{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T20:35:14Z","timestamp":1696624514752},"reference-count":24,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2003,3,21]],"date-time":"2003-03-21T00:00:00Z","timestamp":1048204800000},"content-version":"vor","delay-in-days":140,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2002,11]]},"abstract":"Abstract<\/jats:title>Financial markets can be considered as collective information processing devices, which aggregate the information on relevant events into market prices. We show that, in a simple model, markets are efficient aggregators of information only if the number of traders is sufficiently large compared to the number of relevant events. The transition to an efficient market occurs through a phase transition, well known from critical phenomena in physics. \u00a9 2003 Wiley Periodicals, Inc.<\/jats:p>","DOI":"10.1002\/cplx.10065","type":"journal-article","created":{"date-parts":[[2003,3,24]],"date-time":"2003-03-24T11:59:12Z","timestamp":1048507152000},"page":"20-23","source":"Crossref","is-referenced-by-count":3,"title":["Are financial markets efficient? Phase transition in the aggregation of information"],"prefix":"10.1002","volume":"8","author":[{"given":"Johannes","family":"Berg","sequence":"first","affiliation":[]},{"given":"Matteo","family":"Marsili","sequence":"additional","affiliation":[]},{"given":"Aldo","family":"Rustichini","sequence":"additional","affiliation":[]},{"given":"Riccardo","family":"Zecchina","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2003,3,21]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"An Introduction to Econophysics: Correlations and Complexity in Finance","author":"Mantegna R.N.","year":"2000"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830213"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(97)00401-9"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i1997-00491-5"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/17290"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1889(98)00081-5"},{"key":"e_1_2_1_8_2","volume-title":"Microscopic Simulation of Financial Markets","author":"Levy M.","year":"2000"},{"key":"e_1_2_1_9_2","volume-title":"Introduction to Mathematical Finance: Discrete Time Models","author":"Pliska S.R.","year":"1997"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1086\/260616"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/1911512"},{"key":"e_1_2_1_12_2","first-page":"421","article-title":"Do stock prices move too much to be justified by subsequent changes in dividends?","volume":"71","author":"Shiller R.J.","year":"1981","journal-title":"Am Econ Rev"},{"key":"e_1_2_1_13_2","volume-title":"Irrational Exuberance","author":"Shiller R.J.","year":"2000"},{"key":"e_1_2_1_14_2","volume-title":"The Theory of Learning in Games","author":"Fudenberg D.","year":"1998"},{"key":"e_1_2_1_15_2","first-page":"406","article-title":"Inductive reasoning and bounded rationality","volume":"84","author":"Arthur W.B.","year":"1994","journal-title":"Am Econ Assoc Papers and Proc"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(97)00419-6"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.1824"},{"key":"e_1_2_1_18_2","unstructured":"The adaptive learning mechanism is implemented as follows: The strategy \u03c0is associated with a scoreUvia a monotonic function that tends to 0(1) as the score tends to negative (positive) infinity. The specific function we use is \u03c0= e\u0393Ui+\/1+e\u0393Ui+ where \u0393 is the learning rate and similarly for the strategy \u03c0. The scores are updated at each period by adding (R\u03c9\/p\u03c9\u2212 1) toUifki\u03c9= +1 and to Uif ki\u03c9= \u22121."},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1006\/jeth.1997.2319"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00072"},{"key":"e_1_2_1_21_2","unstructured":"More precisely the conditions for stationarity in terms of the dynamic variables \u03c0are equivalent to the first\u2010order conditions for the minimization of a functionH. In the limit \u0393 \u2192 0 it is also possible to derive a continuum time dynamics that admits a Lyapunov functionH i.e. a function of \u03c0 which is bounded from below and monotonically decreasing along the trajectories of the dynamics. Hence the asymptotic dynamics is described by the minima ofH which forN\u2192 \u221e is simply the squareddistance H= \u2211\u03c9(p\u03c9\u2212R\u03c9) of prices from returns."},{"key":"e_1_2_1_22_2","unstructured":"The term \u201cefficient\u201d does not refer to the \u201cefficient market hypothesis. The latter refers to the ability of the market to predict future prices whereas we refer to the ability of the market to aggregate dispersed information eliminating any opportunity for profitable trading."},{"key":"e_1_2_1_23_2","volume-title":"Spin Glass Theory and Beyond","author":"M\u00e9zard M.","year":"1987"},{"key":"e_1_2_1_24_2","unstructured":"To study analytically the minima ofHand thus the long\u2010term dynamics of the system we use the replica method originally developed to describe disordered magnetic alloys (so\u2010called spin\u2010glasses). We considerHas the energy function in a statistical mechanics problem where the variables \u03c0play the role of phase\u2010space variables like spins in the model of a magnet. The minima ofHare found by taking the \u201ctemperature\u201d in this problem to zero. The same analysis applies when the wealth of agents evolves. Now the phase space variables arez=wi\u03c0andz=wi\u03c0. Because unlike \u03c0these variables are not bounded the phase space is larger and consequently the value of \u03b1cis larger with respect to the model with constant wealth. Some details on the analytical calculations may be found in [24]."},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1080\/713665667"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcplx.10065","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cplx.10065","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T05:08:36Z","timestamp":1694495316000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cplx.10065"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,11]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,11]]}},"alternative-id":["10.1002\/cplx.10065"],"URL":"http:\/\/dx.doi.org\/10.1002\/cplx.10065","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":["Multidisciplinary","General Computer Science"],"published":{"date-parts":[[2002,11]]}}}