Browsing by Subject "Cheap talk"

Now showing 1 - 4 of 4

Open Access
On multi-dimensional and noisy quadratic signaling games and affine equilibria
(IEEE, 2015-07) Sarıtaş, Serkan; Yüksel, Serdar; Gezici, Sinan
This study investigates extensions of the quadratic cheap talk and signaling game problem, which has been introduced in the economics literature. Two main contributions of this study are the extension of Crawford and Sobel's cheap talk formulation to multi-dimensional sources, and the extension to noisy channel setups as a signaling game problem. We show that, in the presence of misalignment, the quantized nature of all equilibrium policies holds for any scalar random source. It is shown that for multi-dimensional setups, unlike the scalar case, equilibrium policies may be of non-quantized nature, and even linear. In the noisy setup, a Gaussian source is to be transmitted over an additive Gaussian channel. The goals of the encoder and the decoder are misaligned by a bias term and encoder's cost also includes a power term scaled by a multiplier. Conditions for the existence of affine equilibrium policies as well as general informative equilibria are presented for both the scalar and multi-dimensional setups. © 2015 American Automatic Control Council.
Open Access
Quadratic multi-dimensional signaling games and affine equilibria
(Institute of Electrical and Electronics Engineers Inc., 2017) Sarıtaş, S.; Yüksel S.; Gezici, Sinan
This paper studies the decentralized quadratic cheap talk and signaling game problems when an encoder and a decoder, viewed as two decision makers, have misaligned objective functions. The main contributions of this study are the extension of Crawford and Sobel's cheap talk formulation to multi-dimensional sources and to noisy channel setups. We consider both (simultaneous) Nash equilibria and (sequential) Stackelberg equilibria. We show that for arbitrary scalar sources, in the presence of misalignment, the quantized nature of all equilibrium policies holds for Nash equilibria in the sense that all Nash equilibria are equivalent to those achieved by quantized encoder policies. On the other hand, all Stackelberg equilibria policies are fully informative. For multi-dimensional setups, unlike the scalar case, Nash equilibrium policies may be of non-quantized nature, and even linear. In the noisy setup, a Gaussian source is to be transmitted over an additive Gaussian channel. The goals of the encoder and the decoder are misaligned by a bias term and encoder's cost also includes a penalty term on signal power. Conditions for the existence of affine Nash equilibria as well as general informative equilibria are presented. For the noisy setup, the only Stackelberg equilibrium is the linear equilibrium when the variables are scalar. Our findings provide further conditions on when affine policies may be optimal in decentralized multi-criteria control problems and lead to conditions for the presence of active information transmission in strategic environments.
Open Access
Signaling and information games with subjective costs or priors and privacy constraints
(2021-08) Kazıklı, Ertan
We investigate signaling game problems where an encoder and a decoder with misaligned objectives communicate. We consider a variety of setups involving cost criterion mismatch, prior mismatch and a particular application to privacy problems. We also consider both Nash and Stackelberg solution concepts. First, we extend the classical results on the scalar cheap talk problem which is intro-duced by Crawford and Sobel. In prior work, it is shown that the encoder must employ a quantization policy under any Nash equilibrium for arbitrary source distributions. We specifically consider sources with a log-concave density and in-vestigate properties of equilibria. For sources with two-sided unbounded support, we prove that, for any finite number of bins, there exists a unique equilibrium. If the source has semi-unbounded support, then there may exist a finite upper bound on the number of bins in equilibrium depending on certain explicit condi-tions. Moreover, we show that an equilibrium with more bins is more informative by showing that 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 that if the encoder and decoder iteratively compute their best responses starting from a given number of bins, then the resulting policies converge to the unique equilibrium with the corresponding number of bins. Second, we model a privacy problem as a signaling game between an encoder and a decoder. Given a pair of correlated observations modeled as jointly Gaus-sian random vectors, the encoder aims to hide one of them and convey the other one to the decoder. In contrast, the aim of the decoder is to accurately estimate both of the random vectors. For the resulting signaling game problem, we show that a payoff dominant Nash equilibrium among all admissible policies is attained by a set of explicitly characterized linear policies. We also show that a payoff dominant Nash equilibrium coincides with a Stackelberg equilibrium. Moreover, we formulate the information bottleneck problem within our Stackelberg frame-work under the mean squared error criterion where the information bottleneck setup has a further restriction that only one of the parameters is observed at the encoder. We show that the Gaussian information bottleneck problem admits a linear solution which is explicitly characterized. Third, we investigate communications through a Gaussian noise channel be-tween an encoder and a decoder with prior mismatch. Although they consider the same cost function, the induced expected costs as a map of their policies are misaligned due to their prior mismatch. We analyze the resulting signaling game problem under Stackelberg equilibria. We first investigate robustness of equilibria and show that the Stackelberg equilibrium cost of the encoder is upper semi continuous, under the Wasserstein metric, as the encoder’s prior approaches the decoder’s prior, and it is also lower semi continuous with Gaussian priors. In addition, we show that the optimality of affine policies for Gaussian signaling no longer holds under prior mismatch. Furthermore, we provide conditions under which there exist informative equilibria under an affine policy restriction. Fourth, we extend Crawford and Sobel’s formulation to a multidimensional source setting. We first provide a set of geometry conditions that decoder actions at a Nash equilibrium has to satisfy considering any multidimensional source. Then, we consider independent and identically distributed sources and charac-terize necessary and sufficient conditions under which an informative linear equi-librium exists. We observe that these conditions involve the bias vector that leads to misaligned costs. Depending on certain conditions on the bias vector, the existence of linear equilibria may require sources with a Gaussian or a sym-metric density. Moreover, we provide a rate-distortion theoretic formulation of the cheap talk problem and obtain achievable rate and distortion pairs for the Gaussian case. Finally, in a communication theoretic setup, we consider modulation classi-fication and symbol decoding problems jointly and propose optimal strategies under various settings. The aim is to decode a sequence of received signals with an unknown modulation scheme. First, the prior probabilities of the candidate modulation schemes are assumed to be known and a formulation is proposed under the Bayesian framework. Second, we address the case when the prior prob-abilities of the candidate modulation schemes are unknown, and provide a method under the minimax framework. Numerical simulations show that the proposed techniques improve the performance under the employed criteria compared to the conventional techniques in a variety of system configurations.
Open Access
Signaling games for log-concave distributions: Number of bins and properties of equilibria
(IEEE, 2021-11-25) Kazıklı, E.; Sarıtaş, Serkan; Gezici, Sinan; Linder, T.; Yüksel, S.
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.