{"id":"https://openalex.org/W7162777021","doi":"https://doi.org/10.48550/arxiv.2605.29042","title":"Differentiable Belief-based Opponent Shaping","display_name":"Differentiable Belief-based Opponent Shaping","publication_year":2026,"publication_date":"2026-05-27","ids":{"openalex":"https://openalex.org/W7162777021","doi":"https://doi.org/10.48550/arxiv.2605.29042"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.29042","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.29042","pdf_url":"https://arxiv.org/pdf/2605.29042","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2605.29042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137313642","display_name":"Aarav G Sane","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sane, Aarav G","raw_affiliation_strings":["Department of Computer Science Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5095376465","display_name":"Karthik Sivachandran","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sivachandran, Karthik","raw_affiliation_strings":["Department of Computer Science Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005412601","display_name":"Rohan Paleja","orcid":"https://orcid.org/0000-0002-0773-8054","observed_orcids":["https://orcid.org/0000-0002-0773-8054"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paleja, Rohan","raw_affiliation_strings":["Department of Computer Science Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science Purdue University","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9603999853134155,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9603999853134155,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.020899999886751175,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.011800000444054604,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/belief-manipulation","display_name":"belief manipulation","score":0.8939999938011169},{"id":"https://openalex.org/keywords/multi-agent-reinforcement-learning","display_name":"multi-agent reinforcement learning","score":0.9100000262260437},{"id":"https://openalex.org/keywords/belief-dynamics","display_name":"belief dynamics","score":0.531000018119812},{"id":"https://openalex.org/keywords/deception","display_name":"deception","score":0.5059999823570251},{"id":"https://openalex.org/keywords/mixed-motive-games","display_name":"mixed-motive games","score":0.6869999766349792}],"concepts":[{"id":"https://openalex.org/C41065033","wikidata":"https://www.wikidata.org/wiki/Q2825412","display_name":"Adversary","level":2,"score":0.5311999917030334},{"id":"https://openalex.org/C2779267917","wikidata":"https://www.wikidata.org/wiki/Q170028","display_name":"Deception","level":2,"score":0.516700029373169},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4948999881744385},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4763999879360199},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4526999890804291},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C145071142","wikidata":"https://www.wikidata.org/wiki/Q1411116","display_name":"Fictitious play","level":3,"score":0.38839998841285706},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.31290000677108765},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C2781162219","wikidata":"https://www.wikidata.org/wiki/Q26250693","display_name":"Replicate","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3043000102043152},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.28209999203681946},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.25600001215934753},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.29042","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.29042","pdf_url":"https://arxiv.org/pdf/2605.29042","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2605.29042","doi":"https://doi.org/10.48550/arxiv.2605.29042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.29042","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2605.29042","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.29042","pdf_url":"https://arxiv.org/pdf/2605.29042","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162777021.pdf","grobid_xml":"https://content.openalex.org/works/W7162777021.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4416714319","https://openalex.org/W2901005701","https://openalex.org/W7124324266","https://openalex.org/W4394774574","https://openalex.org/W7213498607","https://openalex.org/W4229059695","https://openalex.org/W4416384265","https://openalex.org/W3037942570","https://openalex.org/W4390091695","https://openalex.org/W2753984105"],"abstract_inverted_index":{"Human":[0],"coordination":[1],"often":[2,46],"relies":[3],"on":[4,48],"the":[5,9,73,95,99,105,112,154],"ability":[6],"to":[7,23,108,132],"influence":[8],"beliefs":[10],"of":[11],"others":[12],"through":[13,79,125],"strategic":[14],"action.":[15],"In":[16],"multi-agent":[17],"reinforcement":[18],"learning,":[19],"opponent":[20,75,126],"shaping":[21],"attempts":[22],"replicate":[24],"this":[25],"influence,":[26],"though":[27],"existing":[28],"methods":[29],"typically":[30],"operate":[31],"within":[32],"an":[33,120],"opponent's":[34],"parameter,":[35],"policy,":[36],"or":[37,54,89],"value":[38],"space.":[39],"Meanwhile,":[40],"belief-manipulation":[41],"techniques":[42],"in":[43,150,157],"hidden-role":[44,151],"games":[45],"rely":[47],"hard-coded":[49],"objectives,":[50],"such":[51],"as":[52,72,98],"deception":[53],"belief":[55,71,82,96,127,142],"saturation.":[56],"We":[57],"propose":[58],"Differentiable":[59],"Belief-based":[60],"Opponent":[61],"Shaping":[62],"(D-BOS),":[63],"a":[64],"first-order":[65],"method":[66,93],"that":[67],"treats":[68,94],"each":[69],"observer's":[70],"shaped":[74],"state":[76,97],"and":[77,129,148],"differentiates":[78],"$k$-step":[80],"softmax-Bayes":[81],"dynamics.":[83],"Rather":[84],"than":[85],"explicitly":[86],"rewarding":[87],"deceptive":[88],"cooperative":[90],"behavior,":[91],"our":[92],"target":[100],"for":[101],"shaping.":[102],"This":[103,116],"allows":[104],"optimal":[106],"strategy":[107],"emerge":[109],"naturally":[110,130],"from":[111],"environment's":[113],"reward":[114],"structure.":[115],"belief-space":[117],"formulation":[118],"provides":[119],"opponent-shaping":[121],"signal":[122],"by":[123,135],"differentiating":[124],"updates,":[128],"extends":[131],"multiple":[133],"observers":[134],"aggregating":[136],"gradients":[137],"over":[138],"their":[139],"individual":[140],"inferred":[141],"trajectories.":[143],"Empirically,":[144],"D-BOS":[145],"outperforms":[146],"PPO":[147],"BBM":[149],"games,":[152],"with":[153],"largest":[155],"gains":[156],"mixed-motive":[158],"settings.":[159]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-05-30T00:00:00"}