### Abstract

In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of \frac{4}{3}\frac{4}{3} and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best nash equilibrium and of a general optimum. Therefore, we answer an open question posed by fanelli et al. In [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches 2 for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy (achieved for a worst-case order of the arrival of the players). We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of \frac{4}{3}\frac{4}{3}, and provide an upper bound of \frac{26}{19}\frac{26}{19}. To the end, we conjecture and argue that the right answer is \frac{4}{3}\frac{4}{3}.

Original language | English |
---|---|

Title of host publication | Proc. 9th International Conference on Combinatorial Optimization and Applications (COCOA) |

Publisher | Springer |

Pages | 439-451 |

Number of pages | 13 |

DOIs | |

Publication status | Published - 2015 |

### Publication series

Series | Lecture Notes in Computer Science |
---|---|

Volume | 9486 |

## Cite this

Mamageishvili, A., & Mihalák, M. (2015). Multicast Network Design Game on a Ring. In

*Proc. 9th International Conference on Combinatorial Optimization and Applications (COCOA)*(pp. 439-451). Springer. Lecture Notes in Computer Science, Vol.. 9486 https://doi.org/10.1007/978-3-319-26626-8_32