{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/smooth-information-gathering-in-two-player","title":"Smooth Information Gathering in Two-Player Noncooperative Games","arxiv_id":"2404.00733","date":"2024-03-31","proceeding":null,"authors":["Fernando Palafox","Jesse Milzman","Dong Ho Lee","Ryan Park","David Fridovich-Keil"],"abstract":"We present a mathematical framework for modeling two-player noncooperative games in which one player is uncertain of the other player's costs but can preemptively allocate information-gathering resources to reduce this uncertainty. We refer to the players as the uncertain player (UP) and the certain player (CP), respectively. We obtain UP's decisions by solving a two-stage problem where, in Stage 1, UP allocates information-gathering resources that smoothly transform the information structure in the second stage. Then, in Stage 2, a signal (that is, a function of the Stage 1 allocation) informs UP about CP's costs, and both players execute strategies which depend upon the signal's value. This framework allows for a smooth resource allocation, in contrast to existing literature on the topic. We also identify conditions under which the gradient of UP's overall cost with respect to the information-gathering resources is well-defined. Then we provide a gradient-based algorithm to solve the two-stage game. Finally, we apply our framework to a tower-defense game which can be interpreted as a variant of a Colonel Blotto game with smooth payoff functions and uncertainty over battlefield valuations. We include an analysis of how optimal decisions shift with changes in information-gathering allocations and perturbations in the cost functions.","url_abs":"https://arxiv.org/abs/2404.00733v2","url_pdf":"https://arxiv.org/pdf/2404.00733v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"smooth-information-gathering-in-two-player","repo_url":"https://github.com/clearoboticslab/gamesvoi.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}