Hypothesis Testing Under Subjective Priors and Costs as a Signaling Game

Sarıtaş, Serkan; Gezici, Sinan; Yüksel, Serdar

doi:10.1109/tsp.2019.2935908

Cited by 8 publications

(10 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The authors extend the model of Crawford-Sobel to multidimentional sources and noisy channels and they determine whether the optimal policies are linear or based on some quantization. The connection to the binary hypothesis-testing problem was pointed out in [15].…”

Section: B Related Literaturementioning

confidence: 99%

Strategic Communication with Side Information at the Decoder

Treust,

Tomala

2019

Preprint

View full text Add to dashboard Cite

We investigate the problem of strategic point-to-point communication with side information at the decoder, in which the encoder and the decoder have mismatched distortion functions. The decoding process is not supervised, it returns the output sequence that minimizes the decoder's distortion function.The encoding process is designed beforehand and takes into account the decoder's distortion mismatch.When the communication channel is perfect and no side information is available at the decoder, this problem is referred to as the Bayesian persuasion game of Kamenica-Gentzkow in the Economics literature. We formulate the strategic communication scenario as a joint source-channel coding problem with side information at the decoder. The informational content of the source influences the design of the encoding since it impacts differently the two distinct distortion functions. The side information complexifies the analysis since the encoder is uncertain about the decoder's belief on the source statistics.We characterize the single-letter optimal solution by controlling the posterior beliefs induced by the Wyner-Ziv's source coding scheme. This confirms the benefit of sending encoded data bits even if the decoding process is not supervised.

show abstract

Section: B Related Literaturementioning

confidence: 99%

Strategic Communication with Side Information at the Decoder

Treust,

Tomala

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, in such setups, if there is no constraint on messages to transmit between the decision makers such as a power constraint or a limited bandwidth requirement, a decision maker can always reveal more information without causing any performance loss. On the other hand, there exist setups where the decision makers do not share a common goal [1,29,9,30,26,28,33,22,34,35,3,17,18]. In these studies, there are two main themes which lead to misaligned objectives for the decision makers.…”

Section: Introductionmentioning

confidence: 99%

“…In these studies, there are two main themes which lead to misaligned objectives for the decision makers. In the first theme, the decision makers employ different costs function as their goals are inconsistent, e.g., a decision maker wishes to mislead another decision maker [1,29,9,30,26,28,33,22,35,34,17]. The second theme is concerned with the case when the decision makers have subjective beliefs on probability distributions of unknown parameters, which leads to misaligned objectives for the decision makers even though they employ the same cost function [3,18,28].…”

Section: Introductionmentioning

confidence: 99%

Signaling Games in Multiple Dimensions: Geometric Properties of Equilibrium Solutions

Kazikli¹,

Gezici²,

Yüksel³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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. 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 completely characterize conditions under which an informative linear Nash equilibrium 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.

show abstract

“…In the first theme, the decision makers employ different costs function as their goals are inconsistent, e.g., a decision maker wishes to mislead another decision maker [1]- [11]. The second theme is concerned with the case when the decision makers have subjective beliefs on probability distributions of unknown parameters, which leads to misaligned objectives for the decision makers even though they employ the same cost function [6], [12], [13]. These both lead to a game theoretic setup where a suitable equilibrium concept such as the Nash equilibrium and Stackelberg equilibrium is to be used to analyze the system.…”

Section: Introduction and System Modelmentioning

confidence: 99%

Signaling Games in Higher Dimensions: Geometric Properties of Equilibrium Partitions

Kazikli

Gezici

Yüksel

2021

2021 19th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Hypothesis Testing Under Subjective Priors and Costs as a Signaling Game

Cited by 8 publications

References 38 publications

Strategic Communication with Side Information at the Decoder

Strategic Communication with Side Information at the Decoder

Signaling Games in Multiple Dimensions: Geometric Properties of Equilibrium Solutions

Signaling Games in Higher Dimensions: Geometric Properties of Equilibrium Partitions

Contact Info

Product

Resources

About