Nash Equilibrium
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Related Articles from SNS
Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Models
arXiv:2508.11874v2 Announce Type: replace Abstract: Designing polynomial-time algorithms for approximate Nash equilibria (ANE) with provable worst-case guarantees is a fundamental open problem in algorithmic game theory. While large language models (LLMs) can generate candidate algorithms at scale, certifying worst-case guarantees requires formal analysis over all game instances -- a task for which no automated system previously existed. Here, we present LegoNE, a framework encoding expert...
Game connectivity and adaptive dynamics in many-action games
arXiv:2601.05965v2 Announce Type: replace-cross Abstract: We study the typical structure of games in terms of their connectivity properties. A game is `connected' if it has a pure Nash equilibrium and there is a best-response path from every action profile which is not a pure Nash equilibrium to every pure Nash equilibrium; a game is generic if it has no indifferences. In previous work we showed that, among all $n$-player $k$-action generic games that admit a pure Nash equilibrium, the...
Efficient Exploration for Iterative Nash Preference Optimization
arXiv:2606.01382v1 Announce Type: new Abstract: Preference alignment is central to improving large language models, but standard reward-based formulations can be restrictive when human preferences are cyclic, non-transitive, or otherwise not representable by a scalar reward. Nash Learning from Human Feedback (NLHF) addresses this limitation by modeling alignment as a preference game and targeting a Nash equilibrium rather than a reward maximizer. However, the learning-theoretic foundations...
Limit Continuous Poker: A Variant of Continuous Poker with Limited Bet Sizes
Announce Type: cross Abstract: We introduce and analyze Limit Continuous Poker, a variant of Von Neumann's Continuous Poker with variable but limited bet sizes. This simplified variant of poker captures aspects of information asymmetry, bluffing, balancing, and the impact of bet size limits while still being simple enough to solve analytically. We derive the Nash equilibrium strategy profile for this game, showing how the bettor's and caller's strategies depend on the bet size limits.
Symbiosis as a systemic catalyst and the impossibility of coalitions in optimal networks
Announce Type: new Abstract: The stability of complex systems hinges on the tension between individual incentives and collective welfare. Modeling these dynamics through strategic network interactions based on anti-coordination, we formally prove that any globally optimal configuration constitutes a Strong Nash Equilibrium, creating topological barriers against collective deviations. However, in sub-optimal states, strictly individualistic agents remain trapped in stagnant equilibria.
A No-Regret Framework for Adaptive Incentive Design
arXiv:2606.02529v1 Announce Type: cross Abstract: Incentive design studies how a central authority can influence strategic agents through payments, subsidies, or taxes, so that individual objectives align with collective welfare. This paper introduces a No-Regret Adaptive Incentive Design (RAID) framework for nonlinear games with continuous action spaces and private agent costs. In this framework, the authority (planner) designs incentives that regulate the Nash equilibrium toward a socially...
Solution Sets for Inverse Infinite-Horizon Linear-Quadratic Descriptor Differential Games
arXiv:2604.27460v4 Announce Type: replace-cross Abstract: In this letter, we study a model-based inverse problem for infinite-horizon linear-quadratic differential games with descriptor dynamics. Given an observed feedback strategy profile, we seek to identify all cost functions that rationalize it as a feedback Nash equilibrium; this collection is referred to as the solution set. We characterize the solution set, show that it is rectangular and convex, and provide an algorithm for computing...
Pseudo-Equilibria, or: How to Stop Worrying About Crypto and Just Analyze the Game
Announce Type: replace Abstract: We consider the problem of a game theorist analyzing a game that uses cryptographic protocols. Ideally, a theorist abstracts protocols as ideal, implementation-independent primitives, letting conclusions in the "ideal world" carry over to the "real world." This is crucial, since the game theorist cannot--and should not be expected to--handle full cryptographic complexity.
Civilizational Metamaterials: Engineering Coordination Under Capability Gradients and Structural Turbulence
arXiv:2606.00235v1 Announce Type: new Abstract: We argue that governance must transition from a normative discipline to an engineering discipline, and we develop a formal framework, inspired by the physics of metamaterials, to make this transition quantitative and testable. Artificial General Intelligence affects civilization primarily by increasing decision velocity while human verification capacity remains bounded. When the cost of validating AI-generated outputs exceeds the expected...
Civilizational Metamaterials: Engineering Coordination Under Capability Gradients and Structural Turbulence
arXiv:2606.00235v1 Announce Type: cross Abstract: We argue that governance must transition from a normative discipline to an engineering discipline, and we develop a formal framework, inspired by the physics of metamaterials, to make this transition quantitative and testable. Artificial General Intelligence affects civilization primarily by increasing decision velocity while human verification capacity remains bounded. When the cost of validating AI-generated outputs exceeds the expected...