Signaling games in higher dimensions: geometric properties of equilibrium partitions
| Autor: | Sinan Gezici, Ertan Kazikli, Serdar Yüksel |
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| Přispěvatelé: | Kazıklı, Ertan, Gezici, Sinan |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Independent and identically distributed random variables
Computer science Gaussian Quantization (signal processing) Scalar (physics) Rate-distortion theory Upper and lower bounds Nash equilibrium symbols.namesake Signaling games symbols Applied mathematics Multi-dimensional cheap talk Signaling game Encoder |
| Zdroj: | International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt) WiOpt |
| Popis: | Conference Name: 2021 19th International Symposium on Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt) Date of Conference: 18-21 October 2021 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. We investigate a signaling game problem where an encoder observes a multi-dimensional source and conveys a message to a decoder, and the quadratic objectives of the encoder and decoder are misaligned due to a bias vector. For the scalar case, Crawford and Sobel in their seminal paper, show that under certain technical assumptions an encoding policy must be a quantization policy at any Nash equilibrium. We first provide a set of geometry conditions that needs to be satisfied in equilibrium considering any multi-dimensional source. Then, we consider multi-dimensional sources with independent and identically distributed components and completely characterize conditions under which a Nash equilibrium with a linear encoder exists. In particular, we show that if the components of the bias vector are not equal in magnitude, then there exists a linear equilibrium if and only if the source distribution is Gaussian. On the other hand, for a linear equilibrium to exist in the case of equal bias components, it is required that the source density is symmetric around its mean. 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 their team theoretic counterpart. |
| Databáze: | OpenAIRE |
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