Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1109.6220

The Complexity of Nash Equilibria in Limit-Average Games

Michael Ummels·Dominik Wojtczak
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the computational complexity of Nash equilibria in concurrent games with limit-average objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a Nash equilibrium in pure strategies is decidable, even if we put a constraint on the payoff of the equilibrium. Our undecidability result holds even for a restricted class of concurrent games, where nonzero rewards occur only on terminal states. Moreover, we show that the constrained existence problem is undecidable not only for concurrent games but for turn-based games with the same restriction on rewards. Finally, we prove that the constrained existence problem for Nash equilibria in (pure or randomised) stationary strategies is decidable and analyse its complexity.

Explore related subjects

cs.GTcs.CC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Michael Ummels, Dominik Wojtczak. 2011-09-28. The Complexity of Nash Equilibria in Limit-Average Games. https://doi.org/10.1007/978-3-642-23217-6_32

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Learning in Structured Stackelberg Games

We initiate the study of structured Stackelberg games, a novel form of strategic interaction between a leader and a follower where contextual information can be predictive of the follower's (unknown) type. Motivated by applications such as security games and AI safety, we show how this additional structure can help the leader learn a utility-maximizing policy in both the online and distributional settings. In the online setting, we first prove that standard learning-theoretic measures of complexity do not characterize the difficulty of the leader's learning task. Notably, we find that there exists a learning-theoretic measure of complexity, analogous to the Littlestone dimension in online classification, that tightly characterizes the leader's instance-optimal regret. We term this the Stackelberg-Littlestone dimension, and leverage it to provide a provably optimal online learning algorithm. In the distributional setting, we provide analogous results by showing that two new dimensions control the sample complexity upper- and lower-bound.

cs.GT↗
arXiv2026

Equilibrium and Infeasibility: A new solution concept for games

Addressing infeasibility in non-cooperative games has become an important topic, as many problems across different applications face this issue. In this paper, we propose a new solution concept for generalized games with possibly infeasible individual constraints. A solution is defined as the limit of a sequence of generalized Nash equilibria induced by games with penalty terms relaxing the individual constraints. Existence is established for a broad range of games and we provide conditions allowing to characterize a $ψ$-penalized solution as a strategy profile maximizing every player's utility over all her penalty minimizing strategies. A variation of Divide-the-Dollar serves as an illustrative example. We further establish the compatibility with the GNE and the solution to the Nash bargaining.

cs.GT↗
arXiv2026

Subgame-Perfect Nash Equilibria of Plurality Voting with Abstention: a PSPACE-Completeness Result for Restricted Ballots

We consider sequential Plurality elections in which each voter may abstain or vote for a single candidate. Each voter assigns utilities to all candidates; for each voter, this induces a (weak) order over the candidates. Ties are resolved uniformly at random, and voting has a small positive cost, so that a voter prefers to abstain when their vote cannot change the election outcome. We consider a variant of this model where, for each voter, we additionally specify a prefix of her ranking, so that she is only allowed to vote for a candidate from that prefix (or abstain). We prove that for this variant of the model, deciding whether a designated candidate is among the election winners in a subgame-perfect equilibrium of the associated extensive-form game is PSPACE-complete. This partially resolves an open problem from the work of Desmedt and Elkind [2010].

cs.GT↗