Browsing by Subject "Subjective priors"

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Open Access
Hypothesis testing under subjective priors and costs as a signaling game
(IEEE, 2019) Sarıtaş, S.; Gezici, Sinan; Yüksel, S.
Many communication, sensor network, and networked control problems involve agents (decision makers) which have either misaligned objective functions or subjective probabilistic models. In the context of such setups, we consider binary signaling problems in which the decision makers (the transmitter and the receiver) have subjective priors and/or misaligned objective functions. Depending on the commitment nature of the transmitter to his policies, we formulate the binary signaling problem as a Bayesian game under either Nash or Stackelberg equilibrium concepts and establish equilibrium solutions and their properties. We show that there can be informative or non-informative equilibria in the binary signaling game under the Stackelberg and Nash assumptions, and derive the conditions under which an informative equilibrium exists for the Stackelberg and Nash setups. For the corresponding team setup, however, an equilibrium typically always exists and is always informative. Furthermore, we investigate the effects of small perturbations in priors and costs on equilibrium values around the team setup (with identical costs and priors), and show that the Stackelberg equilibrium behavior is not robust to small perturbations whereas the Nash equilibrium is.
Open Access
Quadratic signaling with prior mismatch at an encoder and decoder: equilibria, continuity, and robustness properties
(Institute of Electrical and Electronics Engineers, 2022-01-11) Kazikli, E.; Sartas, S.; Gezici, Sinan
We consider communications through a Gaussian noise channel between an encoder and a decoder which have subjective probabilistic models on the source distribution. Although they consider the same cost function, the induced expected costs are misaligned due to their prior mismatch, which requires a game theoretic approach. We consider two approaches: a Nash setup, with no prior commitment, and a Stackelberg solution concept, where the encoder is committed to a given announced policy apriori. We show that the Stackelberg equilibrium cost of the encoder is upper semi continuous, under the Wasserstein metric, as encoder's prior approaches the decoder's prior, and it is also lower semi continuous with Gaussian priors. For the Stackelberg setup, the optimality of affine policies for Gaussian signaling no longer holds under prior mismatch, and thus team-theoretic optimality of linear/affine policies are not robust to perturbations. We provide conditions under which there exist informative Nash and Stackelberg equilibria with affine policies. Finally, we show existence of fully informative Nash and Stackelberg equilibria for the cheap talk problem under an absolute continuity condition.