230,331 research outputs found
Suboptimality Conditions for Mathematical Programs with Equilibrium Constraints
In this paper we study mathematical programs with equilibrium constraints (MPECs) described by generalized equations in the extended form 0 is an element of the set G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models arise, in particular, from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish new weak and strong suboptimality conditions for the general MPEC problems under consideration in finite-dimensional and infinite-dimensional spaces that do not assume the existence of optimal solutions. This issue is particularly important for infinite-dimensional optimization problems, where the existence of optimal solutions requires quite restrictive assumptions. Our techriiques are mainly based on modern tools of variational analysis and generalized differentiation revolving around the fundamental extremal principle in variational analysis and its analytic counterpart known as the subdifferential variational principle
General Equilibrium with Asymmetric Information: A Dual Approach
We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive trans- actions, the environment is described as a continuum economy with indivis- ible commodities. We characterize incentive constrained eÆcient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external e ects in these markets. Because under certain conditions such e ects may generate non-convexities, random- ization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external e ects may have critical implications for market eÆciency. With ad- verse selection, in fact, cross-subsidization across agents with di erent private information may be necessary for optimality, and so, the market need not even achieve an incentive constrained eÆcient allocation. In contrast, for the case of a single commodity, we nd that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external e ects are fully internalized at a market equilibrium
General equilibrium with asymmetric information : a dual approach
We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive transactions, the environment is described as a continuum economy with indivisible commodities. We characterize incentive efficient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external effects in these markets. Because under certain conditions such effects may generate non-convexities, randomization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external effects may have critical implications for market efficiency. With adverse selection, in fact, cross-subsidization across agents with different private information may be necessary for optimality, and so, the market need not even achieve an incentive efficient allocation. In contrast, for the case of a single commodity, we find that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external effects are fully internalized at a market equilibrium
Signaling Games in Multiple Dimensions: Geometric Properties of Equilibrium Solutions
Signaling game problems investigate communication scenarios where encoder(s)
and decoder(s) have misaligned objectives due to the fact that they either
employ different cost functions or have inconsistent priors. This problem has
been studied in the literature for scalar sources under various setups. In this
paper, we consider multi-dimensional sources under quadratic criteria in the
presence of a bias leading to a mismatch in the criteria, where we show that
the generalization from the scalar setup is more than technical. We show that
the Nash equilibrium solutions lead to structural richness due to the subtle
geometric analysis the problem entails, with consequences in both system
design, presence of linear Nash equilibria, and an information theoretic
problem formulation. We first provide a set of geometric conditions that needs
to be satisfied in equilibrium considering any multi-dimensional source. Then,
we consider independent and identically distributed sources and characterize
necessary and sufficient conditions under which an informative linear Nash
equilibrium exists. These conditions involve the bias vector that leads to
misaligned costs. Depending on certain conditions related to the bias vector,
the existence of linear Nash equilibria requires sources with a Gaussian or a
symmetric density. Moreover, in the case of Gaussian sources, our results have
a rate-distortion theoretic implication that achievable rates and distortions
in the considered game theoretic setup can be obtained from its team theoretic
counterpart.Comment: 16 pages and 4 figure
General Equilibrium with Asymmetric Information: a Dual Approach
We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive transactions, the environment is described as a continuum economy with indivisible commodities. We characterize incentive efficient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external effects in these markets. Because under certain conditions such effects may generate non-convexities, randomization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external effects may have critical implications for market efficiency. With adverse selection, in fact, cross-subsidization across agents with different private information may be necessary for optimality, and so, the market need not even achieve an incentive efficient allocation. In contrast, for the case of a single commodity, we find that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external effects are fully internalized at a market equilibrium.Asymmetric Information, General Equilibrium, Linear Programming
Application of Market Models to Network Equilibrium Problems
We present a general two-side market model with divisible commodities and
price functions of participants. A general existence result on unbounded sets
is obtained from its variational inequality re-formulation. We describe an
extension of the network flow equilibrium problem with elastic demands and a
new equilibrium type model for resource allocation problems in wireless
communication networks, which appear to be particular cases of the general
market model. This enables us to obtain new existence results for these models
as some adjustments of that for the market model. Under certain additional
conditions the general market model can be reduced to a decomposable
optimization problem where the goal function is the sum of two functions and
one of them is convex separable, whereas the feasible set is the corresponding
Cartesian product. We discuss some versions of the partial linearization
method, which can be applied to these network equilibrium problems.Comment: 18 pages, 3 table
Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids
Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold
(M,g). In this paper we study the restrictions on the topology and geometry of
the fibres (the level sets) of the solutions f to (P1). We give a technique
based on certain remarkable property of the fibres (the analytic representation
property) for going from the initial PDE to a global analytical
characterization of the fibres (the equilibrium partition condition). We study
this analytical characterization and obtain several topological and geometrical
properties that the fibres of the solutions must possess, depending on the
topology of M and the metric tensor g. We apply these results to the classical
problem in physics of classifying the equilibrium shapes of both Newtonian and
relativistic static self-gravitating fluids. We also suggest a relationship
with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis
is proved. Please address all correspondence to D. Peralta-Sala
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