We consider a setting where a receiver tries to perfectly recover a source signal privately known to a sender who can send messages via a noisy channel. However, the sender is compromised and may have an incentive to lie about its information. We formulate the problem as a game between the sender and the receiver and show that there is a strategy for the receiver in which it can recover an exponential number of signals. We define a notion of a sender graph and the information extraction capacity of the sender which quantifies the maximum amount of information that can be extracted from the sender. We also show that the rate of information extraction is given by the minimum of the information extraction capacity of the sender and the zero-error capacity of the noisy channel.
We consider a setting where a receiver tries to perfectly recover a source signal privately known to a sender who can send messages via a noisy channel. However, the sender is compromised and may have an incentive to lie about its information. We formulate the problem as a game between the sender and the receiver and show that there is a strategy for the receiver in which it can recover an exponential number of signals. We define a notion of a sender graph and the information extraction capacity of the sender which quantifies the maximum amount of information that can be extracted from the sender. We also show that the rate of information extraction is given by the minimum of the information extraction capacity of the sender and the zero-error capacity of the noisy channel.
We introduce a setting where a receiver aims to perfectly recover a source known privately to a \textit{strategic} sender over a possibly noisy channel. The sender is endowed with a utility function and sends signals to the receiver with the aim of maximizing this utility. Due to the strategic nature of the sender not all the transmitted information is truthful, which leads to question: how much true information can be recovered by the receiver from such a sender? We study this question in this paper. We pose the problem as a game between the sender and receiver, where the receiver tries to maximize the number of sequences that can be recovered perfectly and the sender maximizes its utility. We show that, in spite of the sender being strategic and the presence of noise in the channel, there is a strategy for the receiver by which it can perfectly recover an \textit{exponentially} large number of sequences. Our analysis leads to the notion of the \textit{information extraction capacity} of the sender which quantifies the growth rate of the number of recovered sequences with blocklength, in the presence of a noiseless channel. We identify cases where this capacity is equal to its theoretical maximum, and also when it is strictly less than maximum. In the latter case, we show that the capacity is sandwiched between the independence number and the Shannon capacity of a suitably defined graph. These results lead to an exact characterization of the information extraction capacity in large number of cases. We show that in the presence of a noisy channel, the rate of information extraction achieved by the receiver is the minimum of the zero-error capacity of the channel and the information extraction capacity of the sender. Our analysis leads to insights into a novel regime of communication involving strategic agents.
We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, noncooperative regime of communication involving a strategic sender.
We consider a Gaussian cheap talk game with quadratic cost functions. The cost function of the receiver is equal to the estimation error variance, however, the cost function of each senders contains an extra term which is captured by its private information. Following the cheap talk literature, we model this problem as a game with asymmetric information. We start by the single sender case in which the receiver also has access to a noisy but honest side information in addition to the message transmitted by a strategic sender. We generalize this setup to multiple sender case. For the multiple sender case, we observe that if the senders are not herding (i.e., copying each other policies), the quality of the receiver's estimation degrades rapidly as the number of senders increases.
Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network? In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding. If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself! We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.
A game is introduced to study the effect of privacy in strategic communication between well-informed senders and a receiver. The receiver wants to accurately estimate a random variable. The sender, however, wants to communicate a message that balances a trade-off between providing an accurate measurement and minimizing the amount of leaked private information, which is assumed to be correlated with the to-be-estimated variable. The mutual information between the transmitted message and the private information is used as a measure of the amount of leaked information. An equilibrium is constructed and its properties are investigated.
In a point-to-point communication system which consists of a sender, a receiver and a set of noiseless channels, the sender wishes to transmit a private message to the receiver through the channels which may be eavesdropped by a wiretapper. The set of wiretap sets is arbitrary. The wiretapper can access any one but not more than one wiretap set. From each wiretap set, the wiretapper can obtain some partial information about the private message which is measured by the equivocation of the message given the symbols obtained by the wiretapper. The security strategy is to encode the message with some random key at the sender. Only the message is required to be recovered at the receiver. Under this setting, we define an achievable rate tuple consisting of the size of the message, the size of the key, and the equivocation for each wiretap set. We first prove a tight rate region when both the message and the key are required to be recovered at the receiver. Then we extend the result to the general case when only the message is required to be recovered at the receiver. Moreover, we show that even if stochastic encoding is employed at the sender, the message rate cannot be increased.