{"paper":{"title":"Meta-Bayesian Nash Equilibrium: Existence via Kakutani's Fixed Point Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Meta-Bayesian Nash equilibrium exists when each transformed game has a unique Bayesian Nash equilibrium.","cross_cats":["econ.GN","q-fin.EC"],"primary_cat":"econ.TH","authors_text":"Esmaiel Abounoori, Madjid Eshaghi Gordji, Mohamadali Berahman","submitted_at":"2026-05-16T10:37:06Z","abstract_excerpt":"We extend the concept of meta-Nash equilibrium, introduced by Eshaghi Gordji and Bagha [2026] for complete-information games, to environments with incomplete information. We define a meta-Bayesian Nash equilibrium as a profile of type-dependent mixed meta-strategies together with an environmental move such that no player type can profitably deviate and the environment cannot improve its expected payoff. For each transformed game, meta-payoffs are determined by the unique Bayesian Nash equilibrium of that game. Using Kakutani's fixed point theorem, we establish existence under finiteness assump"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Using Kakutani's fixed point theorem, we establish existence under finiteness assumptions on type spaces, meta-actions, and transformations, together with the assumption that each transformed game admits a unique Bayesian Nash equilibrium.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that each transformed game admits a unique Bayesian Nash equilibrium (stated in the abstract as a prerequisite for applying Kakutani's theorem to the meta-game).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Defines meta-Bayesian Nash equilibrium for incomplete information and proves existence via Kakutani's fixed point theorem assuming finite type spaces, meta-actions, transformations, and unique Bayesian Nash equilibria in transformed games.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Meta-Bayesian Nash equilibrium exists when each transformed game has a unique Bayesian Nash equilibrium.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"aabb5f531857e1b8a0bfe4279bb71de3f8ac6be2ec476a5994c4d3ec7359f522"},"source":{"id":"2605.16926","kind":"arxiv","version":1},"verdict":{"id":"2ad1ec16-78a1-4368-97fc-b532168d0ed4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:06:19.597192Z","strongest_claim":"Using Kakutani's fixed point theorem, we establish existence under finiteness assumptions on type spaces, meta-actions, and transformations, together with the assumption that each transformed game admits a unique Bayesian Nash equilibrium.","one_line_summary":"Defines meta-Bayesian Nash equilibrium for incomplete information and proves existence via Kakutani's fixed point theorem assuming finite type spaces, meta-actions, transformations, and unique Bayesian Nash equilibria in transformed games.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that each transformed game admits a unique Bayesian Nash equilibrium (stated in the abstract as a prerequisite for applying Kakutani's theorem to the meta-game).","pith_extraction_headline":"Meta-Bayesian Nash equilibrium exists when each transformed game has a unique Bayesian Nash equilibrium."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16926/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T20:22:26.648478Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:18.927107Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:10:41.726766Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.258046Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.338857Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"10101276d06df7e405f43f230c9bf3d167fa84dabba7c6867e570b715a280e25"},"references":{"count":10,"sample":[{"doi":"","year":2026,"title":"2026 , note =","work_id":"225f74c0-5c48-4a81-9cb8-368014227bee","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Nash, John F. , title =. Annals of Mathematics , volume =","work_id":"16fb04aa-47f6-4e1e-9fb6-623019fc3f9c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"and Selten, Reinhard , title =","work_id":"515e47fe-4316-4283-bb8a-7c1f2eb1f567","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Schelling, Thomas C. , title =","work_id":"c1f64aaf-7523-4b55-bba8-45fff2664594","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"North, Douglass C. , title =","work_id":"94b73391-c6ed-4162-979e-ce34fe72c729","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":10,"snapshot_sha256":"80eb8f8c34c04c27710e0f475af846b9b66b2a3ce07b72c40aafa540b567964a","internal_anchors":1},"formal_canon":{"evidence_count":1,"snapshot_sha256":"b263f94bfbf1a5ac3475a0ad66cfc522e5b6394b854d0bf4dee4dfa872f8a15d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}