Sampling logit equilibrium and endogenous payoff distortion

[2603.09539] Sampling logit equilibrium and endogenous payoff distortion Skip to main content Search Submit Donate Log in Economics > Theoretical Economics arXiv:2603.09539 (econ) [Submitted on 10 Mar 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Sampling logit equilibrium and endogenous payoff distortion Authors: Minoru Osawa View PDF HTML (experimental) Abstract: We introduce sampling logit equilibrium (SLE) for population games in which agents infer payoffs from a finite sample of $k$ opponents' actions and respond according to a logit choice rule. We find that sampling error systematically distorts incentives. Actions whose inferred payoffs are relatively more variable earn a variance premium, while nonlinear payoffs generate a curvature premium through Jensen effects. For large samples, an SLE is approximated by a logit equilibrium of a virtual game whose payoffs include these premiums. For linear games, when sampling error and logit noise vanish at comparable rates, their interaction around completely mixed Nash equilibria is reduces to a Gaussian--Gumbel limiting model. We also establish exact finite-$k$ uniqueness and stability results. In particular, in two-action coordination games with a $1/k$-dominant action, the unique SLE converges to the risk-dominant equilibrium as logit noise vanishes. Comments: 61 pages, 11 figures Subjects: Theoretical Economics (econ.TH) ; Dynamical Systems (math.DS) Cite as: arXiv:2603.09539 [econ.TH] (or arXiv:2603.09539v2 [econ.TH] for this version) https://doi.org/10.48550/arXiv.2603.09539 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Minoru Osawa [ view email ] [v1] Tue, 10 Mar 2026 11:50:06 UTC (4,531 KB) [v2] Thu, 27 Aug 2026 10:59:41 UTC (6,677 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: econ.TH < prev | next > new | recent | 2026-03 Change to browse by: econ math math.DS References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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