1,548 research outputs found
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games
We address the generalized aggregative equilibrium seeking problem for
noncooperative agents playing average aggregative games with affine coupling
constraints. First, we use operator theory to characterize the generalized
aggregative equilibria of the game as the zeros of a monotone set-valued
operator. Then, we massage the Douglas-Rachford splitting to solve the monotone
inclusion problem and derive a single layer, semi-decentralized algorithm whose
global convergence is guaranteed under mild assumptions. The potential of the
proposed Douglas-Rachford algorithm is shown on a simplified resource
allocation game, where we observe faster convergence with respect to
forward-backward algorithms.Comment: arXiv admin note: text overlap with arXiv:1803.1044
Quasivariational Inequalities for a Dynamic Competitive Economic Equilibrium Problem
The aim of this paper is to consider a dynamic competitive economic equilibrium problem in terms of maximization of utility functions and of excess demand functions. This equilibrium problem is studied by means of a time-dependent quasivariational inequality which is set in the Lebesgue space . This approach allows us to obtain an existence result of time-dependent equilibrium solutions
Computing all solutions of Nash equilibrium problems with discrete strategy sets
The Nash equilibrium problem is a widely used tool to model non-cooperative
games. Many solution methods have been proposed in the literature to compute
solutions of Nash equilibrium problems with continuous strategy sets, but,
besides some specific methods for some particular applications, there are no
general algorithms to compute solutions of Nash equilibrium problems in which
the strategy set of each player is assumed to be discrete. We define a
branching method to compute the whole solution set of Nash equilibrium problems
with discrete strategy sets. This method is equipped with a procedure that, by
fixing variables, effectively prunes the branches of the search tree.
Furthermore, we propose a preliminary procedure that by shrinking the feasible
set improves the performances of the branching method when tackling a
particular class of problems. Moreover, we prove existence of equilibria and we
propose an extremely fast Jacobi-type method which leads to one equilibrium for
a new class of Nash equilibrium problems with discrete strategy sets. Our
numerical results show that all proposed algorithms work very well in practice
Liquidity risks on power exchanges
Financial derivatives are important hedging tool for asset’s manager. Electricity is by its very nature the most volatile commodity, which creates big incentive to share the risk among the market participants through financial contracts. But, even if volume of derivatives contracts traded on Power Exchanges has been growing since the beginning of the restructuring of the sector, electricity markets continue to be considerably less liquid than other commodities. This paper tries to quantify the effect of this insufficient liquidity on power exchange, by introducing a pricing equilibrium model for power derivatives where agents can not hedge up to their desired level. Mathematically, the problem is a two stage stochastic Generalized Nash Equilibrium and its solution is not unique. Computing a large panel of solutions, we show how the risk premium and player’s profit are affected by the illiquidity.illiquidity, electricity, power exchange, artitrage, generalized Nash Equilibrium, equilibrium based model, coherent risk valuation
- …