840 research outputs found
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
Quadratic Multi-Dimensional Signaling Games and Affine Equilibria
This paper studies the decentralized quadratic cheap talk and signaling game
problems when an encoder and a decoder, viewed as two decision makers, have
misaligned objective functions. The main contributions of this study are the
extension of Crawford and Sobel's cheap talk formulation to multi-dimensional
sources and to noisy channel setups. We consider both (simultaneous) Nash
equilibria and (sequential) Stackelberg equilibria. We show that for arbitrary
scalar sources, in the presence of misalignment, the quantized nature of all
equilibrium policies holds for Nash equilibria in the sense that all Nash
equilibria are equivalent to those achieved by quantized encoder policies. On
the other hand, all Stackelberg equilibria policies are fully informative. For
multi-dimensional setups, unlike the scalar case, Nash equilibrium policies may
be of non-quantized nature, and even linear. In the noisy setup, a Gaussian
source is to be transmitted over an additive Gaussian channel. The goals of the
encoder and the decoder are misaligned by a bias term and encoder's cost also
includes a penalty term on signal power. Conditions for the existence of affine
Nash equilibria as well as general informative equilibria are presented. For
the noisy setup, the only Stackelberg equilibrium is the linear equilibrium
when the variables are scalar. Our findings provide further conditions on when
affine policies may be optimal in decentralized multi-criteria control problems
and lead to conditions for the presence of active information transmission in
strategic environments.Comment: 15 pages, 4 figure
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
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
Voronoi languages: Equilibria in cheap-talk games with high-dimensional types and few signals
We study a communication game of common interest in which the sender observes one of infinite types and sends one of finite messages which is interpreted by the receiver. In equilibrium there is no full separation but types are clustered into convex categories. We give a full characterization of the strict Nash equilibria of this game by representing these categories by Voronoi languages. As the strategy set is infinite static stability concepts for finite games such as ESS are no longer sufficient for Lyapunov stability in the replicator dynamics. We give examples of unstable strict Nash equilibria and stable inefficient Voronoi Languages. We derive efficient Voronoi languages with a large number of categories and numerically illustrate stability of some Voronoi languages with large message spaces and non-uniformly distributed types.Cheap Talk, Signaling Game, Communication Game, Dynamic stability, Voronoi tesselation
Communication and Bargaining in the Spatial Model
This paper studies collective choice by participants possessing private information about the consequences of policy decisions in policymaking institutions that involve cheap-talk communication and bargaining. The main result establishes a connection between the extent to which problems of this type posses fully-revealing equilibria that select policies in the full information majority rule core (when it is well-defined) and the extent to which a fictitious sender-receiver game possesses a fully revealing equilibria. This result allows us to extend Banks and Duggan's (2000) core equivalence results to the case of noisy policymaking environments with private information when some combination of nonexclusivity and preference alignment conditions are satisfied.
Dynamic Signaling Games under Nash and Stackelberg Equilibria
In this study, dynamic and repeated quadratic cheap talk and signaling game problems are investigated. These involve encoder and decoders with mismatched performance objectives, where the encoder has a bias term in the quadratic cost functional. We consider both Nash equilibria and Stackelberg equilibria as our solution concepts, under a perfect Bayesian formulation. These two lead to drastically different characteristics for the equilibria. For the cheap talk problem under Nash equilibria, we show that fully revealing equilibria cannot exist and the final state equilibria have to be quantized for a large class of source models; whereas, for the Stackelberg case, the equilibria must be fully revealing regardless of the source model. In the dynamic signaling game where the transmission of a Gaussian source over a Gaussian channel is considered, the equilibrium policies are always linear for scalar sources under Stackelberg equilibria, and affine policies constitute an invariant subspace under best response maps for Nash equilibria
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