Information Design for Strategic Coordination of Autonomous Devices with Non-Aligned Utilities

In this paper, we investigate the coordination of autonomous devices with non-aligned utility functions. Both encoder and decoder are considered as players, that choose the encoding and the decoding in order to maximize their long-run utility functions. The topology of the point-to-point network under investigation, suggests that the decoder implements a strategy, knowing in advance the strategy of the encoder. We characterize the encoding and decoding functions that form an equilibrium, by using empirical coordination. The equilibrium solution is related to an auxiliary game in which both players choose some conditional distributions in order to maximize their expected utilities. This problem is closely related to the literature on "Information Design" in Game Theory. We also characterize the set of posterior distributions that are compatible with a rate-limited channel between the encoder and the decoder. Finally, we provide an example of non-aligned utility functions corresponding to parallel fading multiple access channels.Comment: IEEE Proc. of the Fifty-fourth Annual Allerton Conference Allerton House, UIUC, Illinois, USA September 27 - 30, 201

Maxmin computation and optimal correlation in repeated games with signals

Le maxmin pour une certaine classe de jeux répétés à observation imparfaite est obtenu comme la solution d'un problème d'optimisation défini sur l'ensemble des distributions de probabilités sous contraintes d'entropie. Cette article offre une méthode pour résoudre un tel problème dans le cas d\\ún jeu à trois joueurs où chaque joueur dispose de deux actions à chaque étape.Jeu répété à observation imparfaite;Maxmin;Entropie;Optimisation

State Leakage and Coordination of Actions: Core of the Receiver's Knowledge

We revisit the problems of state masking and state amplification through the lens of empirical coordination by considering a state-dependent channel in which the encoder has causal and strictly causal state knowledge. We show that the problem of empirical coordination provides a natural framework in which to jointly study the problems of reliable communication, state masking, and state amplification. We characterize the regions of rate-equivocation-coordination trade-offs for several channel models with causal and strictly causal state knowledge. We introduce the notion of `core of the receiver's knowledge' to capture what the decoder can infer about all the signals involved in the model. We exploit this result to solve a channel state estimation zero-sum game in which the encoder prevents the decoder to estimate the channel state accurately.Comment: preliminary draf

Entropy and the value of information for investors

Consider any investor who fears ruin when facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure $\alpha$ is more informative than information structure $\beta$ if, whenever he is willing to buy $\beta$ at some price, he is also willing to buy $\alpha$ at that price. We show that this informativeness ordering is complete and is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth, or investment problem. We also show that no prior-independent informativeness ordering based on similar premises exists.Informativeness ; Information structures ; Entropy ; Decision under uncertainty ; Investment ; Blackwell ordering

Strategic Communication with Side Information at the Decoder

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

Joint Empirical Coordination of Source and Channel

In a decentralized and self-configuring network, the communication devices are considered as autonomous decision-makers that sense their environment and that implement optimal transmission schemes. It is essential that these autonomous devices cooperate and coordinate their actions, to ensure the reliability of the transmissions and the stability of the network. We study a point-to-point scenario in which the encoder and the decoder implement decentralized policies that are coordinated. The coordination is measured in terms of empirical frequency of symbols of source and channel. The encoder and the decoder perform a coding scheme such that the empirical distribution of the symbols is close to a target joint probability distribution. We characterize the set of achievable target probability distributions for a point-to-point source-channel model, in which the encoder is non-causal and the decoder is strictly causal i.e., it returns an action based on the observation of the past channel outputs. The objectives of the encoder and of the decoder, are captured by some utility function, evaluated with respect to the set of achievable target probability distributions. In this article, we investigate the maximization problem of a utility function that is common to both encoder and decoder. We show that the compression and the transmission of information are particular cases of the empirical coordination.Comment: accepted to IEEE Trans. on I

Empirical Distributions of Beliefs Under Imperfect Observation

Let (xn)n be a process with values in a finite set X and law P, and let yn = f(xn) be a function of the process. At stage n, the conditional distribution pn = P(xn | x1,...,xn–1), element of = (X), is the belief that a perfect observer, who observes the process online, holds on its realization at stage n. A statistician observing the signals y1,...,yn holds a belief en = P(pn | x1,...,xn) () on the possible predictions of the perfect observer. Given X and f, we characterize the set of limits of expected empirical distributions of the process (en) when P ranges over all possible laws of (xn)n