2,110 research outputs found
On the Structure of Equilibrium Strategies in Dynamic Gaussian Signaling Games
This paper analyzes a finite horizon dynamic signaling game motivated by the
well-known strategic information transmission problems in economics. The
mathematical model involves information transmission between two agents, a
sender who observes two Gaussian processes, state and bias, and a receiver who
takes an action based on the received message from the sender. The players
incur quadratic instantaneous costs as functions of the state, bias and action
variables. Our particular focus is on the Stackelberg equilibrium, which
corresponds to information disclosure and Bayesian persuasion problems in
economics. Prior work solved the static game, and showed that the Stackelberg
equilibrium is achieved by pure strategies that are linear functions of the
state and the bias variables. The main focus of this work is on the dynamic
(multi-stage) setting, where we show that the existence of a pure strategy
Stackelberg equilibrium, within the set of linear strategies, depends on the
problem parameters. Surprisingly, for most problem parameters, a pure linear
strategy does not achieve the Stackelberg equilibrium which implies the
existence of a trade-off between exploiting and revealing information, which
was also encountered in several other asymmetric information games.Comment: will appear in IEEE Multi-Conference on Systems and Control 201
Nash and Stackelberg Equilibria for Dynamic Cheap Talk and Signaling Games
Simultaneous (Nash) and sequential (Stackelberg) equilibria of two-player dynamic quadratic cheap talk and signaling game problems are investigated under a perfect Bayesian formulation. For the dynamic scalar and multidimensional cheap talk, the Nash equilibrium cannot be fully revealing whereas the Stackelberg equilibrium is always fully revealing. Further, the final state Nash equilibria have to be essentially quantized when the source is scalar and has a density, and non-revealing for the multi-dimensional case. In the dynamic signaling game where the transmission of a Gauss-Markov source over a memoryless Gaussian channel is considered, affine policies constitute an invariant subspace under best response maps for both scalar and multi-dimensional sources under Nash equilibria; however, the Stackelberg equilibrium policies are always linear for scalar sources but may be non-linear for multi-dimensional sources. Further, under the Stackelberg setup, the conditions under which the equilibrium is non-informative are derived for scalar sources
On the Number of Bins in Equilibria for Signaling Games
We investigate the equilibrium behavior for the decentralized quadratic cheap
talk problem in which an encoder and a decoder, viewed as two decision makers,
have misaligned objective functions. In prior work, we have shown that the
number of bins under any equilibrium has to be at most countable, generalizing
a classical result due to Crawford and Sobel who considered sources with
density supported on . In this paper, we refine this result in the
context of exponential and Gaussian sources. For exponential sources, a
relation between the upper bound on the number of bins and the misalignment in
the objective functions is derived, the equilibrium costs are compared, and it
is shown that there also exist equilibria with infinitely many bins under
certain parametric assumptions. For Gaussian sources, it is shown that there
exist equilibria with infinitely many bins.Comment: 25 pages, single colum
Quadratic Signaling Games with Channel Combining Ratio
In this study, Nash and Stackelberg equilibria of single-stage and multi-stage quadratic signaling games between an encoder and a decoder are investigated. In the considered setup, the objective functions of the encoder and the decoder are misaligned, there is a noisy channel between the encoder and the decoder, the encoder has a soft power constraint, and the decoder has also noisy observation of the source to be estimated. We show that there exist only linear encoding and decoding strategies at the Stackelberg equilibrium, and derive the equilibrium strategies and costs. Regarding the Nash equilibrium, we explicitly characterize affine equilibria for the single-stage setup and show that the optimal encoder (resp. decoder) is affine for an affine decoder (resp. encoder) for the multi-stage setup. On the decoder side, between the information coming from the encoder and noisy observation of the source, our results describe what should be the combining ratio of these two channels. Regarding the encoder, we derive the conditions under which it is meaningful to transmit a message
Quadratic Signaling Games with Channel Combining Ratio
In this study, Nash and Stackelberg equilibria of single-stage and
multi-stage quadratic signaling games between an encoder and a decoder are
investigated. In the considered setup, the objective functions of the encoder
and the decoder are misaligned, there is a noisy channel between the encoder
and the decoder, the encoder has a soft power constraint, and the decoder has
also noisy observation of the source to be estimated. We show that there exist
only linear encoding and decoding strategies at the Stackelberg equilibrium,
and derive the equilibrium strategies and costs. Regarding the Nash
equilibrium, we explicitly characterize affine equilibria for the single-stage
setup and show that the optimal encoder (resp. decoder) is affine for an affine
decoder (resp. encoder) for the multi-stage setup. For the decoder side,
between the information coming from the encoder and noisy observation of the
source, our results describe what should be the combining ratio of these two
channels. Regarding the encoder, we derive the conditions under which it is
meaningful to transmit a message.Comment: 19 pages, 2 figure
Dynamic signaling games with quadratic criteria under Nash and Stackelberg equilibria
This paper considers dynamic (multi-stage) signaling games involving an encoder and a decoder who have subjective models on the cost functions. We consider both Nash (simultaneous-move) and Stackelberg (leader-follower) equilibria of dynamic signaling games under quadratic criteria. For the multi-stage scalar cheap talk, we show that the final stage equilibrium is always quantized and under further conditions the equilibria for all time stages must be quantized. In contrast, the Stackelberg equilibria are always fully revealing. In the multi-stage signaling game where the transmission of a Gauss-Markov source over a memoryless Gaussian channel is considered, affine policies constitute an invariant subspace under best response maps for Nash equilibria; whereas the Stackelberg equilibria always admit linear policies for scalar sources but such policies may be nonlinear for multi-dimensional sources. We obtain an explicit recursion for optimal linear encoding policies for multi-dimensional sources, and derive conditions under which Stackelberg equilibria are informative. (C) 2020 Elsevier Ltd. All rights reserved
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