Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W3196015235', 'doi': 'https://doi.org/10.48550/arxiv.2101.10685', 'title': 'Subgame-perfect Equilibria in Mean-payoff Games', 'display_name': 'Subgame-perfect Equilibria in Mean-payoff Games', 'publication_year': 2021, 'publication_date': '2021-01-01', 'ids': {'openalex': 'https://openalex.org/W3196015235', 'doi': 'https://doi.org/10.48550/arxiv.2101.10685', 'mag': '3196015235'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2101.10685', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['arxiv', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/2101.10685', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5077895295', 'display_name': 'Léonard Brice', 'orcid': 'https://orcid.org/0000-0001-7748-7716'}, 'institutions': [{'id': 'https://openalex.org/I4210152518', 'display_name': "Laboratoire d'Informatique Gaspard-Monge", 'ror': 'https://ror.org/04t50yk91', 'country_code': 'FR', 'type': 'facility', 'lineage': ['https://openalex.org/I1294671590', 'https://openalex.org/I142631665', 'https://openalex.org/I4210145102', 'https://openalex.org/I4210152518', 'https://openalex.org/I4210154111', 'https://openalex.org/I4210159245']}, {'id': 'https://openalex.org/I4210154111', 'display_name': 'Université Gustave Eiffel', 'ror': 'https://ror.org/03x42jk29', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I4210154111']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Léonard Brice', 'raw_affiliation_strings': ["LIGM - Laboratoire d'Informatique Gaspard-Monge (Université Gustave Eiffel, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2 - France)"], 'affiliations': [{'raw_affiliation_string': "LIGM - Laboratoire d'Informatique Gaspard-Monge (Université Gustave Eiffel, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2 - France)", 'institution_ids': ['https://openalex.org/I4210152518', 'https://openalex.org/I4210154111']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5050196522', 'display_name': 'Jean-François Raskin', 'orcid': 'https://orcid.org/0000-0002-3673-1097'}, 'institutions': [{'id': 'https://openalex.org/I132053463', 'display_name': 'Université Libre de Bruxelles', 'ror': 'https://ror.org/01r9htc13', 'country_code': 'BE', 'type': 'education', 'lineage': ['https://openalex.org/I132053463']}], 'countries': ['BE'], 'is_corresponding': False, 'raw_author_name': 'Jean-François Raskin', 'raw_affiliation_strings': ["ULB - Département d'Informatique [Bruxelles] (Campus de la Plaine ULB\xa0CP212, boulevard du Triomphe, 1050 Bruxelles - Belgium)"], 'affiliations': [{'raw_affiliation_string': "ULB - Département d'Informatique [Bruxelles] (Campus de la Plaine ULB\xa0CP212, boulevard du Triomphe, 1050 Bruxelles - Belgium)", 'institution_ids': ['https://openalex.org/I132053463']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5077805575', 'display_name': 'Marie van den Bogaard', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I4210152518', 'display_name': "Laboratoire d'Informatique Gaspard-Monge", 'ror': 'https://ror.org/04t50yk91', 'country_code': 'FR', 'type': 'facility', 'lineage': ['https://openalex.org/I1294671590', 'https://openalex.org/I142631665', 'https://openalex.org/I4210145102', 'https://openalex.org/I4210152518', 'https://openalex.org/I4210154111', 'https://openalex.org/I4210159245']}, {'id': 'https://openalex.org/I4210154111', 'display_name': 'Université Gustave Eiffel', 'ror': 'https://ror.org/03x42jk29', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I4210154111']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Marie van den Bogaard', 'raw_affiliation_strings': ["LIGM - Laboratoire d'Informatique Gaspard-Monge (Université Gustave Eiffel, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2 - France)"], 'affiliations': [{'raw_affiliation_string': "LIGM - Laboratoire d'Informatique Gaspard-Monge (Université Gustave Eiffel, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2 - France)", 'institution_ids': ['https://openalex.org/I4210152518', 'https://openalex.org/I4210154111']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 2, 'citation_normalized_percentile': {'value': 0.866742, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 67, 'max': 72}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11031', 'display_name': 'Game Theory and Applications', 'score': 0.9976, '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'}}, 'topics': [{'id': 'https://openalex.org/T11031', 'display_name': 'Game Theory and Applications', 'score': 0.9976, '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'}}, {'id': 'https://openalex.org/T10991', 'display_name': 'Game Theory and Voting Systems', 'score': 0.9943, 'subfield': {'id': 'https://openalex.org/subfields/2002', 'display_name': 'Economics and Econometrics'}, 'field': {'id': 'https://openalex.org/fields/20', 'display_name': 'Economics, Econometrics and Finance'}, 'domain': {'id': 'https://openalex.org/domains/2', 'display_name': 'Social Sciences'}}, {'id': 'https://openalex.org/T12137', 'display_name': 'Economic theories and models', 'score': 0.9702, 'subfield': {'id': 'https://openalex.org/subfields/2002', 'display_name': 'Economics and Econometrics'}, 'field': {'id': 'https://openalex.org/fields/20', 'display_name': 'Economics, Econometrics and Finance'}, 'domain': {'id': 'https://openalex.org/domains/2', 'display_name': 'Social Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/subgame-perfect-equilibrium', 'display_name': 'Subgame perfect equilibrium', 'score': 0.8320546}, {'id': 'https://openalex.org/keywords/corollary', 'display_name': 'Corollary', 'score': 0.6306205}, {'id': 'https://openalex.org/keywords/stochastic-game', 'display_name': 'Stochastic game', 'score': 0.5644068}, {'id': 'https://openalex.org/keywords/subgame', 'display_name': 'Subgame', 'score': 0.4607251}, {'id': 'https://openalex.org/keywords/characterization', 'display_name': 'Characterization', 'score': 0.44205615}], 'concepts': [{'id': 'https://openalex.org/C175983524', 'wikidata': 'https://www.wikidata.org/wiki/Q1615834', 'display_name': 'Subgame perfect equilibrium', 'level': 3, 'score': 0.8320546}, {'id': 'https://openalex.org/C2780012671', 'wikidata': 'https://www.wikidata.org/wiki/Q1343870', 'display_name': 'Corollary', 'level': 2, 'score': 0.6306205}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.60816145}, {'id': 'https://openalex.org/C22171661', 'wikidata': 'https://www.wikidata.org/wiki/Q1074380', 'display_name': 'Stochastic game', 'level': 2, 'score': 0.5644068}, {'id': 'https://openalex.org/C14036430', 'wikidata': 'https://www.wikidata.org/wiki/Q3736076', 'display_name': 'Function (biology)', 'level': 2, 'score': 0.54671144}, {'id': 'https://openalex.org/C153269930', 'wikidata': 'https://www.wikidata.org/wiki/Q430001', 'display_name': 'Decidability', 'level': 2, 'score': 0.54651433}, {'id': 'https://openalex.org/C144237770', 'wikidata': 'https://www.wikidata.org/wiki/Q747534', 'display_name': 'Mathematical economics', 'level': 1, 'score': 0.5145797}, {'id': 'https://openalex.org/C199776023', 'wikidata': 'https://www.wikidata.org/wiki/Q202875', 'display_name': 'Negotiation', 'level': 2, 'score': 0.4959596}, {'id': 'https://openalex.org/C17095337', 'wikidata': 'https://www.wikidata.org/wiki/Q2375229', 'display_name': 'Piecewise linear function', 'level': 2, 'score': 0.48543364}, {'id': 'https://openalex.org/C13576547', 'wikidata': 'https://www.wikidata.org/wiki/Q3965283', 'display_name': 'Subgame', 'level': 5, 'score': 0.4607251}, {'id': 'https://openalex.org/C2780841128', 'wikidata': 'https://www.wikidata.org/wiki/Q5073781', 'display_name': 'Characterization (materials science)', 'level': 2, 'score': 0.44205615}, {'id': 'https://openalex.org/C9376300', 'wikidata': 'https://www.wikidata.org/wiki/Q168817', 'display_name': 'Algebraic number', 'level': 2, 'score': 0.41107208}, {'id': 'https://openalex.org/C126255220', 'wikidata': 'https://www.wikidata.org/wiki/Q141495', 'display_name': 'Mathematical optimization', 'level': 1, 'score': 0.38563448}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.3275675}, {'id': 'https://openalex.org/C46814582', 'wikidata': 'https://www.wikidata.org/wiki/Q23389', 'display_name': 'Nash equilibrium', 'level': 2, 'score': 0.3044414}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.2918925}, {'id': 'https://openalex.org/C32407928', 'wikidata': 'https://www.wikidata.org/wiki/Q2733833', 'display_name': 'Best response', 'level': 3, 'score': 0.17399457}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.07477346}, {'id': 'https://openalex.org/C141824439', 'wikidata': 'https://www.wikidata.org/wiki/Q307521', 'display_name': 'Epsilon-equilibrium', 'level': 4, 'score': 0.068873495}, {'id': 'https://openalex.org/C192562407', 'wikidata': 'https://www.wikidata.org/wiki/Q228736', 'display_name': 'Materials science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C78458016', 'wikidata': 'https://www.wikidata.org/wiki/Q840400', 'display_name': 'Evolutionary biology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C17744445', 'wikidata': 'https://www.wikidata.org/wiki/Q36442', 'display_name': 'Political science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199539241', 'wikidata': 'https://www.wikidata.org/wiki/Q7748', 'display_name': 'Law', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C171250308', 'wikidata': 'https://www.wikidata.org/wiki/Q11468', 'display_name': 'Nanotechnology', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2101.10685', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/2101.10685', 'pdf_url': 'http://arxiv.org/pdf/2101.10685', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://hal.science/hal-03676752', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-03676752', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.2101.10685', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2101.10685', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4309911979', 'https://openalex.org/W4282813745', 'https://openalex.org/W3126144651', 'https://openalex.org/W3125676384', 'https://openalex.org/W3123332159', 'https://openalex.org/W2417008058', 'https://openalex.org/W2340986233', 'https://openalex.org/W1760610438', 'https://openalex.org/W169328966', 'https://openalex.org/W1505636692'], 'abstract_inverted_index': {'In': [0], 'this': [1, 25], 'paper,': [2], 'we': [3, 27, 65, 87], 'provide': [4], 'an': [5], 'effective': [6], 'characterization': [7], 'of': [8, 31, 36, 60, 91], 'all': [9], 'the': [10, 29, 34, 42, 56, 61, 68, 79, 89, 92, 103], 'subgame-perfect': [11], 'equilibria': [12], 'in': [13, 102], 'infinite': [14], 'duration': [15], 'games': [16], 'played': [17], 'on': [18], 'finite': [19], 'graphs': [20], 'with': [21, 55], 'mean-payoff': [22], 'objectives.': [23], 'To': [24], 'end,': [26], 'introduce': [28], 'notion': [30, 35], 'requirement,': [32], 'and': [33, 74], 'negotiation': [37, 62, 69], 'function.': [38, 63], 'We': [39], 'establish': [40], 'that': [41, 44, 52, 67], 'plays': [43], 'are': [45, 49, 53], 'supported': [46], 'by': [47], 'SPEs': [48], 'exactly': [50], 'those': [51], 'consistent': [54], 'least': [57], 'fixed': [58], 'point': [59], 'Finally,': [64], 'show': [66], 'function': [70], 'is': [71], 'piecewise': [72], 'linear,': [73], 'can': [75], 'be': [76], 'analyzed': [77], 'using': [78], 'linear': [80], 'algebraic': [81], 'tool': [82], 'box.': [83], 'As': [84], 'a': [85], 'corollary,': [86], 'prove': [88], 'decidability': [90], 'SPE': [93], 'constrained': [94], 'existence': [95], 'problem,': [96], 'whose': [97], 'status': [98], 'was': [99], 'left': [100], 'open': [101], 'literature.': [104]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3196015235', 'counts_by_year': [{'year': 2023, 'cited_by_count': 1}], 'updated_date': '2024-12-24T09:52:17.530535', 'created_date': '2021-08-30'}