{"paper":{"title":"An Exact Solution of the Two-Ball Multi-Look Search Game with Three Boxes and Heterogeneous Costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Igor Kleiner","submitted_at":"2026-08-05T20:59:57Z","abstract_excerpt":"A Hider distributes two identical balls among three boxes whose search costs satisfy $a\\ge b\\ge c>0$. A Searcher opens boxes adaptively until both balls are found; every opening incurs the corresponding box cost and recovers at most one ball. We give an exact solution of this heterogeneous multi-look search-cost game. The value is the maximum of three explicit rational functions. In the three parameter regimes, an optimal Hider strategy is the product-form distribution restricted respectively to three, five, or all six placements. Every non-wasteful deterministic Searcher policy is payoff-equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05406","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05406/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}