Game Theory

Existence of Competitive Equilibrium in Piecewise Linear and Concave Exchange Economies and the non-symmetric Nash Bargaining Solution

  • Somdeb Lahiri
    • Categories Finance and Economics, Game Theory Tags , , , ,

    In this paper we show that for concave piecewise linear exchange economies every competitive equilibrium satisfies the property that the competitive allocation is a non-symmetric Nash bargaining solution with weights being the initial income of individual agents evaluated at the equilibrium price vector. We prove the existence of competitive equilibrium for concave piecewise linear exchange … Read more

    Scheduling of Two Agents Task Chains with a Central Selection Mechanism

  • Alessandro Agnetis
  • Gaia Nicosia
  • Ulrich Pferschy
  • Andrea Pacifici
    • Categories Combinatorial Optimization, Game Theory, Scheduling Tags , , ,

    In this paper we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. Each agent decides on a fixed order to submit its tasks to an external coordination subject, who sequences them according to a known priority rule. We consider the problem from different perspectives. First, we … Read more

    A game-theoretic approach to computation offloading in mobile cloud computing

  • Valeria Cardellini
  • Francisco Facchinei
  • Veronica Piccialli
  • Vittoria De Nitto Persone'
  • Valerio Di Valerio
  • Vincenzo Grassi
  • Francesco Lo Presti
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Game Theory

    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

    Stochastic linear programming games with concave preferences

  • Nelson A. Uhan
    • Categories Game Theory, Stochastic Programming

    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

    Nonlinear Equilibrium for optimal resource allocation

  • Roman Polyak
    • Categories Complementarity and Variational Inequalities, Game Theory Tags , , , , ,

    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

    Smoothness Properties of a Regularized Gap Function for Quasi-Variational Inequalities

  • Nadja Harms
  • Oliver Stein
  • Christian Kanzow
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Game Theory Tags , , , , ,

    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

    Optimal Power Grid Protection through A Defender-Attacker-Defender Model

  • Wei Yuan
  • Bo Zeng
  • Long Zhao
    • Categories Applications - Science and Engineering, Game Theory

    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

    A New Error Bound Result for Generalized Nash Equilibrium Problems and its Algorithmic Application

  • Axel Dreves
  • Francisco Facchinei
  • Andreas Fischer
  • Markus Herrich
    • Categories Complementarity and Variational Inequalities, Game Theory, Nonlinear Optimization Tags , , , , ,

    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

    The Subset Sum Game

  • Andreas Darmann
  • Gaia Nicosia
  • Ulrich Pferschy
  • Joachim Schauer
    • Categories Combinatorial Optimization, Game Theory Tags , , ,

    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

    Equilibria on the Day-Ahead Electricity Market

  • Margarida Carvalho
  • João Pedro Pedroso
    • Categories Finance and Economics, Game Theory

    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