Nash Equilibrium Existence without Convexity

Conrad Kosowsky

Home/Archive/arXiv

arXiv · 2308.11597

Nash Equilibrium Existence without Convexity

Conrad Kosowsky

View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, I prove the existence of a pure-strategy Nash equilibrium for a large class of games with nonconvex strategy spaces. Specifically, if each player's strategies form a compact, connected Euclidean neighborhood retract and if all best-response correspondences are null-homotopic, then the game has a pure-strategy Nash equilibrium. As an application, I show how this result can prove the fundamental theorem of algebra.

Explore related subjects

econ.TH

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Conrad Kosowsky. 2023-08-22. Nash Equilibrium Existence without Convexity. https://arxiv.org/abs/2308.11597

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

KEEP EXPLORING

Related papers

arXiv2026

Measurement of Trustworthiness of the Online Reviews

Online review platforms shape consumer decisions, yet reported ratings and comments may be unreliable when reviewers behave inconsistently. This paper models online reviews as a sequential choice problem and proposes a formal rationality pattern function that links a reviewer's current review to their revealed preference history. Building on a two-way consistency axiom for choices from nested sets, we derive an object-specific support trajectory and an associated degree measure in [0,1] (Average Propensity to Choose a Pattern, APCP) that quantifies review trustworthiness. The measure is designed to support information updating and reduce asymmetric information by discounting reviews that are inconsistent with past behavior. A worked example illustrates how the approach assigns trustworthiness grades to reviews for different objects and how these grades can complement aggregate rating statistics. Finally, a generalized theory has been established.

econ.TH↗

arXiv2026

The Cesàro average criterion on infinite utility streams and its extensions

When evaluating policies that affect future generations, the most commonly used criterion is the discounted utilitarian rule. However, in terms of intergenerational fairness, it is difficult to justify prioritizing the current generation over future generations. This paper axiomatically examines impartial utilitarian rules over infinite-dimensional utility streams. We provide simple characterizations of the social welfare ordering that evaluates utility streams by their long-run average on the domain where the average exists. Furthermore, we derive the necessary and sufficient conditions for the same axioms to hold in a more general domain, the set of bounded utility streams. Some of these results are closely related to the Banach limits, a well-known generalization of the classical limit concept for streams. Thus, this paper can be seen as proposing an appealing subclass of Banach limits through axiomatic analysis.

econ.TH↗

arXiv2026

The Institutional Window: Occupation- and Jurisdiction-Specific Calibration of Liability Signaling for Preserved Human Fallback Capability

Generative AI makes expert output uninformative about the human fallback capability its provider keeps in reserve. A liability commitment can signal that capability: a provider whose staff rescue more of the cases the AI fails pays damages less often, so the commitment certifies an asset built by keeping people on cases and lost by taking them off. This paper asks where contract law leaves room for such a signal. Four legal primitives map a posted cap into retained exposure and close the message space from both sides: litigation viability, the penalty doctrine, displacement of liability to the state or an indemnity pool, and mandatory control of standard terms. Where the law leaves an option of zero exposure, low types pool at zero, intermediate types separate on a schedule anchored at the mandatory floor, and high types pool at the ceiling; where it does not, separation starts at the bottom type. A statutory floor removes the lower pool but pushes the schedule toward the ceiling, so its net effect is not monotone. The penalty doctrine decides whether recovery adequate for deterrence can be restored by contract or only by investing in verifiability. Holding fallback skill constant demands more human engagement the less often the AI fails. A calibration to five occupations and twelve legal configurations in Germany, Austria, Switzerland, the United Kingdom and the United States locates the binding margin of each cell and supports no ranking by legal family or contracting channel.

econ.TH↗