{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T20:21:26Z","timestamp":1774124486321,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:00:00Z","timestamp":1626220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:00:00Z","timestamp":1626220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s40314-021-01578-4","type":"journal-article","created":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T22:02:27Z","timestamp":1626300147000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Markovian Stackelberg game approach for computing an optimal dynamic mechanism"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5918-4671","authenticated-orcid":false,"given":"Julio B.","family":"Clempner","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,14]]},"reference":[{"issue":"11","key":"1578_CR1","first-page":"1893","volume":"45","author":"AS Antipin","year":"2005","unstructured":"Antipin AS (2005) An extraproximal method for solving equilibrium programming problems and games. Computational Mathematics and Mathematical Physics 45(11), 1893\u20131914","journal-title":"Comput Math Math Phys"},{"issue":"11","key":"1578_CR2","doi-asserted-by":"publisher","first-page":"3591","DOI":"10.1007\/s00500-018-3225-7","volume":"23","author":"E Asiain","year":"2019","unstructured":"Asiain E, Clempner JB, Poznyak AS (2019) Controller exploitation-exploration: A reinforcement learning architecture. Soft Comput 23(11):3591\u20133604","journal-title":"Soft Comput"},{"issue":"6","key":"1578_CR3","doi-asserted-by":"publisher","first-page":"2463","DOI":"10.3982\/ECTA6995","volume":"81","author":"S Athey","year":"2013","unstructured":"Athey S, Segal I (2013) An efficient dynamic mechanism. Econometrica 81(6), 2463\u20132485","journal-title":"Econometrica"},{"key":"1578_CR4","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1016\/0167-6245(84)90006-4","volume":"1","author":"D Baron","year":"1984","unstructured":"Baron D, Besanko D (1984) Regulation and information in a continuing relationship. Information Economics and Policy 1:447\u2013470","journal-title":"Inf Econ Policy"},{"issue":"3","key":"1578_CR5","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1257\/0002828054201369","volume":"95","author":"M Battaglini","year":"2005","unstructured":"Battaglini M (2005) Long-term contracting with Markovian consumers. Am Econ Rev 95(3):637\u2013658","journal-title":"Am Econ Rev"},{"key":"1578_CR6","first-page":"1511","volume-title":"Wiley encyclopedia of operations research and management science","author":"D Bergemann","year":"2011","unstructured":"Bergemann D, Said M (2011) Wiley Encyclopedia Of Operations Research And Management Science. Wiley, Hoboken, pp 1511\u20131522"},{"key":"1578_CR7","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1057\/978-1-349-95121-5_2386-1","volume-title":"New Palgrave dictionary of economics","author":"D Bergemann","year":"2008","unstructured":"Bergemann D, V\u00e4lim\u00e4ki J (2008) New Palgrave Dictionary of Economics. Palgrave Macmillan, chap Bandit Problems, New York, pp 336\u2013340"},{"issue":"2","key":"1578_CR8","doi-asserted-by":"publisher","first-page":"771","DOI":"10.3982\/ECTA7260","volume":"78","author":"D Bergemann","year":"2010","unstructured":"Bergemann D, V\u00e4lim\u00e4ki J (2010) The dynamic pivot mechanism. Econometrica 78(2), 771\u2013789","journal-title":"Econometrica"},{"key":"1578_CR9","doi-asserted-by":"crossref","unstructured":"Berry CA, Hobbs BF, Meroney WA, O\u2019Neill RP, Stewart WR Jr (1999) Understanding how market power can arise in network competition: a game theoretic approach. Utili Policy 8:139\u2013158","DOI":"10.1016\/S0957-1787(99)00016-8"},{"key":"1578_CR10","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0165-1765(85)90122-3","volume":"17","author":"D Besanko","year":"1985","unstructured":"Besanko D (1985) Multiperiod contracts between principal and agent with adverse selection. Economics Letters 17:33\u201337","journal-title":"Econ Lett"},{"key":"1578_CR11","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1016\/j.jet.2006.08.005","volume":"136","author":"S Board","year":"2007","unstructured":"Board S (2007) Selling options\u201d, journal of economic theory. Journal of Economic Theory 136:324\u2013340.","journal-title":"Journal of Economic Theory"},{"issue":"4","key":"1578_CR12","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.1086\/686713","volume":"124","author":"S Board","year":"2016","unstructured":"Board S, Skrzypacz A (2016) Revenue management with forward-looking buyers forward-looking buyers. Journal of Political Economy. 124(4):1046\u20131087","journal-title":"J Polit Econ"},{"issue":"4","key":"1578_CR13","first-page":"41","volume":"50","author":"JB Clempner","year":"2016","unstructured":"Clempner JB, Poznyak AS (2016a) Analyzing an optimistic attitude for the leader firm in duopoly models: A strong stackelberg equilibrium based on a lyapunov game theory approach. Economic Computation & Economic Cybernetics Studies & Research 50(4):41\u201360","journal-title":"Econ Comput Econ Cybern Stud Res"},{"key":"1578_CR14","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1016\/j.eswa.2015.11.006","volume":"46","author":"JB Clempner","year":"2016","unstructured":"Clempner JB, Poznyak AS (2016b) Convergence analysis for pure stationary strategies in repeated potential games: nash, lyapunov and correlated equilibria. Expert Syst Appl 46:474\u2013484","journal-title":"Expert Syst Appl"},{"issue":"11","key":"1578_CR15","doi-asserted-by":"publisher","first-page":"1996","DOI":"10.1080\/0305215X.2017.1418866","volume":"50","author":"JB Clempner","year":"2018","unstructured":"Clempner JB, Poznyak AS (2018a) A tikhonov regularization parameter approach for solving lagrange constrained optimization problems. Eng Optim 50(11):1996\u20132012","journal-title":"Eng Optim"},{"key":"1578_CR16","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.cam.2017.07.032","volume":"328","author":"JB Clempner","year":"2018","unstructured":"Clempner JB, Poznyak AS (2018b) A tikhonov regularized penalty function approach for solving polylinear programming problems. J Comput Appl Math 328:267\u2013286","journal-title":"J Comput Appl Math"},{"key":"1578_CR17","doi-asserted-by":"crossref","unstructured":"Clempner JB, Poznyak AS (2019a) Observer and control design in partially observable finite Markov chains. Automatica (To be publushed)","DOI":"10.1016\/j.automatica.2019.108587"},{"key":"1578_CR18","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.automatica.2019.108587","volume":"110","author":"JB Clempner","year":"2019","unstructured":"Clempner JB, Poznyak AS (2019b) Observer and control design in partially observable finite markov chains. Automatica 110:110","journal-title":"Automatica"},{"key":"1578_CR19","doi-asserted-by":"publisher","first-page":"103876","DOI":"10.1016\/j.engappai.2020.103876","volume":"95","author":"JB Clempner","year":"2020","unstructured":"Clempner JB, Poznyak AS (2020) A nucleus for bayesian partially observable markov games: Joint observer and mechanism design. Engineering Applications of Artificial Intelligence 95:103876","journal-title":"Engi Appl Artif Intell"},{"key":"1578_CR20","doi-asserted-by":"crossref","unstructured":"Clempner JB, Poznyak AS (2021) Analytical method for mechanism design in partiallyobservable markov games. Mathematics (To be published)","DOI":"10.3390\/math9040321"},{"key":"1578_CR21","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1111\/1467-937X.00150","volume":"67","author":"P Courty","year":"2000","unstructured":"Courty P, Li H (2000) Sequential screening. Review of Economic Studies 67:697\u2013717","journal-title":"Rev Econ Stud"},{"issue":"3","key":"1578_CR22","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1111\/j.1467-937X.2007.00442.x","volume":"74","author":"P Es\u00f6","year":"2007","unstructured":"Es\u00f6 P, Szentes B (2007) Optimal information disclosure in auctions and the handicap auction. Review of Economic Studies 74(3), 705\u2013731","journal-title":"Rev Econ Stud"},{"issue":"3","key":"1578_CR23","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1109\/TASE.2007.912717","volume":"5","author":"D Garg","year":"2008","unstructured":"Garg D, Narahari Y (2008) Mechanism design for single leader stackelberg problems and application to procurement auction design. IEEE Transactions On Automation Science And Engineering 5(3):377\u2013393","journal-title":"IEEE Trans Autom Sci Eng"},{"issue":"2","key":"1578_CR24","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1257\/mic.1.2.168","volume":"1","author":"A Gershkov","year":"2009","unstructured":"Gershkov A, Moldovanu B (2009) Dynamic revenue maximization with heterogenous objects: A mechanism design approach. American Economic Journal: Microeconomics 1(2):168\u2013198","journal-title":"Am Econ J Microecon"},{"key":"1578_CR25","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1016\/j.jet.2013.12.012","volume":"151","author":"M Golosov","year":"2014","unstructured":"Golosov M, Skreta V, Tsyvinski A, Wilson A (2014) Dynamic strategic information transmission. Journal of Economic Theory 151:304\u2013341","journal-title":"J Econ Theory"},{"issue":"10","key":"1578_CR26","doi-asserted-by":"publisher","first-page":"3102","DOI":"10.1257\/aer.20130712","volume":"105","author":"JD Hartline","year":"2015","unstructured":"Hartline JD, Lucier B (2015) Non-optimal mechanism design. American Economic Review 105(10):3102\u20133124","journal-title":"Am Econ Rev"},{"key":"1578_CR27","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1109\/59.867153","volume":"15","author":"B Hobbs","year":"2000","unstructured":"Hobbs B, Metzler C, Pang J (2000) Strategic gaming analysis for electric power networks: an mpec approach. IEEE Trans Power Syst 15:638\u2013645","journal-title":"IEEE Trans Power Syst"},{"key":"1578_CR28","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s10957-011-9901-8","volume":"151","author":"M Hu","year":"2011","unstructured":"Hu M, Fukushima M (2011) Variational inequality formulation of a class of multi-leader-follower games. Journal of Optimization Theory and Applications 151:455\u2013473","journal-title":"J Optim Theory Appl"},{"key":"1578_CR29","first-page":"27","volume-title":"Mathematical methods in the social sciences","author":"L Hurwicz","year":"1960","unstructured":"Hurwicz L (1960) Optimality and informational efficiency in resource allocation processes. In: Arrow KJ, Karlin S, Suppes P (eds) Mathematical methods in the social sciences. Stanford University Press, California, pp 27\u201346"},{"issue":"4","key":"1578_CR30","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1287\/opre.2013.1194","volume":"61","author":"S Kakade","year":"2013","unstructured":"Kakade S, Lobel I, Nazerzadeh H (2013) Optimal dynamic mechanism design and the virtual-pivot mechanism. Operations Research 61(4), 837\u2013854","journal-title":"Oper Res"},{"issue":"6","key":"1578_CR31","doi-asserted-by":"publisher","first-page":"1767","DOI":"10.2307\/1912116","volume":"51","author":"RB Myerson","year":"1983","unstructured":"Myerson RB (1983) Mechanism design by an informed principal. Econometrica 51(6), 1767\u20131797","journal-title":"Econometrica"},{"key":"1578_CR32","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/978-1-349-20215-7_20","volume-title":"Allocation, information and markets. The New Palgrave","author":"RB Myerson","year":"1989","unstructured":"Myerson RB (1989) Allocation, information and markets, The New Palgrave. Palgrave Macmillan, London, pp 191\u2013206"},{"key":"1578_CR33","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10287-004-0010-0","volume":"2","author":"J Pang","year":"2005","unstructured":"Pang J, Fukushima M (2005) Quasi-variational inequalities, generalized nash equilibria, and multileader-follower games. Computational Management Science 2:21\u201356","journal-title":"CMS"},{"issue":"2","key":"1578_CR34","doi-asserted-by":"publisher","first-page":"601","DOI":"10.3982\/ECTA10269","volume":"82","author":"A Pavan","year":"2014","unstructured":"Pavan A, Segal I, Toikka J (2014) Dynamic mechanism design: A myersonian approach. Econometrica 82(2):601\u2013653","journal-title":"Econometrica"},{"issue":"2\u20133","key":"1578_CR35","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0377-0427(88)90403-7","volume":"22","author":"DG Saari","year":"1988","unstructured":"Saari DG (1988) On the types of information and mechanism design. Journal of Computational and Applied Mathematics 22(2\u20133), 231\u2013242","journal-title":"J Comput Appl Math"},{"issue":"4","key":"1578_CR36","doi-asserted-by":"publisher","first-page":"703","DOI":"10.2478\/amcs-2019-0052","volume":"29","author":"C Solis","year":"2019","unstructured":"Solis C, Clempner JB, Poznyak AS (2019) Robust extremum seeking for a second order uncertain plant using a sliding mode controller. International Journal of Applied Mathematics and Computer Science 29(4), 703\u2013712","journal-title":"Int J Appl Math Comput Sci"},{"issue":"2","key":"1578_CR37","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1515\/amcs-2015-0026","volume":"25","author":"KK Trejo","year":"2015","unstructured":"Trejo KK, Clempner JB, Poznyak AS (2015a) Computing the stackelberg\/nash equilibria using the extraproximal method: Convergence analysis and implementation details for markov chains games. Int J Appl Math Comput Sci 25(2):337\u2013351","journal-title":"Int J Appl Math Comput Sci"},{"key":"1578_CR38","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.engappai.2014.09.002","volume":"37","author":"KK Trejo","year":"2015","unstructured":"Trejo KK, Clempner JB, Poznyak AS (2015b) A stackelberg security game with random strategies based on the extraproximal theoretic approach. Eng Appl Artif Intell 37:145\u2013153","journal-title":"Eng Appl Artif Intell"},{"key":"1578_CR39","first-page":"13749","volume":"38","author":"X Wang","year":"2011","unstructured":"Wang X, Chin KS, Yin H (2011) Design of optimal double auction mechanism with multi-objectives. Expert Systems with Applications 38:13749\u201313756","journal-title":"Expert Syst Appl"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01578-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01578-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01578-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,24]],"date-time":"2021-09-24T19:30:11Z","timestamp":1632511811000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01578-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,14]]},"references-count":39,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["1578"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01578-4","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,14]]},"assertion":[{"value":"21 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"186"}}