Abstract

In this paper, we study turn-based multiplayer quantitative non zero-sum games played on finite graphs with reachability objectives. In this framework each player aims at reaching his own goal as soon as possible. We focus on existence results for two solution concepts: Nash equilibrium and secure equilibrium. We prove the existence of finite-memory Nash (resp. secure) equilibria in n-player (resp. 2-player) games. For the case of Nash equilibria, we extend our result in two directions. First, we show that finite-memory Nash equilibria still exist when the model is enriched by allowing n-tuples of positive costs on edges (one cost by player). Secondly, we prove the existence of Nash equilibria in quantitative games with both reachability and safety objectives.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.