Vector quantization and signal compression
Vector quantization and signal compression
Implementation with a bounded action space
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Auctions with severely bounded communication
Journal of Artificial Intelligence Research
High-resolution quantization theory and the vector quantizer advantage
IEEE Transactions on Information Theory
Asymptotically optimal block quantization
IEEE Transactions on Information Theory
Asymptotic quantization error of continuous signals and the quantization dimension
IEEE Transactions on Information Theory
A lower bound on the average error of vector quantizers (Corresp.)
IEEE Transactions on Information Theory
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We analyze a nonlinear pricing model with limited information. Each buyer can purchase a large variety, d, of goods. His preference for each good is represented by a scalar and his preference over d goods is represented by a d-dimensional vector. The type space of each buyer is given by a compact subset of Rd+ with a continuum of possible types. By contrast, the seller is limited to offer a finite number M of d-dimensional choices. We provide necessary conditions that the optimal finite menu of the social welfare maximizing problem has to satisfy. We establish an underlying connection to the theory of quantization and provide an estimate of the welfare loss resulting from the usage of the d-dimensional M-class menu. We show that the welfare loss converges to zero at a rate proportional to d/M2/d. We show that in higher dimensions, a significant reduction in the welfare loss arises from an optimal partition of the d-dimensional type space that takes advantage of the correlation among the d parameters.