We consider a three-tier architecture for mobile and pervasive computing scenarios, consisting of a local tier of mobile nodes, a middle tier (cloudlets) of nearby computing nodes, typically located at the mobile nodes access points but characterized by a limited amount of resources, and a remote tier of distant cloud servers, which have practically infinite … Read more
We study stochastic linear programming games: a class of stochastic cooperative games whose payoffs under any realization of uncertainty are determined by a specially structured linear program. These games can model a variety of settings, including inventory centralization and cooperative network fortification. We focus on the core of these games under an allocation scheme that … Read more
We consider Nonlinear Equilibrium (NE) for optimal allocation of limited resources. The NE is a generalization of the Walras-Wald equilibrium, which is equivalent to J. Nash equilibrium in an n-person concave game. Finding NE is equivalent to solving a variational inequality (VI) with a monotone and smooth operator on $\Omega = \Re_+^n\cross\Re_+^m$. The projection on … Read more
This article studies continuity and differentiability properties for a reformulation of a finite-dimensional quasi-variational inequality (QVI) problem using a regularized gap function approach. For a special class of QVIs, this gap function is continuously differentiable everywhere, in general, however, it has nondifferentiability points. We therefore take a closer look at these nondifferentiability points and show, … Read more
Power grid vulnerability is a major concern of modern society, and its protection problem is often formulated as a tri-level defender-attacker-defender model. However, this tri-level problem is compu- tationally challenging. In this paper, we design and implement a Column-and-Constraint Generation algorithm to derive its optimal solutions. Numerical results on an IEEE system show that: (i) … Read more
We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on an error bound and provide a new sufficient condition for it to hold that … Read more
In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its own items included in … Read more
In the energy sector, there has been a transition from monopolistic to oligopolistic situations (pool markets); each time more companies’ optimization revenues depend on the strategies of their competitors. The market rules vary from country to country. In this work, we model the Iberian Day-Ahead Duopoly Market and find exactly which are the outcomes (Nash … Read more
In multi-objective optimization the objective is to reach a point which is Pareto ecient. However we usually encounter many such points and choosing a point amongst them possesses another problem. In many applications we are required to choose a point having a good spread over all objective functions which is a direct consequence of the … Read more
We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market … Read more