{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T18:48:07Z","timestamp":1758394087374,"version":"3.37.3"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,3,2]],"date-time":"2019-03-02T00:00:00Z","timestamp":1551484800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"University of Zielona Gora"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s13235-019-00305-3","type":"journal-article","created":{"date-parts":[[2019,3,2]],"date-time":"2019-03-02T06:23:08Z","timestamp":1551507788000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Equilibria in Altruistic Economic Growth Models"],"prefix":"10.1007","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3181-5187","authenticated-orcid":false,"given":"\u0141ukasz","family":"Balbus","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8480-7850","authenticated-orcid":false,"given":"Anna","family":"Ja\u015bkiewicz","sequence":"additional","affiliation":[]},{"given":"Andrzej S.","family":"Nowak","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,3,2]]},"reference":[{"key":"305_CR1","volume-title":"Infinite dimensional analysis: a hitchhiker\u2019s guide","author":"C Aliprantis","year":"2006","unstructured":"Aliprantis C, Border K (2006) Infinite dimensional analysis: a hitchhiker\u2019s guide. Springer, New York"},{"key":"305_CR2","doi-asserted-by":"publisher","unstructured":"Balbus \u0141 (2018) Markov perfect equilibria in OLG models with risk sensitive agents. Top Meth Nonlinear Anal. https:\/\/doi.org\/10.12775\/TMNA.2019.016","DOI":"10.12775\/TMNA.2019.016"},{"key":"305_CR3","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.jmaa.2015.02.062","volume":"427","author":"\u0141 Balbus","year":"2015","unstructured":"Balbus \u0141, Ja\u015bkiewicz A, Nowak AS (2015a) Bequest games with unbounded utility functions. J Math Anal Appl 427:515\u2013524","journal-title":"J Math Anal Appl"},{"key":"305_CR4","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.geb.2015.02.017","volume":"90","author":"\u0141 Balbus","year":"2015","unstructured":"Balbus \u0141, Ja\u015bkiewicz A, Nowak AS (2015b) Stochastic bequest games. Games Econ Behav 90:247\u2013256","journal-title":"Games Econ Behav"},{"key":"305_CR5","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s10957-014-0555-1","volume":"165","author":"\u0141 Balbus","year":"2015","unstructured":"Balbus \u0141, Ja\u015bkiewicz A, Nowak AS (2015c) Existence of stationary Markov perfect equilibria in stochastic altruistic growth economies. J Optim Theory Appl 165:295\u2013315","journal-title":"J Optim Theory Appl"},{"key":"305_CR6","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.jmateco.2015.12.002","volume":"63","author":"\u0141 Balbus","year":"2016","unstructured":"Balbus \u0141, Ja\u015bkiewicz A, Nowak AS (2016) Non-paternalistic intergenerational altruism revisited. J Math Econ 63:27\u201333","journal-title":"J Math Econ"},{"key":"305_CR7","doi-asserted-by":"crossref","unstructured":"Balbus \u0141, Ja\u015bkiewicz A, Nowak AS (2018) Markov perfect equilibria in a dynamic decision model with quasi-hyperbolic discounting. Ann Oper Res (in press)","DOI":"10.1007\/s10479-018-2778-2"},{"key":"305_CR8","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1016\/j.jedc.2013.01.005","volume":"37","author":"\u0141 Balbus","year":"2013","unstructured":"Balbus \u0141, Reffett K, Wo\u017any \u0141 (2013) A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism. J Econ Dyn Control 37:1019\u20131039","journal-title":"J Econ Dyn Control"},{"key":"305_CR9","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1007\/978-3-319-44374-4_18","volume-title":"Handbook of dynamic game theory","author":"\u0141 Balbus","year":"2018","unstructured":"Balbus \u0141, Reffett K, Wo\u017any \u0141 (2018a) Dynamic games in macroeconomics. In: Ba\u015far T, Zaccour G (eds) Handbook of dynamic game theory, vol 2. Springer, Cham, pp 729\u2013778"},{"key":"305_CR10","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1086\/260266","volume":"82","author":"R Barro","year":"1974","unstructured":"Barro R (1974) Are government bonds net wealth? J Polit Econ 82:1095\u20131118","journal-title":"J Polit Econ"},{"key":"305_CR11","unstructured":"Bernheim D, Ray D (1983) Altruistic growth economies I. Existence of bequest equilibria. Technical report no 419, Institute for Mathematical Studies in the Social Sciences, Stanford University"},{"key":"305_CR12","volume-title":"Stochastic optimal control: the discrete time case","author":"DP Bertsekas","year":"1978","unstructured":"Bertsekas DP, Shreve SE (1978) Stochastic optimal control: the discrete time case. Academic Press, New York"},{"key":"305_CR13","volume-title":"Convergence of probability measures","author":"P Billingsley","year":"1968","unstructured":"Billingsley P (1968) Convergence of probability measures. Wiley, New York"},{"key":"305_CR14","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/0022-0531(90)90006-6","volume":"50","author":"JH Boyd III","year":"1990","unstructured":"Boyd JH III (1990) Recursive utility and the Ramsey problem. J Econ Theory 50:326\u2013345","journal-title":"J Econ Theory"},{"key":"305_CR15","volume-title":"Capital theory equilibrum analysis and recursive utility","author":"R Becker","year":"1997","unstructured":"Becker R, Boyd JH (1997) Capital theory equilibrum analysis and recursive utility. Wiley, New York"},{"key":"305_CR16","volume-title":"Fixed point theory","author":"J Dugundji","year":"2003","unstructured":"Dugundji J, Granas A (2003) Fixed point theory. Springer, New York"},{"key":"305_CR17","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s001990050016","volume":"15","author":"J Dur\u00e1n","year":"2000","unstructured":"Dur\u00e1n J (2000) On dynamic programming with unbounded returns. Econ Theory 15:339\u2013352","journal-title":"Econ Theory"},{"key":"305_CR18","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s00199-002-0316-5","volume":"22","author":"J Dur\u00e1n","year":"2003","unstructured":"Dur\u00e1n J (2003) Discounting long run average growth in stochastic dynamic programs. Econ Theory 22:395\u2013413","journal-title":"Econ Theory"},{"key":"305_CR19","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF01211440","volume":"2","author":"PK Dutta","year":"1992","unstructured":"Dutta PK, Sundaram R (1992) Markovian equilibrium in a class of stochastic games: existence theorems for discounted and undiscounted models. Econ Theory 2:197\u2013214","journal-title":"Econ Theory"},{"key":"305_CR20","doi-asserted-by":"crossref","first-page":"937","DOI":"10.2307\/1913778","volume":"57","author":"LG Epstein","year":"1989","unstructured":"Epstein LG, Zin SE (1989) Substitution, risk aversion, and the temporal behavior consumption and asset returns: a theoretical framework. Econometrica 57:937\u2013969","journal-title":"Econometrica"},{"key":"305_CR21","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.3982\/ECTA13937","volume":"85","author":"S Galperti","year":"2017","unstructured":"Galperti S, Strulovici B (2017) A theory of intergenerational altruism. Econometrica 85:1175\u20131218","journal-title":"Econometrica"},{"key":"305_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0561-6","volume-title":"Further topics on discrete-time Markov control processes","author":"O Hern\u00e1ndez-Lerma","year":"1999","unstructured":"Hern\u00e1ndez-Lerma O, Lasserre JB (1999) Further topics on discrete-time Markov control processes. Springer, New York"},{"key":"305_CR23","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1006\/jeth.1996.2243","volume":"73","author":"H Hori","year":"1997","unstructured":"Hori H (1997) Dynamic allocation in an altruistic overlapping generations economy. J Econ Theory 73:292\u2013315","journal-title":"J Econ Theory"},{"key":"305_CR24","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s13235-011-0013-8","volume":"1","author":"A Ja\u015bkiewicz","year":"2011","unstructured":"Ja\u015bkiewicz A, Nowak AS (2011) Stochastic games with unbounded payoffs: applications to robust control in economics. Dyn Games Appl 1:253\u2013279","journal-title":"Dyn Games Appl"},{"key":"305_CR25","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/978-3-319-44374-4_33","volume-title":"Handbook of dynamic game theory","author":"A Ja\u015bkiewicz","year":"2018","unstructured":"Ja\u015bkiewicz A, Nowak AS (2018a) Non-zero-sum stochastic games. In: Ba\u015far T, Zaccour G (eds) Handbook of dynamic game theory, vol 1. Springer, Cham, pp 281\u2013344"},{"key":"305_CR26","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s11750-017-0465-0","volume":"26","author":"A Ja\u015bkiewicz","year":"2018","unstructured":"Ja\u015bkiewicz A, Nowak AS (2018b) On symmetric stochastic games of resource extraction with weakly continuous transitions. TOP 26:239\u2013256","journal-title":"TOP"},{"key":"305_CR27","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.orl.2014.03.004","volume":"42","author":"A Ja\u015bkiewicz","year":"2014","unstructured":"Ja\u015bkiewicz A, Matkowski J, Nowak AS (2014) Generalised discounting in dynamic programming with unbounded returns. Oper Res Lett 42:231\u2013233","journal-title":"Oper Res Lett"},{"key":"305_CR28","doi-asserted-by":"crossref","first-page":"349","DOI":"10.2307\/2297633","volume":"53","author":"W Leininger","year":"1986","unstructured":"Leininger W (1986) The existence of perfect equilibria in model of growth with altruism between generations. Rev Econ Stud 53:349\u2013368","journal-title":"Rev Econ Stud"},{"key":"305_CR29","doi-asserted-by":"crossref","first-page":"843","DOI":"10.2307\/1912506","volume":"49","author":"G Loury","year":"1981","unstructured":"Loury G (1981) Intergenerational transfers and the distribution of earnings. Econometrica 49:843\u2013867","journal-title":"Econometrica"},{"key":"305_CR30","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s13235-015-0177-8","volume":"6","author":"L Maliar","year":"2016","unstructured":"Maliar L, Maliar S (2016) Ruling out multiplicity of smooth equilibria in dynamic games: a hyperbolic discounting example. Dyn Games Appl 6:243\u2013261","journal-title":"Dyn Games Appl"},{"key":"305_CR31","first-page":"1","volume":"127","author":"J Matkowski","year":"1975","unstructured":"Matkowski J (1975) Integral solutions of functional equations. Dissertationes Mathematicae 127:1\u201368","journal-title":"Dissertationes Mathematicae"},{"key":"305_CR32","doi-asserted-by":"crossref","first-page":"157","DOI":"10.2307\/2951479","volume":"62","author":"P Milgrom","year":"1994","unstructured":"Milgrom P, Shannon C (1994) Monotone comparative statics. Econometrica 62:157\u2013180","journal-title":"Econometrica"},{"key":"305_CR33","first-page":"215","volume-title":"Foundations of Microeconomic Theory, A volume in honor of Hugo F. Sonnenschein","author":"DG Pearce","year":"2008","unstructured":"Pearce DG (2008) Nonpatemalistic sympathy and the inefficiency of consistent intertemporal plans. In: Jackson MO, McLennan A (eds) Foundations of Microeconomic Theory, A volume in honor of Hugo F. Sonnenschein. Springer, Berlin, pp 215\u2013231"},{"key":"305_CR34","doi-asserted-by":"crossref","first-page":"195","DOI":"10.2307\/2296547","volume":"35","author":"E Phelps","year":"1968","unstructured":"Phelps E, Pollak R (1968) On second best national savings and game equilibrium growth. Rev Econ Stud 35:195\u2013199","journal-title":"Rev Econ Stud"},{"key":"305_CR35","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/0022-0531(87)90008-1","volume":"40","author":"D Ray","year":"1987","unstructured":"Ray D (1987) Nonpaternalistic intergenerational altruism. J Econ Theory 40:112\u2013132","journal-title":"J Econ Theory"},{"key":"305_CR36","first-page":"380","volume":"44","author":"R Serfozo","year":"1982","unstructured":"Serfozo R (1982) Convergence of Lebesgue integrals with varying measures. Sankhya Indian J Statist 44:380\u2013402","journal-title":"Sankhya Indian J Statist"},{"key":"305_CR37","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/0022-0531(89)90107-5","volume":"47","author":"RK Sundaram","year":"1989","unstructured":"Sundaram RK (1989) Perfect equilibrium in a class of symmetric dynamic games. J Econ Theory 47:153\u2013177 (Corrigendum: J Econ Theory 49:385\u2013187)","journal-title":"J Econ Theory"},{"key":"305_CR38","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1287\/opre.26.2.305","volume":"26","author":"D Topkis","year":"1978","unstructured":"Topkis D (1978) Minimizing a submodular function on a lattice. Oper Res 26:305\u2013321","journal-title":"Oper Res"},{"key":"305_CR39","doi-asserted-by":"crossref","DOI":"10.1515\/9781400822539","volume-title":"Supermodularity and complementarity","author":"D Topkis","year":"1998","unstructured":"Topkis D (1998) Supermodularity and complementarity. Princeton University Press, New Jersey"},{"key":"305_CR40","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/0022-247X(77)90210-4","volume":"58","author":"J Wessels","year":"1977","unstructured":"Wessels J (1977) Markov programming by successive approximations with respect to weighted supremum norms. J Math Anal Appl 58:326\u2013335","journal-title":"J Math Anal Appl"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-019-00305-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13235-019-00305-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-019-00305-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,29]],"date-time":"2020-11-29T02:25:48Z","timestamp":1606616748000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13235-019-00305-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,2]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["305"],"URL":"https:\/\/doi.org\/10.1007\/s13235-019-00305-3","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"type":"print","value":"2153-0785"},{"type":"electronic","value":"2153-0793"}],"subject":[],"published":{"date-parts":[[2019,3,2]]},"assertion":[{"value":"2 March 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}