Strategic Successive Refinement With Interdependent Decoders Cost Functions

In decentralized and decision-oriented communication paradigms, autonomous devices strategically implement information compression policies. In this work, we study a strategic communication game between an encoder and two decoders. An i.i.d. information source, observed by the encoder, is transmitted to the decoders via two perfect links, one reaching the first decoder only and the other reaching both decoders, as in the successive refinement setup. All three communicating devices are assumed to be rational, i.e., they want to minimize their respective cost functions, that depend on the source variable and the output symbols of both decoder. The game takes place as follows: the encoder commits to implementing an encoding strategy which induces a Bayesian game among the two decoders. The encoder is the Stackelberg leader and the two decoders are the Stackelberg followers, they select simultaneously the output sequences that minimize their respective long-run costs. We characterize the asymptotic behavior of the long-run optimal cost of the encoder, when the decoders implement decoding strategies that form a Bayes-Nash equilibrium. We show that this optimal cost converges to a single-letter expression which involves two auxiliary random variables and single-letter incentive constraints of the decoders.