The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
Michael Ummels,Dominik Wojtczak +1 more
- pp 297-308
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In this paper, the complexity of finding Nash equilibria in simple stochastic multiplayer games was analyzed and it was shown that the problem is undecidable and restricted to strategies with (unbounded) finite memory.Abstract:
We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. 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 $\mathcal G$, does there exist a pure-strategy Nash equilibrium of $\mathcal G$ where player 0 wins with probability 1. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if mixed strategies are allowed, decidability remains an open problem. One way to obtain a provably 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.read more
Citations
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Book ChapterDOI
The complexity of nash equilibria in limit-average games
Michael Ummels,Dominik Wojtczak +1 more
TL;DR: It is shown that the constrained existence problem for Nash equilibria in (pure or randomised) stationary strategies is decidable and the result holds even for a restricted class of concurrent games, where nonzero rewards occur only on terminal states.
Journal ArticleDOI
Iterated Boolean games
TL;DR: This work investigates the computational complexity of their associated game-theoretic decision problems, as well as semantic conditions characterising classes of LTL properties that are preserved by equilibrium points (pure-strategy Nash equilibria) whenever they exist.
Book ChapterDOI
Automatic verification of competitive stochastic systems
TL;DR: This work defines a temporal logic called rPATL for expressing quantitative properties of stochastic multi-player games and gives a model checking algorithm for verifying properties expressed in this logic and implements the techniques in a probabilistic model checker based on the PRISM tool.
Book ChapterDOI
Nash equilibria for reachability objectives in multi-player timed games
TL;DR: This work proposes a procedure for computing Nash equilibria in multi-player timed games with reachability objectives based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibrium in (possibly infinite) concurrent games.
Book ChapterDOI
The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
Michael Ummels,Dominik Wojtczak +1 more
TL;DR: It is shown that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability, and a common lower bound of NP and upper bounds ofNP and PSpace are obtained.
References
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