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We consider markets in the classical Arrow-Debreu model. There are n agents and m goods. Each buyer has a concave utility function (of the bundle of goods he/she buys) and an initial bundle. At an ldquoequilibriumrdquo set of prices for goods, if each individual buyer separately ex-changes the initial bundle for an optimal bundle at the set prices, the market clears, i.e., all goods are exactly consumed...
We study the problem of computing the minimum volume enclosing ellipsoid (MVEE) containing a given set of ellipsoids S = {E1, E2, hellip, En} sube Ropfd. We show how to efficiently compute a small set X sube S of size at most a = |X| = O(d2/epsi ) whose minimum volume ellipsoid is an (1 + epsi)-approximation to the minimum volume ellipsoid of S. We use an augmented real num ber model of computation...
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