# Route Selection Decision-Making in an Intermodal Transport Network Using Game Theory

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Rational Choice in Game Theory Environment

## 4. Decision-Making Process in Game Theory

- (a)
- Payoff matrix (years of imprisonment) for different combinations of the first and second player strategies.
- (b)
- The first player assumes a probability of 20% where the second player will choose:
- i.
- The “Deny” strategy (payoff matrix in Table 1b favors to Nash equilibrium),
- ii.
- “admit-admit “equilibrium.

- (c)
- If the first player is sure with a probability of 80%, the second player will choose:
- i.
- The “Deny” strategy (the payoff matrices in Table 1c pulls other player),
- ii.
- The “Deny” strategy.

#### 4.1. Transport Network Graph in Normal and Extensive Form

#### 4.2. Transformation of the Game from Normal to Extensive Form

_{ij}, b

_{ij}) = f (A

_{i}, B

_{j})

## 5. Coordinated Use of the Transport Network

#### 5.1. Geographical Position and Berth Productivity of Ports

^{2}, allowing cargo flow growth without any risk of congestion or bottleneck formation [35].

#### 5.2. Congestion Game in Selecting Railway Routes

- Congestion exists only on routes between ports and Budapest,
- There is no congestion between ports,
- Each transport on the route between port and Budapest is one player.

- ${c}_{trainkm}$—cost of train kilometer [€/trainkm];
- $l$—rail distance [km];
- $THC$—terminal handling cost [€/TEU];
- ${N}_{k}^{t}$—number of containers per train [TEU/train].

- ${N}_{k}^{max}$—maximum number of containers per train [TEU];
- ${N}_{k}^{r}$—real number of containers on a train [TEU].

- Trieste–Koper = 148.43 €;
- Koper–Rijeka = 172.60 €.

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Version of the transport network and equilibrium route selection. Source: [29].

**Figure 2.**Game in extensive form. Source: [15].

**Figure 3.**The framework of the decision-making process in intermodal network congestion game. Source: Authors.

**Figure 5.**A second (

**a**), third (

**b**), and fourth (

**c**) scenarios of route choice in a congestion game. Source: Authors.

(a) | (b) | (c) | ||||||
---|---|---|---|---|---|---|---|---|

admit | deny | admit | deny | admit | deny | |||

admit | (1, 1) | (10, 0) | admit | (0.20, 0.20) | (8, 0) | admit | (0.8, 0.8) | (2, 0) |

deny | (0, 10) | (5, 5) | deny | (0, 2) | (4, 4) | deny | (0, 8) | (1, 1) |

B_{1} | B_{2} | |

A_{1} | (a_{11}, b_{11}) | (a_{12}, b_{12}) |

A_{2} | (a_{21}, b_{21}) | (a_{22}, b_{22}) |

Seaport Terminal | Throughput Change [TEU] | Length Change [m] | TEU/Berth Length [%] | TEU/Crane Hour [%] |
---|---|---|---|---|

Trieste | +228,830 | −650 | 275.66 | 103.70 |

Koper ^{1} | +625,806 | +146 | 191.29 | 92.90 |

Rijeka | +83,011 | +159 | 40.36 | 87.94 |

^{1}4 new STS cranes. Source: [6].

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**MDPI and ACS Style**

Bukvić, L.; Pašagić Škrinjar, J.; Abramović, B.; Zitrický, V.
Route Selection Decision-Making in an Intermodal Transport Network Using Game Theory. *Sustainability* **2021**, *13*, 4443.
https://doi.org/10.3390/su13084443

**AMA Style**

Bukvić L, Pašagić Škrinjar J, Abramović B, Zitrický V.
Route Selection Decision-Making in an Intermodal Transport Network Using Game Theory. *Sustainability*. 2021; 13(8):4443.
https://doi.org/10.3390/su13084443

**Chicago/Turabian Style**

Bukvić, Lucija, Jasmina Pašagić Škrinjar, Borna Abramović, and Vladislav Zitrický.
2021. "Route Selection Decision-Making in an Intermodal Transport Network Using Game Theory" *Sustainability* 13, no. 8: 4443.
https://doi.org/10.3390/su13084443