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It is known that cybercriminal black markets that trade in illicit digital goods and services belong to markets for lemons due to the information asymmetry of quality of goods and services between sellers and buyers. Based on the seminal work of Akerlof [1], Franklin et al. [3] suggests that “Lemonizing the Market” be an effective way to crack down the well-developed cybercriminal underground market. In our work, we provide a game theoretical framework to analyze whether cybercriminal black markets can be effectivitely lemonized. First, we investigate if signaling quality through an extra provision, such as the offer of trial periods or a money-back guarantee, observed in this marketplace (see the Panda security report [6]) provides cybercriminals selling real illicit data (i.e., the peach group) with a solution to address the lemon market problem. We also study the relation between the market lemonization and the cost constraint on seller’s implementation of signaling of quality. We find that, because of the effectiveness of resolving quality uncertainty through perfect signaling of quality, law enforcement cannot clamp down the operation of this underground economy through “Lemonizing the Market” by joining the group of “pure lemons”, that is, joining the group of sellers with no crime products offered to sell (i.e., ripoff sellers). If no information of quality is disclosed, the market demand shrinks increasingly as lemons in the market increases. However, to secure the market demand, cybercriminals with real illicit data for sale always attempt to implement quality signaling to single out their quality products, accepting a higher amount of cost constraints on applying quality signaling as the portion of lemons in the market escalates.

We consider inventory control problems in discrete time. The horizon is infinite, and we consider discounted payoffs as well nondiscounted payoffs (ergodic control). We may have backlog or not. We may have set-up costs or not. In the traditional framework, the demand is modeled as a sequence of i.i.d. random variables. The ordering strategy is given by a base stock policy or an s, S policy, whether or not there is a set-up cost. We consider here the situation when the demand is modeled by a Markov chain. We show how the base stock policy and the s, S policy can be extended.

Entrepreneurs face investment decisions on privacy-preserving technology (PPT) adoption as privacy-concerned consumers may decide whether to use firms' services based on the extent of privacy that firms are able to provide. Kantarcioglu et.al. (2010) [9] contributes to guidelines for entrepreneurs' adoption decisions through a novel framework, which combines copula functions and a Stackelberg leader-follower game with consumers taking the role of the follower (referred as static-copula-game model hereafter). The valuation requires a clearly defined bivariate distribution function of two random variables, the consumer's valuation of private information and the consumer's profitability to a firm. Copula functions are used to construct the bivariate distribution function from arbitrarily univariate marginals with various dependence structures fitting into different market/industry segments. This study extends the static-copula-game model to include project value uncertainty, simultaneously considering different market competition structures and the regulatory promise of random arrival of government mandatory adoption. The project value from the static-copula-game model is used as an estimate of the initial (current) project value for the stochastic evolution. By doing so, we retain the advantages of applying copulas and preserve the established valuation property exclusively applicable to the valuation of PPT adoption. The extension model makes several improvements including: (1) Reduce concerns about myopic PPT adoption decisions that may result when static valuation is employed. (2) Overcome the potential biased PPT adoption decision that may arise due to negligence of market competition impact. (3) Understand the regulatory influence of government mandatory adoption with uncertainty. We find that: (1) If one can link univariate marginals and dependence structures to industry groups, one can determine for which industries project value uncertainty has no impact on the entrepreneur's immediate PPT adoption decision. For these industries, there is no need for government intervention/regulation to accelerate/induce PPT adoption even though the project value is uncertain. (2) Under project value uncertainty, competition may suggest either a later or an earlier PPT adoption compared with the monopoly case. (3) The promise of government mandatory adoption has the potential to accelerate PPT adoption. The PPT adoption guidelines considering competition and regulatory promises of government mandatory adoption when the project value is uncertain bring useful recommendations to both entrepreneurs and policymakers.

In this article, we complete the theory of estimation of Linear Random Functionals, introduced by the Author, in order to extend the Kalman filter to infinite dimensional linear systems. The objective is to show that all properties for the finite dimensional case remain valid in the framework of Linear Random Functionals (this is thanks to linearity of course).

Let O be an open bounded smooth domain of ℝ n , and let Γ = αO be its boundary. We denote by n the normal vector at the boundary Γ, oriented towards the outside of O. Let us consider the canonical process $$\begin{gathered} \Omega = C^0 ([0,\infty );\bar O), \hfill \\ y(t,w) \equiv w(t), if w \in \Omega , \hfill \\ \mathfrak{F}^t = \sigma (y(s),0 \leqslant s \leqslant t). \hfill \\ \end{gathered} $$

We shall consider systems of the type $$ - {D_i}a_i^v\left( {x,Du} \right) + {f^v} = 0,\;v = 1, \ldots ,N,$$ (8.1) with $$u = \left( {{u^1}, \ldots ,{u^N}} \right)$$ .

In this chapter we assemble many technical results that will be used throughout the book. Function spaces play a central role, and we recall first some notation, fundamental definitions, and properties.

We refer for a full justification of the physical setting to the articles [4], [35], [50], [51], [88], [90], [100]. We follow here the presentation of [83].

We show in this chapter how to obtain general regularity results for solutions of PDEs or systems of PDEs. We shall stress the techniques for obtaining W l,p and C δ regularity. We shall then derive additional regularity. In the sequel everything is self-contained, except that we shall make use of the W 2,p regularity results for the linear Dirichlet problem. For equations we rely heavily on O.A. Ladyzhenskaya, N.N. Ural’tseva [66].

In this chapter (which is a continuation of Chapter 9 and will rely heavily on it) we are interested in specific models of plasticity. We shall need to attach to tensor σ its deviator $${\sigma _D} = \sigma - 1/nI\;tr\;\sigma ,$$ which has trace 0. We will consider two models of plasticity, the Hencky model, which is a model of perfect plasticity where, $$|{\sigma _D}|\mu $$ (µ is a given constant), and the Norton—Hoff model, which is an approximation to the Hencky model, where the constraint of perfect plasticity is relaxed with a penalty term. In fact, the Norton—Hoff model will be a particular case of the models considered in Chapter 9, but we shall consider a sequence of these models. Again these models are formulated as variational problems in which the unknown is the stress tensor and the displacement is recovered indirectly. The convergence of the approximation is very natural in the context of variational problems and follows from general penalty methods (see R. Temam [101], G. Duvaut, J.L. Lions [15], J.L. Lions [70], P. Le Tallec [69]).

We study here the regularity of solutions of the stationary Navier—Stokes equations. For the usual Navier—Stokes equations for incompressible fluids on a bounded domain, where the time variable intervenes, the issue of regularity of weak solutions is an open problem in dimension n = 3 (see J. Leray [68] or O.A. Ladyzenskaya, V.A. Solonnikov, N.N. Ural’tseva [67] for the background). Only partial regularity is available; see L. Caffarelli, R. Kohn, L. Nirenberg [9].

One can get a quick idea of the dual approach by simply considering the Dirichlet problem $$ - \Delta u = f,\;u\left| \Gamma \right. = 0$$ and setting $$\sigma = - Du$$

The objective of this section is to present some results concerning a class of stochastic games for N players, obtained from the study of nonlinear elliptic systems, the Bellman system. The method consists in applying the dynamic programming approach. The value functions are the solutions of a system of partial differential equations. From regularity results, one is able to construct continuous feedbacks, which will represent optimal controls for each player. The standard verification approach will show the optimality. The optimality is to be taken in the sense of Nash [82]; see also J.P. Aubin [3].

In Chapter 3 we considered Bellman systems of equations arising from the theory of stochastic games. L ∞ estimates were instrumental in deriving the other types of estimates (in H 1, W 1,p ,C δ ), and the maximum principle was the main tool used to achieve this goal.

Representation theory for finite dimensional systems has been the subject of a great deal of discussion in recent years. In the case of linear systems defined over fields an account of the theory can be found in the books of BROCKETT and KALMAN-FALB-ARBIB and in the case of systems defined over rings in the book of EILENBERG, the papers of ROUCHALEAU-WYMAN-KALMAN, ROUCHALEAU-WYMAN and the thesis of JOHNSTON. For a lucid survey of results on systems defined over commutative rings, see SONTAG.

In serveral papers, H. Albach has stressed the importance of the analysis of growth of firms for the development of management science and the understanding of economic systems (Albach 1967a, 1967b; 1976). In fact, the literature on corporate growth or, more generally, on firm dynamics has considerably increased in the last years and probably for two separate reasons: (1) The diffusion of the knowledge of control theory has given to economists a very convenient tool to extend to dynamics the scope of optimization. (2) The firm is more and more recognized as an anticipating, planning, adapting organism plunged into a changing environment and having to face delays, rigidities and uncertainties.

We consider a class of problems in stochastic control theory involving stochastic systems with small parameters. Using both analytical and probabilistic methods adapted to the special structures of singularly perturbed stochastic control problems, we develop a systematic methodology for their analysis.

We study the Dynamic Programming Equation arising in the problem of stochastic control in discrete time over an infinite horozon. The data are unbounded, in which case the solution is not unique. Our results deal with the structure of the set of solutions.