国际消费类电子产品展览会,简称国际消费电子展,常简称为CES,每年1月在美国内华达州拉斯维加斯举行,由消费电子协会赞助。

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In this paper, we bring consumer theory to bear in the analysis of Fisher markets whose buyers have arbitrary continuous, concave, homogeneous (CCH) utility functions representing locally non-satiated preferences. The main tools we use are the dual concepts of expenditure minimization and indirect utility maximization. First, we use expenditure functions to construct a new convex program whose dual, like the dual of the Eisenberg-Gale program, characterizes the equilibrium prices of CCH Fisher markets. We then prove that the subdifferential of the dual of our convex program is equal to the negative excess demand in the associated market, which makes generalized gradient descent equivalent to computing equilibrium prices via t\^atonnement. Finally, we use our novel characterization of equilibrium prices via expenditure functions to show that a discrete t\^atonnement process converges at a rate of $O\left(\frac{1}{t}\right)$ in Fisher markets with continuous, strictly concave, homogeneous (CSCH) utility functions -- a class of utility functions beyond the class of CES utility functions, the largest class for which convergence results were previously known. CSCH Fisher markets include nested and mixed CES Fisher markets, thus providing a meaningful expansion of the space of Fisher markets that is solvable via t\^atonnement.

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