1,182 research outputs found
Stackelberg strategies in linear-quadratic stochastic differential games
This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution
Bose-Fermi Degeneracies in Large Adjoint QCD
We analyze the large limit of adjoint QCD, an gauge theory with
flavors of massless adjoint Majorana fermions, compactified on . We focus on the weakly-coupled confining small- regime. If
the fermions are given periodic boundary conditions on , we show that
there are large cancellations between bosonic and fermionic contributions to
the twisted partition function. These cancellations follow a pattern previously
seen in the context of misaligned supersymmetry, and lead to the absence of
Hagedorn instabilities for any size , even though the bosonic and
fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in
the confining phase for any , explaining how it is able to enjoy
large volume independence for any . The large boson-fermion
cancellations take place in a setting where adjoint QCD is manifestly
non-supersymmetric at any finite , and are consistent with the recent
conjecture that adjoint QCD has emergent fermionic symmetries in the large
limit.Comment: 35 pages, 5 figures. v3: further minor correction
Consensus with Linear Objective Maps
A consensus system is a linear multi-agent system in which agents communicate
to reach a so-called consensus state, defined as the average of the initial
states of the agents. Consider a more generalized situation in which each agent
is given a positive weight and the consensus state is defined as the weighted
average of the initial conditions. We characterize in this paper the weighted
averages that can be evaluated in a decentralized way by agents communicating
over a directed graph. Specifically, we introduce a linear function, called the
objective map, that defines the desired final state as a function of the
initial states of the agents. We then provide a complete answer to the question
of whether there is a decentralized consensus dynamics over a given digraph
which converges to the final state specified by an objective map. In
particular, we characterize not only the set of objective maps that are
feasible for a given digraph, but also the consensus dynamics that implements
the objective map. In addition, we present a decentralized algorithm to design
the consensus dynamics
Casimir energy of confining large gauge theories
Four-dimensional asymptotically-free large gauge theories compactified on
have a weakly-coupled confining regime when is
small compared to the strong scale. We compute the vacuum energy of a variety
of confining large non-supersymmetric gauge theories in this calculable
regime, where the vacuum energy can be thought of as the Casimir energy.
The renormalized vacuum energy turns out to vanish in all of the
large gauge theories we have examined, confirming a striking prediction of
temperature-reflection symmetry.Comment: 4 pages, 1 figure. v2: added clarifications and typo corrections,
conclusions unchange
Distributed Evaluation and Convergence of Self-Appraisals in Social Networks
We consider in this paper a networked system of opinion dynamics in
continuous time, where the agents are able to evaluate their self-appraisals in
a distributed way. In the model we formulate, the underlying network topology
is described by a rooted digraph. For each ordered pair of agents , we
assign a function of self-appraisal to agent , which measures the level of
importance of agent to agent . Thus, by communicating only with her
neighbors, each agent is able to calculate the difference between her level of
importance to others and others' level of importance to her. The dynamical
system of self-appraisals is then designed to drive these differences to zero.
We show that for almost all initial conditions, the trajectory generated by
this dynamical system asymptotically converges to an equilibrium point which is
exponentially stable
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