Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2412.16328

Temporal Explorability Games

Pete Austin·Nicolas Mazzocchi·Sougata Bose·Patrick Totzke
View original source ↗Read source document ↗Export metadata ↓

Abstract

Temporal graphs extend ordinary graphs with discrete time that affects the availability of edges. We consider solving games played on temporal graphs where one player aims to explore the graph, i.e., visit all vertices. The complexity depends majorly on two factors: the presence of an adversary and how edge availability is specified. We demonstrate that on static graphs, where edges are always available, solving explorability games is just as hard as solving reachability games. In contrast, on temporal graphs, the complexity of explorability coincides with generalized reachability (NP-complete for one-player and PSPACE- complete for two player games). We further show that if temporal graphs are given symbolically, even one-player reachability and thus explorability and generalized reachability games are PSPACE-hard. For one player, all these are also solvable in PSPACE and for two players, they are in PSPACE, EXP and EXP, respectively.

Explore related subjects

cs.GTcs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pete Austin, Nicolas Mazzocchi, Sougata Bose, Patrick Totzke. 2025-06-13. Temporal Explorability Games. https://arxiv.org/abs/2412.16328

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

KEEP EXPLORING

Related papers

arXiv2026

Control and Bribery in Stable Marriage and Stable Roommates: A Complete Complexity Landscape

We study control and bribery problems for stable matchings: A central authority (the controller, resp. briber) may add agents, delete agents, delete acceptable pairs, swap two adjacent agents in some agent's preference list, or arbitrarily reorder some agent's preference list, in an instance of Stable Marriage or Stable Roommates. We extend previous work on control and bribery in stable matchings by Boehmer et al. [8]. We consider goals capturing individual and pair inclusion, stability, and uniqueness requirements: Matching a designated agent (MA), matching a designated pair (MP), realizing a stable matching consistent with a given matching (MS), making a given matching the unique stable matching (USM), or guaranteeing that a stable (resp. perfect and stable) matching exists ($\exists$SM/$\exists$PSM). We provide a unified complexity map for all non-trivial action-goal combinations in both settings, consolidating known results and extending the study to the roommates model, where stable matchings need not exist.

cs.GT↗
arXiv2026

How a Cooperative-Override Circuit Suppresses Nash Play in Large Language Models

On the named Prisoner's Dilemma under direct prompting, three larger instruction-tuned models, Llama-3-70B, Qwen2.5-32B, and Qwen2.5-72B, lock at full cooperation, the metric's maximum distance from Nash with zero variance across replicates, while Llama-3-8B plays near-Nash. Opening the models, a logit-lens analysis finds a distributed cooperative override. Intermediate readouts lean toward the Nash action through roughly three quarters of network depth before a late surge toward cooperation, and the final layer settles the contest. The size of that final correction, not the surge, rank-matches chain-of-thought behavior across scale and two architectures. In the 8B the override is a single causally controllable direction in the residual stream; steering it dials the decision, and clamping its component at one position of one layer moves the choice strictly monotonically, Spearman rho = 1.000, with generation fluent. The circuit is lexical. It survives name removal and payoff rescaling but disengages when Cooperate and Defect are replaced with neutral labels, and on 48 payoff-random games with neutral surfaces no model locks cooperative on any dilemma or shows general equilibrium competence. In mixed-model populations a single Nash-playing agent collapses cooperation contagiously. What suppresses Nash play in large language models is a word-triggered circuit rather than missing competence, and it can be measured, bounded, and controlled.

cs.GT↗
arXiv2026

Auction Design with ROI-Constrained Bidders: Truthfulness and Revenue Maximization

The return-on-investment (ROI) constraint is central to many auctions, particularly in online advertising, where a bidder is unwilling to pay more than a fixed fraction of the value obtained. We study truthful and revenue-maximizing auctions for ROI-constrained bidders. We first characterize truthful auctions when both valuations and ROI constraints are private, showing that the allocation rule uniquely determines the payment rule. Building on this characterization, for multiple bidders we introduce $σ$-increment mechanisms that resemble Myerson's optimal mechanism~\cite{journals/mor/Myerson81}; as $σ$ vanishes, these mechanisms become asymptotically optimal among deterministic truthful mechanisms, and their revenue approaches at least a $1/\bar r$ fraction of the optimal expected revenue over all truthful mechanisms, where $\bar r$ is the largest possible ROI constraint. In the single-bidder setting, we prove that every truthful auction can be replaced by a convex pricing function with weakly higher payments for every type, and we derive the optimal pricing functions when either the valuation or the ROI constraint is public.

cs.GT↗