Computer Science – Computer Science and Game Theory
Scientific paper
2011-09-19
LMCS 7 (3:20) 2011
Computer Science
Computer Science and Game Theory
Scientific paper
10.2168/LMCS-7(3:20)2011
We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a Nash equilibrium of G where Player 0 wins with probability 1? Moreover, this problem remains undecidable when restricted to pure strategies or (pure) strategies with finite memory. One way to obtain a decidable variant of the problem is to restrict the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively. Finally, we single out a special case of the general problem that, in many cases, admits an efficient solution. In particular, we prove that deciding the existence of an equilibrium in which each player either wins or loses with probability 1 can be done in polynomial time for games where the objective of each player is given by a parity condition with a bounded number of priorities.
Ummels Michael
Wojtczak Dominik
No associations
LandOfFree
The Complexity of Nash Equilibria in Stochastic Multiplayer Games does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Complexity of Nash Equilibria in Stochastic Multiplayer Games, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Complexity of Nash Equilibria in Stochastic Multiplayer Games will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-96791