21,122 research outputs found
Equilibrium in Labor Markets with Few Firms
We study competition between firms in labor markets, following a
combinatorial model suggested by Kelso and Crawford [1982]. In this model, each
firm is trying to recruit workers by offering a higher salary than its
competitors, and its production function defines the utility generated from any
actual set of recruited workers. We define two natural classes of production
functions for firms, where the first one is based on additive capacities
(weights), and the second on the influence of workers in a social network. We
then analyze the existence of pure subgame perfect equilibrium (PSPE) in the
labor market and its properties. While neither class holds the gross
substitutes condition, we show that in both classes the existence of PSPE is
guaranteed under certain restrictions, and in particular when there are only
two competing firms. As a corollary, there exists a Walrasian equilibrium in a
corresponding combinatorial auction, where bidders' valuation functions belong
to these classes.
While a PSPE may not exist when there are more than two firms, we perform an
empirical study of equilibrium outcomes for the case of weight-based games with
three firms, which extend our analytical results. We then show that stability
can in some cases be extended to coalitional stability, and study the
distribution of profit between firms and their workers in weight-based games
Multiplexing regulated traffic streams: design and performance
The main network solutions for supporting QoS rely on traf- fic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only ag- gregates regulated). The regulator proposed could be based on the (dual) leaky-bucket mechanism. This explains the interest in network element per- formance (loss, delay) for leaky-bucket regulated traffic. This paper describes a novel approach to the above problem. Explicitly using the correlation structure of the sources’ traffic, we derive approxi- mations for both small and large buffers. Importantly, for small (large) buffers the short-term (long-term) correlations are dominant. The large buffer result decomposes the traffic stream in a stream of constant rate and a periodic impulse stream, allowing direct application of the Brownian bridge approximation. Combining the small and large buffer results by a concave majorization, we propose a simple, fast and accurate technique to statistically multiplex homogeneous regulated sources. To address heterogeneous inputs, we present similarly efficient tech- niques to evaluate the performance of multiple classes of traffic, each with distinct characteristics and QoS requirements. These techniques, applica- ble under more general conditions, are based on optimal resource (band- width and buffer) partitioning. They can also be directly applied to set GPS (Generalized Processor Sharing) weights and buffer thresholds in a shared resource system
Rigorous results on the threshold network model
We analyze the threshold network model in which a pair of vertices with
random weights are connected by an edge when the summation of the weights
exceeds a threshold. We prove some convergence theorems and central limit
theorems on the vertex degree, degree correlation, and the number of prescribed
subgraphs. We also generalize some results in the spatially extended cases.Comment: 21 pages, Journal of Physics A, in pres
Fermionic construction of tau functions and random processes
Tau functions expressed as fermionic expectation values are shown to provide
a natural and straightforward description of a number of random processes and
statistical models involving hard core configurations of identical particles on
the integer lattice, like a discrete version simple exclusion processes (ASEP),
nonintersecting random walkers, lattice Coulomb gas models and others, as well
as providing a powerful tool for combinatorial calculations involving paths
between pairs of partitions. We study the decay of the initial step function
within the discrete ASEP (d-ASEP) model as an example.Comment: 53 pages, 13 figures, a contribution to Proc. "Mathematics and
Physics of Growing Interfaces
Constructive Tensor Field Theory
We provide an up-to-date review of the recent constructive program for field
theories of the vector, matrix and tensor type, focusing not on the models
themselves but on the mathematical tools used.Comment: arXiv admin note: text overlap with arXiv:1401.500
Analyticity results for the cumulants in a random matrix model
The generating function of the cumulants in random matrix models, as well as
the cumulants themselves, can be expanded as asymptotic (divergent) series
indexed by maps. While at fixed genus the sums over maps converge, the sums
over genera do not. In this paper we obtain alternative expansions both for the
generating function and for the cumulants that cure this problem. We provide
explicit and convergent expansions for the cumulants, for the remainders of
their perturbative expansion (in the size of the maps) and for the remainders
of their topological expansion (in the genus of the maps). We show that any
cumulant is an analytic function inside a cardioid domain in the complex plane
and we prove that any cumulant is Borel summable at the origin
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