Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.24292

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

Edith Elkind
View original source ↗Read source document ↗Export metadata ↓

Abstract

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].

Explore related subjects

cs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Edith Elkind. 2026-09-21. Subgame-Perfect Nash Equilibria of Plurality Voting with Abstention: a PSPACE-Completeness Result for Restricted Ballots. https://arxiv.org/abs/2609.24292

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

Polyhedral Methods for Cooperative Games: Small Lifts and Hard Faces

We study the computational complexity of fundamental algorithmic problems -- membership testing, separation, valid-inequality testing, and linear optimization -- over polytopes and cones arising from cooperative games (also known as pseudo-Boolean functions). A central obstacle in the study of such problems is that a general cooperative game on $n$ players requires $2^n$ values, so the input size is $2^n$ for a game with $n$ players, making these computational tasks theoretically trivial. Restricting to $k$-additive games reduces the input size to $O(n^k)$, making such games a natural target for meaningful questions about the existence of efficient algorithms. On the positive side, we give an explicit extended formulation of size $O(n^k)$ for the core of $k$-additive $k$-monotone games, allowing all four problems to be solved by a single polynomial-size linear program -- in particular, circumventing the ellipsoid method that is needed when building from earlier tractability results of Deng and Papadimitriou, or of Edmonds. For the cone of $k$-additive $(k{-}1)$-monotone games, we give a complete characterization of its extreme rays and derive the same $O(n^k)$ bound on extension complexity, yielding a geometry-based proof and generalization of a result of Billionnet and Minoux. On the negative side, we show that for $l \leq k-2$ the cone of $k$-additive $l$-monotone games is computationally intractable: membership testing is not in NP (unless NP\,=\,coNP), valid-inequality testing is NP-complete, and extension complexity is at least $1.5^n$. Our hardness results yield, as a special case, a result of Crama and of Gallo and Simone. Furthermore, our hardness results also explain the lack of any good characterization of the extreme rays of the cone of $k$-additive $(k{-}2)$-monotone games.

cs.GT↗