{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T20:40:29Z","timestamp":1770842429076,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,8,11]],"date-time":"2016-08-11T00:00:00Z","timestamp":1470873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>We analyse active space debris removal efforts from a strategic, game-theoretical perspective. Space debris is non-manoeuvrable, human-made objects orbiting Earth, which pose a significant threat to operational spacecraft. Active debris removal missions have been considered and investigated by different space agencies with the goal to protect valuable assets present in strategic orbital environments. An active debris removal mission is costly, but has a positive effect for all satellites in the same orbital band. This leads to a dilemma: each agency is faced with the choice between the individually costly action of debris removal, which has a positive impact on all players; or wait and hope that others jump in and do the \u2018dirty\u2019 work. The risk of the latter action is that, if everyone waits, the joint outcome will be catastrophic, leading to what in game theory is referred to as the \u2018tragedy of the commons\u2019. We introduce and thoroughly analyse this dilemma using empirical game theory and a space debris simulator. We consider two- and three-player settings, investigate the strategic properties and equilibria of the game and find that the cost\/benefit ratio of debris removal strongly affects the game dynamics.<\/jats:p>","DOI":"10.3390\/g7030020","type":"journal-article","created":{"date-parts":[[2016,8,11]],"date-time":"2016-08-11T10:29:29Z","timestamp":1470911369000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Space Debris Removal: A Game Theoretic Analysis"],"prefix":"10.3390","volume":"7","author":[{"given":"Richard","family":"Klima","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK"}]},{"given":"Daan","family":"Bloembergen","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1262-7831","authenticated-orcid":false,"given":"Rahul","family":"Savani","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK"}]},{"given":"Karl","family":"Tuyls","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK"}]},{"given":"Daniel","family":"Hennes","sequence":"additional","affiliation":[{"name":"DFKI GmbH, 28359 Bremen, Germany"}]},{"given":"Dario","family":"Izzo","sequence":"additional","affiliation":[{"name":"Advanced Concepts Team, European Space Agency, 2201 AZ Noordwijk, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,11]]},"reference":[{"key":"ref_1","unstructured":"NORAD Two-Line Element Sets Current Data. Available online: https:\/\/celestrak.com\/NORAD\/elements\/."},{"key":"ref_2","first-page":"407","article-title":"Investigating orbital debris events using numerical methods with full force model orbit propagation","volume":"130","author":"Carrico","year":"2008","journal-title":"Adv. Astronaut. Sci."},{"key":"ref_3","unstructured":"NASA Orbital Debris Program Office (2007). Chinese Anti-Satellite Test Creates Most Severe Orbital Debris Cloud in History, NASA Orbital Debris Quarterly News."},{"key":"ref_4","unstructured":"NASA Orbital Debris Program Office (2009). Satellite Collision Leaves Significant Debris Clouds, NASA Orbital Debris Quarterly News."},{"key":"ref_5","unstructured":"NASA Orbital Debris Program Office (2011). International Space Station Again Dodges Debris, NASA Orbital Debris Quarterly News."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/0176-2680(94)90033-7","article-title":"Carbon dioxide abatement as a differential game","volume":"10","author":"Tahvonen","year":"1994","journal-title":"Eur. J. Polit. Econ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2637","DOI":"10.1029\/JA083iA06p02637","article-title":"Collision frequency of artificial satellites: The creation of a Debris belt","volume":"83","author":"Kessler","year":"1978","journal-title":"J. Geophys. Res."},{"key":"ref_8","unstructured":"Kessler, D.J., Johnson, N.L., Liou, J.C., and Matney, M. (2010, January 6\u201310). The Kessler syndrome: Implications to future space operations. Proceedings of the American Astronautical Society\u2014Guidance Control Conference, Breckenridge, CO, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.actaastro.2008.07.009","article-title":"A sensitivity study of the effectiveness of active debris removal in LEO","volume":"64","author":"Liou","year":"2009","journal-title":"Acta Astronaut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.actaastro.2009.08.005","article-title":"Controlling the growth of future LEO debris populations with active debris removal","volume":"66","author":"Liou","year":"2010","journal-title":"Acta Astronaut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1865","DOI":"10.1016\/j.asr.2011.02.003","article-title":"An active debris removal parametric study for LEO environment remediation","volume":"47","author":"Liou","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1093\/restud\/rds011","article-title":"Climate contracts: A game of emissions, investments, negotiations, and renegotiations","volume":"79","author":"Harstad","year":"2012","journal-title":"Rev. Econ. Stud."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"322","DOI":"10.2307\/3003416","article-title":"The great fish war: An example using a dynamic Cournot-Nash solution","volume":"11","author":"Levhari","year":"1980","journal-title":"Bell J. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1126\/science.162.3859.1243","article-title":"The tragedy of the commons","volume":"162","author":"Hardin","year":"1968","journal-title":"Science"},{"key":"ref_15","unstructured":"Walsh, W., Das, R., Tesauro, G., and Kephart, J. (August, January 28). Analyzing complex strategic interactions in multi-agent systems. Proceedings of the AAAI-02 Workshop on Game-Theoretic and Decision-Theoretic Agents, Edmonton, AB, Canada."},{"key":"ref_16","first-page":"1552","article-title":"Methods for empirical game-theoretic analysis","volume":"Volume 21","author":"Wellman","year":"2006","journal-title":"Proceedings of the Twenty-First National Conference on Artificial Intelligence and the Eighteenth Innovative Applications of Artificial Intelligence Conference"},{"key":"ref_17","first-page":"1063","article-title":"Searching for approximate equilibria in empirical games","volume":"Volume 2","author":"Jordan","year":"2008","journal-title":"Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems"},{"key":"ref_18","unstructured":"Wellman, M.P., Jordan, P.R., Kiekintveld, C., Miller, J., and Reeves, D.M. (2006, January 8\u201310). Empirical game-theoretic analysis of the TAC market games. Proceedings of the AAMAS-06 Workshop on Game-Theoretic and Decision-Theoretic Agents, Hakodate, Japan."},{"key":"ref_19","first-page":"101","article-title":"An evolutionary game-theoretic comparison of two double-auction market designs","volume":"Volume 3435","author":"Faratin","year":"2005","journal-title":"Agent-Mediated Electronic Commerce VI. Theories for and Engineering of Distributed Mechanisms and Systems"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.entcom.2009.09.002","article-title":"An evolutionary game-theoretic analysis of poker strategies","volume":"1","author":"Ponsen","year":"2009","journal-title":"Entertain. Comput."},{"key":"ref_21","unstructured":"Hennes, D., Claes, D., and Tuyls, K. (2013, January 6\u201310). Evolutionary advantage of reciprocity in collision avoidance. Proceedings of the AAMAS 2013 Workshop on Autonomous Robots and Multirobot Systems (ARMS 2013), Saint Paul, MN, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wellman, M.P., and Prakash, A. (2014, January 6\u20137). Empirical game-theoretic analysis of an adaptive cyber-defense scenario (preliminary report). Proceedings of Conference on Decision and Game Theory for Security.","DOI":"10.1007\/978-3-319-12601-2_3"},{"key":"ref_23","first-page":"10","article-title":"Metastrategies in large-scale bargaining settings","volume":"7","author":"Hennes","year":"2015","journal-title":"ACM Trans. Intell. Syst. Technol. (TIST)"},{"key":"ref_24","unstructured":"Izzo, D. (2012). Pygmo and Pykep: Open Source Tools for Massively Parallel Optimization in Astrodynamics (The Case of Interplanetary Trajectory Optimization), Advanced Concept Team\u2014European Space Research and Technology Centre (ESTEC). Technical Report."},{"key":"ref_25","unstructured":"Liou, J.C., Kessler, D., Matney, M., and Stansbery, G. (2003, January 17\u201321). A new approach to evaluate collision probabilities among asteroids, comets, and Kuiper Belt objects. Proceedings of the Lunar and Planetary Science Conference, League City, TX, USA."},{"key":"ref_26","first-page":"2006","article-title":"Revisiting spacetrack report #3","volume":"6753","author":"Vallado","year":"2006","journal-title":"AIAA"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1016\/S0273-1177(01)00423-9","article-title":"Nasa\u2019s new breakup model of EVOLVE 4.0","volume":"28","author":"Johnson","year":"2001","journal-title":"Adv. Space Res."},{"key":"ref_28","unstructured":"Klinkrad, H. (2010). Encyclopedia of Aerospace Engineering, The American Institute of Aeronautics and Astronautics."},{"key":"ref_29","unstructured":"Gibbons, R. (1992). A Primer in Game Theory, Financial Times Prentice Hall, Pearson Education."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"286","DOI":"10.2307\/1969529","article-title":"Non-cooperative games","volume":"54","author":"Nash","year":"1951","journal-title":"Ann. Math."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"85","DOI":"10.2307\/2297471","article-title":"On the existence of Cournot equilibrium","volume":"52","author":"Novshek","year":"1985","journal-title":"Rev. Econ. Stud."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"587","DOI":"10.2307\/1911656","article-title":"Existence of Cournot equilibrium in large markets","volume":"53","year":"1985","journal-title":"Econometrica"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.geb.2004.10.007","article-title":"Strategic complements and substitutes, and potential games","volume":"54","author":"Dubey","year":"2006","journal-title":"Games Econ. Behav."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.geb.2003.06.007","article-title":"Best response dynamics in finite games with additive aggregation","volume":"48","author":"Kukushkin","year":"2004","journal-title":"Games Econ. Behav."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0165-1765(94)90072-8","article-title":"A fixed-point theorem for decreasing mappings","volume":"46","author":"Kukushkin","year":"1994","journal-title":"Econ. Lett."},{"key":"ref_36","unstructured":"Kukushkin, N.S. Strategic supplements in games with polylinear interactions. Available online: http:\/\/www.eco.uc3m.es\/temp\/StrSuppl.pdf."},{"key":"ref_37","unstructured":"Weibull, J.W. (1997). Evolutionary Game Theory, MIT Press."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1613\/jair.4818","article-title":"Evolutionary dynamics of multi-agent learning: A survey","volume":"53","author":"Bloembergen","year":"2015","journal-title":"J. Artif. Intell. Res."}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/7\/3\/20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:28:14Z","timestamp":1760210894000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/7\/3\/20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,11]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,9]]}},"alternative-id":["g7030020"],"URL":"https:\/\/doi.org\/10.3390\/g7030020","relation":{},"ISSN":["2073-4336"],"issn-type":[{"value":"2073-4336","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8,11]]}}}