{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:24:33Z","timestamp":1760243073187,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,8,31]],"date-time":"2015-08-31T00:00:00Z","timestamp":1440979200000},"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 propose a bargaining process supergame over the strategies to play in a  non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game.  We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner\u2019s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games.<\/jats:p>","DOI":"10.3390\/g6030273","type":"journal-article","created":{"date-parts":[[2015,9,1]],"date-time":"2015-09-01T10:55:58Z","timestamp":1441104958000},"page":"273-298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Bargaining over Strategies of Non-Cooperative Games"],"prefix":"10.3390","volume":"6","author":[{"given":"Giuseppe","family":"Attanasi","sequence":"first","affiliation":[{"name":"BETA, University of Strasbourg, 61 Av. de la Foret Noire, 67000 Strasbourg, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aurora","family":"Garc\u00eda-Gallego","sequence":"additional","affiliation":[{"name":"LEE & Department of Economics, Universitat Jaume I, Avda. Sos Baynat s\/n, Campus Riu Sec,  12071 Castello\u0301n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikolaos","family":"Georgantz\u00eds","sequence":"additional","affiliation":[{"name":"LEE & Department of Economics, Universitat Jaume I, Avda. Sos Baynat s\/n, Campus Riu Sec,  12071 Castello\u0301n, Spain"},{"name":"School of Agriculture Policy and Development, University of Reading, P.O. Box 237,  Reading RG6 6AR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aldo","family":"Montesano","sequence":"additional","affiliation":[{"name":"Department of Economics, Bocconi University, 1 via Roentgen, 20136 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2296617","article-title":"A non-cooperative equilibrium for supergames","volume":"38","author":"Friedman","year":"1971","journal-title":"Rev. Econ. Stud."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1617","DOI":"10.2307\/1911925","article-title":"The prisoner\u2019s dilemma and dynamical systems associated to non-cooperative games","volume":"48","author":"Smale","year":"1980","journal-title":"Econometrica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"798","DOI":"10.2307\/2234975","article-title":"Rationally justifiable play and the theory of non-cooperative games","volume":"104","author":"Cubitt","year":"1994","journal-title":"Econ. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0899-8256(90)90023-N","article-title":"Bargaining without commitment","volume":"2","author":"Muthoo","year":"1990","journal-title":"Games Econ. Behav."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2307\/1912531","article-title":"Perfect equilibrium in a bargaining model","volume":"50","author":"Rubinstein","year":"1982","journal-title":"Econometrica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1162\/jeea.2010.8.1.7","article-title":"Bargaining and cooperation in strategic form games","volume":"8","author":"Hart","year":"2010","journal-title":"J. Eur. Econ. Assoc."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Brams, S.J. (1994). Theory of Moves, Cambridge University Press.","DOI":"10.1017\/CBO9780511558979"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.obhdp.2012.12.001","article-title":"An experiment on prisoner\u2019s dilemma with confirmed proposals","volume":"120","author":"Attanasi","year":"2013","journal-title":"Organ. Behav. Hum. Decis. Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/246015a0","article-title":"The logic of animal conflict","volume":"246","author":"Smith","year":"1973","journal-title":"Nature"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Attanasi, G., Battigalli, P., and Manzoni, E. (2015). Incomplete information models of guilt aversion in the trust game. Manag. Sci., in press.","DOI":"10.1287\/mnsc.2015.2154"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/S0899-8256(05)80017-X","article-title":"Learning to be imperfect: The ultimatum game","volume":"8","author":"Binmore","year":"1995","journal-title":"Games Econ. Behav."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/0167-2681(82)90011-7","article-title":"An experimental analysis of ultimatum bargaining","volume":"3","author":"Schmittberger","year":"1982","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1007\/BF01210566","article-title":"A note on bargaining over a finite number of feasible agreements","volume":"1","author":"Muthoo","year":"1991","journal-title":"Econ. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"709","DOI":"10.2307\/2297715","article-title":"Non-cooperative bargaining theory: An introduction","volume":"53","author":"Sutton","year":"1986","journal-title":"Rev. Econ. Stud."},{"key":"ref_15","unstructured":"Osborne, M.J., and Rubinstein, A. (1990). Bargaining and Markets, Academic Press."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1142\/S0219198909002170","article-title":"An n-person Rubinstein bargaining game","volume":"11","author":"Torstensson","year":"2009","journal-title":"Int. Game Theory Rev."},{"key":"ref_17","unstructured":"Jun, B.H. (1987). A structural consideration on 3-person bargaining. [Ph.D. Thesis, University of Pennsylvania]."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/0165-1765(88)90118-8","article-title":"The unique perfect equilibrium of an n-person bargaining game","volume":"28","author":"Chae","year":"1988","journal-title":"Econ. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1006\/jeth.1994.1005","article-title":"An n-person pure bargaining game","volume":"62","author":"Chae","year":"1994","journal-title":"J. Econ. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"61","DOI":"10.2307\/2298115","article-title":"Multilateral bargaining","volume":"63","author":"Krishna","year":"1996","journal-title":"Rev. Econ. Stud."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/0899-8256(92)90013-I","article-title":"A unique solution to n-person sequential bargaining","volume":"4","author":"Asheim","year":"1992","journal-title":"Games Econ. Behav."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Greenberg, J. (1990). The Theory of Social Situations: An Alternative Game-Theoretic Approach, Cambridge University Press.","DOI":"10.1017\/CBO9781139173759"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1006\/game.1996.0013","article-title":"Cooperation without reputation: Experimental evidence from prisoner\u2019s dilemma games","volume":"12","author":"Cooper","year":"1996","journal-title":"Games Econ. Behav."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.jebo.2005.12.008","article-title":"Fairness and reciprocity in the hawk-dove game","volume":"66","author":"Neugebauer","year":"2008","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wittek, R., Snijders, T., and Nee, V. (2013). Handbook of Rational Choice Social Research, Russell Sage.","DOI":"10.1515\/9780804785501"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s00199-006-0145-z","article-title":"Forward induction and entry deterrence: An experiment","volume":"33","author":"Brandts","year":"2006","journal-title":"Econ. Theory"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1006\/game.2000.0829","article-title":"The relevance of equal splits in ultimatum games","volume":"37","author":"Huck","year":"2001","journal-title":"Games Econ. Behav."}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/6\/3\/273\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:47:46Z","timestamp":1760215666000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/6\/3\/273"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,31]]},"references-count":27,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,9]]}},"alternative-id":["g6030273"],"URL":"https:\/\/doi.org\/10.3390\/g6030273","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2015,8,31]]}}}