{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:59:46Z","timestamp":1760241586626,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,5,17]],"date-time":"2018-05-17T00:00:00Z","timestamp":1526515200000},"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 discuss the strategy that rational agents can use to maximize their expected long-term payoff in the co-action minority game. We argue that the agents will try to get into a cyclic state, where each of the    ( 2 N + 1 )    agents wins exactly N times in any continuous stretch of    ( 2 N + 1 )    days. We propose and analyse a strategy for reaching such a cyclic state quickly, when any direct communication between agents is not allowed, and only the publicly available common information is the record of total number of people choosing the first restaurant in the past. We determine exactly the average time required to reach the periodic state for this strategy. We show that it varies as     ( N \/ ln 2 )  [ 1 + \u03b1  cos  ( 2 \u03c0  log 2  N )  ]    , for large N, where the amplitude   \u03b1   of the leading term in the log-periodic oscillations is found be      8  \u03c0 2     ( ln 2 )  2   exp  ( \u2212 2  \u03c0 2  \/ ln 2 )  \u2248 7 \u00d7  10  \u2212 11      .<\/jats:p>","DOI":"10.3390\/g9020027","type":"journal-article","created":{"date-parts":[[2018,5,17]],"date-time":"2018-05-17T03:49:29Z","timestamp":1526528969000},"page":"27","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Achieving Perfect Coordination amongst Agents in the Co-Action Minority Game"],"prefix":"10.3390","volume":"9","author":[{"given":"Hardik","family":"Rajpal","sequence":"first","affiliation":[{"name":"Centre for Complexity Science and Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK"}]},{"given":"Deepak","family":"Dhar","sequence":"additional","affiliation":[{"name":"Department of Physics, Indian Institute for Science Education and Research, Pune 411008, India"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/S0378-4371(97)00419-6","article-title":"Emergence of cooperation and organization in an evolutionary game","volume":"246","author":"Challet","year":"1997","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_2","unstructured":"Korutcheva, E., and Cuerno, R. (2004). Minority Games: An introductory guide. Advances in Condensed Matter and Statistical Physics, Nova Science Publishers."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1111\/j.1467-6419.2011.00686.x","article-title":"Learning with Fixed Rules: The Minority Game","volume":"26","author":"Kets","year":"2011","journal-title":"J. Econ. Surv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Challet, D., Marsili, M., and Zhang, Y.C. (2005). Minority Games, Oxford University Press.","DOI":"10.1093\/oso\/9780198566403.001.0001"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s00712-006-0211-9","article-title":"The Mathematical Theory of Minority Games. Statistical Mechanics of Interacting Agents","volume":"88","author":"Challet","year":"2006","journal-title":"J. Econ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.physa.2014.02.007","article-title":"Strategy switches and co-action equilibria in a minority game","volume":"402","author":"Sasidevan","year":"2014","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.2307\/2951699","article-title":"Adaptive Dynamics in Coordination Games","volume":"63","author":"Crawford","year":"1995","journal-title":"Econometrica"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"161302","DOI":"10.1103\/PhysRevLett.97.161302","article-title":"Surface tension and the cosmological constant","volume":"97","author":"Samuel","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","unstructured":"Sedgewick, R., and Flajolet, P. (2013). An Introduction to the Analysis of Algorithms, Addison Wesley."},{"key":"ref_10","first-page":"251","article-title":"Periodic Oscillations in the Analysis of Algorithms and Their Cancellations","volume":"3","author":"Prodinger","year":"2004","journal-title":"J. Iran. Stat. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/0001-8708(82)90005-6","article-title":"Periodic oscillations of coefficients of power series that satisfy functional equations","volume":"44","author":"Odlyzko","year":"1982","journal-title":"Adv. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1140\/epjb\/e2007-00353-6","article-title":"\u201cIllusion of control\u201d in Time-Horizon Minority and Parrondo Games","volume":"60","author":"Satinover","year":"2007","journal-title":"Eur. Phys. J. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3477","DOI":"10.1016\/j.physa.2011.05.014","article-title":"Emergent cooperation amongst competing agents in minority games","volume":"390","author":"Dhar","year":"2011","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2420","DOI":"10.1016\/j.physa.2009.02.039","article-title":"the Kolkata Paise Restaurant problem and resource utilization","volume":"388","author":"Chakrabarti","year":"2009","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chakrabarti, B.K., Chatterjee, A., Ghosh, A., Mukherjee, S., and Tamir, B. (2017). Econophys. of the Kolkata Restaurant Problem and Related Games, Springer.","DOI":"10.1007\/978-3-319-61352-9"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1080\/1351847X.2011.601657","article-title":"Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask","volume":"19","author":"Geraskin","year":"2013","journal-title":"Eur. J. Financ."},{"key":"ref_17","unstructured":"We are thankful to Prof. J. Radhakrishnan for this observation."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10955-006-9098-7","article-title":"Quenched Averages for Self-Avoiding Walks and Polygons on Deterministic Fractals","volume":"125","author":"Sumedha","year":"2006","journal-title":"J. Stat. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Akkermans, E., Benichou, O., Dunne, G.V., Teplyaev, A., and Voituriez, R. (2012). Spatial log-periodic oscillations of first-passage observables in fractals. Phys. Rev. E, 86.","DOI":"10.1103\/PhysRevE.86.061125"}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/9\/2\/27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:04:37Z","timestamp":1760195077000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/9\/2\/27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,17]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["g9020027"],"URL":"https:\/\/doi.org\/10.3390\/g9020027","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2018,5,17]]}}}