1,899 research outputs found
Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly
In this note we investigate stochastic Nash equilibrium problems by means of
monotone variational inequalities in probabilistic Lebesgue spaces. We apply
our approach to a class of oligopolistic market equilibrium problems where the
data are known through their probability distributions.Comment: 19 pages, 2 table
Data-Driven Estimation in Equilibrium Using Inverse Optimization
Equilibrium modeling is common in a variety of fields such as game theory and
transportation science. The inputs for these models, however, are often
difficult to estimate, while their outputs, i.e., the equilibria they are meant
to describe, are often directly observable. By combining ideas from inverse
optimization with the theory of variational inequalities, we develop an
efficient, data-driven technique for estimating the parameters of these models
from observed equilibria. We use this technique to estimate the utility
functions of players in a game from their observed actions and to estimate the
congestion function on a road network from traffic count data. A distinguishing
feature of our approach is that it supports both parametric and
\emph{nonparametric} estimation by leveraging ideas from statistical learning
(kernel methods and regularization operators). In computational experiments
involving Nash and Wardrop equilibria in a nonparametric setting, we find that
a) we effectively estimate the unknown demand or congestion function,
respectively, and b) our proposed regularization technique substantially
improves the out-of-sample performance of our estimators.Comment: 36 pages, 5 figures Additional theorems for generalization guarantees
and statistical analysis adde
A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks
A climate of increasing deregulation in traditional highway transportation,
where the private sector has an expanded role in the provision of traditional
transportation services, provides a background for practical policy issues to be investigated.
One of the key issues of interest, and the focus of this chapter, would
be the equilibrium decision variables offered by participants in this market. By assuming
that the private sector participants play a Nash game, the above problem can
be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from
the classical Cournot-Nash game because each and every player’s actions is constrained
by another variational inequality describing the equilibrium route choice of
users on the network. In this chapter, we discuss this BLVI and suggest a heuristic
coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm
is subsequently tested on example problems drawn from the literature. The numerical
experiments suggest that the proposed algorithm is a viable solution method for
this problem
Iterative Methods for Stochastic Variational Inequalities
In this work, we consider stochastic variational inequalities arising from a certain class of equilibrium problems with uncertainties. Uncertainties in the models are introduced through data that are known through their probabilistic distributions. We consider several extragradient methods for the solutions of the variational inequalities and compare their relative efficiency and eectiveness through thorough numerical comparisons. Several applications such as trac equilibrium, environmental games, and oligopolistic market equilibrium are considered
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