhard Neck. 2018. "Game of Thrones: Accommodating Monetary Policies in a Monetary Union" *Games* 9, no. 1: 9.
https://doi.org/10.3390/g9010009