Signaling games for log-concave distributions: Number of bins and properties of equilibria
| Autor: | Ertan Kazikli, Serkan Saritas, Tamas Linder, Sinan Gezici, Serdar Yüksel |
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| Přispěvatelé: | Sarıtaş, Serkan, Gezici, Sinan |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Information Theory Context (language use) 02 engineering and technology Library and Information Sciences Upper and lower bounds Nash equilibrium Lloyd–Max algorithm 0202 electrical engineering electronic engineering information engineering Countable set Applied mathematics Finite set Mathematics Lloyd-Max algorithm Information Theory (cs.IT) Optimal quantization 020206 networking & telecommunications Cheap talk Payoff dominant equilibria Computer Science Applications Distribution (mathematics) Best response Signaling games Probability distribution Random variable Information Systems |
| Zdroj: | IEEE Transactions on Information Theory |
| Popis: | We investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown that the number of bins in any equilibrium has to be countable, generalizing a classical result due to Crawford and Sobel who considered sources with density supported on $[0,1]$. In this paper, we first refine this result in the context of log-concave sources. For sources with two-sided unbounded support, we prove that, for any finite number of bins, there exists a unique equilibrium. In contrast, for sources with semi-unbounded support, there may be a finite upper bound on the number of bins in equilibrium depending on certain conditions stated explicitly. Moreover, we prove that for log-concave sources, the expected costs of the encoder and the decoder in equilibrium decrease as the number of bins increases. Furthermore, for strictly log-concave sources with two-sided unbounded support, we prove convergence to the unique equilibrium under best response dynamics which starts with a given number of bins, making a connection with the classical theory of optimal quantization and convergence results of Lloyd's method. In addition, we consider more general sources which satisfy certain assumptions on the tail(s) of the distribution and we show that there exist equilibria with infinitely many bins for sources with two-sided unbounded support. Further explicit characterizations are provided for sources with exponential, Gaussian, and compactly-supported probability distributions. Comment: 27 pages and 1 figure. arXiv admin note: text overlap with arXiv:1901.06738 |
| Databáze: | OpenAIRE |
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