平衡Tatonnement的健壮性和收敛性
Balancing the Robustness and Convergence of Tatonnement
摘要：
算法博弈论的一个主要目标是从算法和复杂性的角度证明均衡概念的合理性。一种吸引人的方法是确定鲁棒的自然分布式算法，快速收敛到一个平衡。本文讨论了缺乏鲁棒性的离散形式的tatonnement，包括事实上，它不需要收敛时，买家有线性效用函数的现有收敛结果。这项工作实现了更大的鲁棒性，通过寻求近似，而不是在大的市场设置的精确收敛。更具体地说，本文表明，对于费舍尔市场的买家CES效用函数，包括线性效用函数，tatonnement将迅速收敛到一个近似均衡（即在线性率），模一个合适的大市场假设。近似的质量是大市场假设参数的函数。
英文摘要：
A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify robust natural distributed algorithms that converge quickly to an equilibrium. This paper addresses a lack of robustness in existing convergence results for discrete forms of tatonnement, including the fact that it need not converge when buyers have linear utility functions. This work achieves greater robustness by seeking approximate rather than exact convergence in large market settings. More specifically, this paper shows that for Fisher markets with buyers having CES utility functions, including linear utility functions, tatonnement will converge quickly to an approximate equilibrium (i.e. at a linear rate), modulo a suitable large market assumption. The quality of the approximation is a function of the parameters of the large market assumption.
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