## Abstract

Network games are widely used as a model for selfish resource-allocation problems. In the classical model, each player selects a path connecting her source and target vertex. The cost of traversing an edge depends on the number of players that traverse it. Thus, it abstracts the fact that different users may use a resource at different times and for different durations, which plays an important role in defining the costs of the users in reality. For example, when transmitting packets in a communication network, routing traffic in a road network, or processing a task in a production system, the traversal of the network involves an inherent delay, and so sharing and congestion of resources crucially depends on time. We study timed network games, which add a time component to network games. Each vertex v in the network is associated with a cost function, mapping the load on v to the price that a player pays for staying in v for one time unit with this load. In addition, each edge has a guard, describing time intervals in which the edge can be traversed, forcing the players to spend time on vertices. Unlike earlier work that add a time component to network games, the time in our model is continuous and cannot be discretized. In particular, players have uncountably many strategies, and a game may have uncountably many pure Nash equilibria. We study properties of timed network games with cost-sharing or congestion cost functions: their stability, equilibrium inefficiency, and complexity. In particular, we show that the answer to the question whether we can restrict attention to boundary strategies, namely ones in which edges are traversed only at the boundaries of guards, is mixed.

Original language | English |
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Title of host publication | 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 |

Editors | Kim G. Larsen, Jean-Francois Raskin, Hans L. Bodlaender |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770460 |

DOIs | |

State | Published - 1 Nov 2017 |

Externally published | Yes |

Event | 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 - Aalborg, Denmark Duration: 21 Aug 2017 → 25 Aug 2017 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 83 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 |
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Country/Territory | Denmark |

City | Aalborg |

Period | 21/08/17 → 25/08/17 |

### Bibliographical note

Funding Information:∗ The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013, ERC grant no 278410) and the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award).

Publisher Copyright:

© Guy Avni, Shibashis Guha, and Orna Kupferman; licensed under Creative Commons License CC-BY.

## Keywords

- Equilibrium Inefficiency
- Nash Equilibrium
- Network Games
- Timed Automata

## ASJC Scopus subject areas

- Software