6,723 research outputs found
Common Information Approach for Static Team Problems with Polish Spaces and Existence of Optimal Policies
In this paper, we demonstrate the existence of team-optimal strategies for
static teams under observation-sharing information structures. Assuming that
agents can access shared observations, we begin by converting the team problem
into an equivalent centralized stochastic control problem through the
introduction of a topology on policies. We subsequently apply conventional
methods from stochastic control to prove the existence of team-optimal
strategies. This study expands upon the widely recognized common information
approach for team problems, originally designed for discrete scenarios, and
adapts it to a more abstract continuous framework. The primary difficulty in
this context is to establish the appropriate topology on policies.Comment: arXiv admin note: text overlap with arXiv:1711.0063
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
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