{"paper":{"title":"Solution Sets for Inverse Infinite-Horizon Linear-Quadratic Descriptor Differential Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The set of all cost functions that make an observed feedback strategy profile a Nash equilibrium in infinite-horizon linear-quadratic descriptor differential games is rectangular and convex.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Aaditya Kumar, Puduru Viswanadha Reddy","submitted_at":"2026-04-30T06:00:48Z","abstract_excerpt":"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 an admissible realization whenever it is nonempty. We also show that descriptor dynamics modify the geometry of the solution set and may reduce identifiability. "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We characterize the solution set, show that it is rectangular and convex, and provide an algorithm to compute an admissible realization.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The observed feedback strategy profile is a feedback Nash equilibrium of the infinite-horizon linear-quadratic descriptor game for some quadratic cost functions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The solution set of cost functions rationalizing observed strategies as feedback Nash equilibria in infinite-horizon LQ descriptor games is rectangular and convex.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The set of all cost functions that make an observed feedback strategy profile a Nash equilibrium in infinite-horizon linear-quadratic descriptor differential games is rectangular and convex.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3d0a3f9f60e5495adc963982c6add0bbad23c69437cc2140636f0ad5c063bcc2"},"source":{"id":"2604.27460","kind":"arxiv","version":2},"verdict":{"id":"0620f254-9744-4436-b7a1-b61e911120be","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T09:59:04.771097Z","strongest_claim":"We characterize the solution set, show that it is rectangular and convex, and provide an algorithm to compute an admissible realization.","one_line_summary":"The solution set of cost functions rationalizing observed strategies as feedback Nash equilibria in infinite-horizon LQ descriptor games is rectangular and convex.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The observed feedback strategy profile is a feedback Nash equilibrium of the infinite-horizon linear-quadratic descriptor game for some quadratic cost functions.","pith_extraction_headline":"The set of all cost functions that make an observed feedback strategy profile a Nash equilibrium in infinite-horizon linear-quadratic descriptor differential games is rectangular and convex."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.27460/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T19:15:19.651742Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6ff0231e2f31bd47ffc0b60588c40908887e716fbd0ba049de69079814d34d4d"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}