Signaling game problems investigate communication scenarios where encoder(s) and decoder(s) have misaligned objectives due to the fact that they either employ different cost functions or have inconsistent priors. This problem has been studied in the literature for scalar sources under various setups. In this paper, we consider multi-dimensional sources under quadratic criteria in the presence of a bias leading to a mismatch in the criteria, where we show that the generalization from the scalar setup is more than technical. We show that the equilibrium solutions lead to structural richness due to the subtle geometric analysis the problem entails, with consequences in both system design, presence of linear equilibria, and an information theoretic problem formulation. We first provide a set of geometry conditions that needs to be satisfied in equilibrium considering any multi-dimensional source. Then, we consider independent and identically distributed sources and characterize necessary and sufficient conditions under which an informative linear equilibrium exists. These conditions involve the bias vector that leads to misaligned costs. Depending on certain conditions related to the bias vector, the existence of linear equilibria requires sources with a Gaussian or a symmetric density. Moreover, in the case of Gaussian sources, our results have a rate-distortion theoretic implication that achievable rates and distortions in the considered game theoretic setup can be obtained from its team theoretic counterpart.
翻译:信号游戏问题调查了由于编码器和解码器使用不同的成本功能或前后前后不一致而导致目标不匹配的通信情况。 这个问题已在各种设置下用于卡路里源的文献中研究过。 在本文中,我们考虑在四维标准下的多维源,但有偏差导致标准不匹配,我们显示,从缩略图设置中的一般化不仅仅是技术性的。我们表明,平衡解决方案导致结构上的丰富,因为对问题进行微妙的几何分析,在系统设计、线性平衡存在和信息性理论问题配制方面产生了后果。 我们首先提供了一系列在平衡中需要满足的几维条件,同时考虑到任何多维来源。 然后,我们考虑独立和相同的分布源,并描述在必要和充分的条件下存在信息性线性平衡。 这些条件涉及导致偏差成本的偏差矢量。 根据与偏差矢量相关的某些条件,线性松动的存在要求在系统设计、线性平衡存在的后果, 线性平衡性平衡和信息论问题的配对等值配值配值配值公式的源, 。 高正比值的定率率率是高正比值的, 。