紀要論文

予算ゲームと混雑ゲームの共通の一般化におけるナッシュ均衡

Nash equilibria in a common generalization of budget games and congestion games

jpn

24368083

https://doi.org/10.15002/00025409

法政大学大学院理工学研究科

法政大学大学院紀要. 理工学研究科編

63

1

2

2022-03-24

Version of Record

Budget games are a variant of congestion games. In budget games, a player chooses a subset of resources strategically and maximizes her utility. In the general case, Nash equilibria do not exist in budget games. But Drees et al. showed that the game has a Nash equilibrium under an assumption that the strategy space of each player is the base family of a matroid and each player has a fixed demand for all resources. In this thesis, we generalize the utility functions in budget games to set functions to provide a common generalization of budget games and congestion games. We then extend the theorem of Drees et al. to this generalized model. We have also found a counterexample to a proof of another theorem on the time complexity of finding a Nash equilibrium by Drees et al.

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