The index coding problem includes a server, a group of clients, and a set of data chunks. While each client wants a subset of the data chunks and already has another subset as its side information, the server transmits some uncoded data chunks or coded data chunks to the clients over a noiseless broadcast channel. The objective of the problem is to satisfy the demands of all clients with the minimum number of transmissions. In this paper, we investigate the index coding setting from a game-theoretical perspective. We consider selfish clients, where each selfish client has private side information and a private valuation of each data chunk it wants. In this context, our objectives are following: 1) to motivate each selfish client to reveal the correct side information and true valuation of each data chunk it wants; 2) to maximize the social welfare, i.e., the total valuation of the data chunks recovered by the clients minus the total cost incurred by the transmissions from the server. Our main contribution is to jointly develop coding schemes and incentive schemes for achieving the first objective perfectly and achieving the second objective optimally or approximately with guaranteed approximation ratios (potentially within some restricted sets of coding matrices).

中文翻译：

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自私客户联合指标编码与激励设计

索引编码问题包括一个服务器、一组客户端和一组数据块。虽然每个客户端都需要数据块的一个子集并且已经有另一个子集作为其辅助信息，但服务器通过无噪声广播信道向客户端传输一些未编码的数据块或编码的数据块。该问题的目标是用最少的传输次数满足所有客户端的需求。在本文中，我们从博弈论的角度研究了索引编码设置。我们考虑自私的客户端，其中每个自私的客户端都有私人的边信息和它想要的每个数据块的私人估值。在这种情况下，我们的目标如下： 1）激励每个自私的客户揭示它想要的每个数据块的正确辅助信息和真实估值；2）社会福利最大化，即，客户端恢复的数据块的总估值减去从服务器传输所产生的总成本。我们的主要贡献是共同开发编码方案和激励方案，以完美地实现第一个目标，并以保证的近似比率（可能在一些受限的编码矩阵集内）最优或近似地实现第二个目标。