合作博弈的信息论核心
Cores of Cooperative Games in Information Theory
摘要：
合作博弈的核心在信息论中无处不在，并且在涉及多个用户的各种场景中的基本限制的表征中最频繁地出现。例子包括网络信息论中的经典设置，如Slepian-Wolf信源编码和多址信道，统计学中的经典设置，如鲁棒假设检验，以及网络和统计学交叉点的新设置，如传感器网络的分布式估计问题。合作博弈论允许人们从一个新鲜和统一的角度来理解所有这些问题的各个方面，将用户视为游戏中的玩家，有时会导致新的见解。这些分析的核心是在合作博弈的背景下长期研究的基本对偶性;出于信息论的目的，这些是一方面信息不平等与另一方面速率、容量或其他资源分配区域属性之间的对偶性。
英文摘要：
Cores of cooperative games are ubiquitous in information theory, and arise most frequently in the characterization of fundamental limits in various scenarios involving multiple users. Examples include classical settings in network information theory such as Slepian-Wolf source coding and multiple access channels, classical settings in statistics such as robust hypothesis testing, and new settings at the intersection of networking and statistics such as distributed estimation problems for sensor networks. Cooperative game theory allows one to understand aspects of all of these problems from a fresh and unifying perspective that treats users as players in a game, sometimes leading to new insights. At the heart of these analyses are fundamental dualities that have been long studied in the context of cooperative games; for information theoretic purposes, these are dualities between information inequalities on the one hand and properties of rate, capacity or other resource allocation regions on the other.
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