### Abstract

At the heart of multi-agent systems is the ability to cooperate to improve the performance of individual agents and/or the system as a whole. While a widespread assumption in the literature is that such cooperation is essentially unrestricted, in many realistic settings this assumption does not hold. A highly influential approach for modelling such scenarios are graph-restricted games introduced by Myerson [36]. In this approach, agents are represented by nodes in a graph, edges represent communication channels, and a group can generate an arbitrary value only if there exists a direct or indirect communication channel between every pair of agents within the group. Two fundamental solution-concepts that were proposed for such games are the Myerson value and the Shapley value. While an algorithm has been developed to compute the Shapley value in arbitrary graph-restricted games, no such general-purpose algorithm has been developed for the Myerson value to date. With this in mind, we set out to develop for such games a general-purpose algorithm to compute the Myerson value, and a more efficient algorithm to compute the Shapley value. Since the computation of either value involves enumerating all connected induced subgraphs of the game's underlying graph, we start by developing an algorithm dedicated to this enumeration, and then we show empirically that it is faster than the state of the art in the literature. Finally, we present a sample application of both algorithms, in which we test the Myerson value and the Shapley value as advanced measures of node centrality in networks.

Original language | English (US) |
---|---|

Article number | a15 |

Journal | ACM Transactions on Intelligent Systems and Technology |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- Algorithms
- Coalitional games
- Depth-first search
- Myerson value

### ASJC Scopus subject areas

- Theoretical Computer Science
- Artificial Intelligence

### Cite this

*ACM Transactions on Intelligent Systems and Technology*,

*10*(2), [a15]. https://doi.org/10.1145/3235026

**Enumerating connected subgraphs and computing the Myerson and Shapley values in graph-restricted games.** / Skibski, Oskar; Rahwan, Talal; Michalak, Tomasz P.; Wooldridge, Michael.

Research output: Contribution to journal › Article

*ACM Transactions on Intelligent Systems and Technology*, vol. 10, no. 2, a15. https://doi.org/10.1145/3235026

}

TY - JOUR

T1 - Enumerating connected subgraphs and computing the Myerson and Shapley values in graph-restricted games

AU - Skibski, Oskar

AU - Rahwan, Talal

AU - Michalak, Tomasz P.

AU - Wooldridge, Michael

PY - 2019/1/1

Y1 - 2019/1/1

N2 - At the heart of multi-agent systems is the ability to cooperate to improve the performance of individual agents and/or the system as a whole. While a widespread assumption in the literature is that such cooperation is essentially unrestricted, in many realistic settings this assumption does not hold. A highly influential approach for modelling such scenarios are graph-restricted games introduced by Myerson [36]. In this approach, agents are represented by nodes in a graph, edges represent communication channels, and a group can generate an arbitrary value only if there exists a direct or indirect communication channel between every pair of agents within the group. Two fundamental solution-concepts that were proposed for such games are the Myerson value and the Shapley value. While an algorithm has been developed to compute the Shapley value in arbitrary graph-restricted games, no such general-purpose algorithm has been developed for the Myerson value to date. With this in mind, we set out to develop for such games a general-purpose algorithm to compute the Myerson value, and a more efficient algorithm to compute the Shapley value. Since the computation of either value involves enumerating all connected induced subgraphs of the game's underlying graph, we start by developing an algorithm dedicated to this enumeration, and then we show empirically that it is faster than the state of the art in the literature. Finally, we present a sample application of both algorithms, in which we test the Myerson value and the Shapley value as advanced measures of node centrality in networks.

AB - At the heart of multi-agent systems is the ability to cooperate to improve the performance of individual agents and/or the system as a whole. While a widespread assumption in the literature is that such cooperation is essentially unrestricted, in many realistic settings this assumption does not hold. A highly influential approach for modelling such scenarios are graph-restricted games introduced by Myerson [36]. In this approach, agents are represented by nodes in a graph, edges represent communication channels, and a group can generate an arbitrary value only if there exists a direct or indirect communication channel between every pair of agents within the group. Two fundamental solution-concepts that were proposed for such games are the Myerson value and the Shapley value. While an algorithm has been developed to compute the Shapley value in arbitrary graph-restricted games, no such general-purpose algorithm has been developed for the Myerson value to date. With this in mind, we set out to develop for such games a general-purpose algorithm to compute the Myerson value, and a more efficient algorithm to compute the Shapley value. Since the computation of either value involves enumerating all connected induced subgraphs of the game's underlying graph, we start by developing an algorithm dedicated to this enumeration, and then we show empirically that it is faster than the state of the art in the literature. Finally, we present a sample application of both algorithms, in which we test the Myerson value and the Shapley value as advanced measures of node centrality in networks.

KW - Algorithms

KW - Coalitional games

KW - Depth-first search

KW - Myerson value

UR - http://www.scopus.com/inward/record.url?scp=85060061216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060061216&partnerID=8YFLogxK

U2 - 10.1145/3235026

DO - 10.1145/3235026

M3 - Article

AN - SCOPUS:85060061216

VL - 10

JO - ACM Transactions on Intelligent Systems and Technology

JF - ACM Transactions on Intelligent Systems and Technology

SN - 2157-6904

IS - 2

M1 - a15

ER -