We study the problem of designing prediction markets for random variables with continuous or countably infinite outcomes on the real line. Our interval betting languages allow traders to bet on any interval of their choice. Both the call market mechanism and two automated market maker mechanisms, logarithmic market scoring rule (LMSR) and dynamic parimutuel markets (DPM), are generalized to han...

1. D. A. Darling, On a class of problems related to the random division of an interval, Ann. Math. Statist. 24 (1953) 239–253. 2. B. V. Gnedenko, The Theory of Probability, 4th ed., Chelsea, New York, 1968. 3. R. Honsberger, Ingenuity in Mathematics, Mathematical Association of America, Washington, D.C., 1970. 4. M. G. Kendall and P. A. P. Moran, Geometrical Probability, Griffin, London, 1963. ...