Search results for "Applied Mathematic"
showing 10 items of 4398 documents
Convex semi-infinite games
1986
This paper introduces a generalization of semi-infinite games. The pure strategies for player I involve choosing one function from an infinite family of convex functions, while the set of mixed strategies for player II is a closed convex setC inRn. The minimax theorem applies under a condition which limits the directions of recession ofC. Player II always has optimal strategies. These are shown to exist for player I also if a certain infinite system verifies the property of Farkas-Minkowski. The paper also studies certain conditions that guarantee the finiteness of the value of the game and the existence of optimal pure strategies for player I.
Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity
2018
Abstract This paper focuses on multiproduct trading with indivisibilities and where a representative agent may have non-monotonic preferences. In this framework, the set of firms’ profits (which comes from efficient subgame perfect Nash equilibria) is the Pareto frontier of some projection of the core of the game. We show that under monotonicity efficient subgame perfect Nash equilibria are achieved by single offers and the equilibrium characterization is easy to obtain. When dealing with non-monotonic preferences the problem becomes more challenging. Then, we define a pair of primal–dual linear programming problems that fully identifies the core of the game. A set of modified versions of t…
NASH EQUILIBRIA IN A MODEL OF MULTIPRODUCT PRICE COMPETITION: AN ASSIGNMENT PROBLEM
2003
We study the market interaction of a finite number of single-product firms and a representative buyer, where the buyer consumes bundles of these goods. The buyers' value function determines their willingness to pay for subsets of goods. We show that subgame perfect Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exits. The (subgame perfect) Nash-equilibrium price set is characterized by the Pareto frontier of the associated dual problem's projection on the firms' price vectors. We identify the Nash-equilibrium prices for monotonic buyers' value functions and, more importantly, we show that some central soluti…
Competitive versus efficient extraction of a common property resource: The groundwater case
2001
Abstract In this paper socially optimal and private extraction of a common property aquifer are compared. Open-loop equilibrium and feedback equilibrium in linear strategies have been computed to characterize private extraction. The use of these two equilibrium concepts allows us to distinguish between cost and strategic externalities as long as the open-loop solution captures only the cost externality, and the feedback solution captures both. The results show that strategic behaviour increases the overexploitation of the aquifer compared to the open-loop solution. However, if the groundwater storage capacity is large, the difference between the socially optimal and private extraction, the …
Properties and constraints of cheating-immune secret sharing schemes
2006
AbstractA secret sharing scheme is a cryptographic protocol by means of which a dealer shares a secret among a set of participants in such a way that it can be subsequently reconstructed by certain qualified subsets. The setting we consider is the following: in a first phase, the dealer gives in a secure way a piece of information, called a share, to each participant. Then, participants belonging to a qualified subset send in a secure way their shares to a trusted party, referred to as a combiner, who computes the secret and sends it back to the participants.Cheating-immune secret sharing schemes are secret sharing schemes in the above setting where dishonest participants, during the recons…
Mean Field Linear Quadratic Games with Set Up Costs
2013
This paper studies linear quadratic games with set up costs monotonic on the number of active players, namely, players whose action is non-null. Such games arise naturally in joint replenishment inventory systems. Building upon a preliminary analysis of the properties of the best response strategies and Nash equilibria for the given game, the main contribution is the study of the same game under large population. We also analyze the influence of an additional disturbance in the spirit of the literature on H∞ control. Numerical illustrations are provided. © 2012 Springer Science+Business Media New York.
Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets
2013
In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.
An Explicit Model for the Thermal-Mechanical Analysis of Hot Metal Forming Processes
1995
Abstract In the paper the authors propose a new finite element code for the coupled thermal-mechanical analysis of hot metal forming processes. As regards the mechanical problem, an explicit algorithm based on the solution of the dynamic equilibrium equation and an explicit time integration scheme is used, while the heat transfer analysis is based on the solution of the thermal equilibrium equations; in order to put the thermal problem in an explicit linear form a three level scheme has been employed for the discretization of the time variable. The model is based on a staggered procedure, in which the mechanical and the thermal analysis are carried out with respect to different time horizon…
Gibbs equation in the nonlinear nonequilibrium thermodynamics of dilute nonviscous gases
2003
AbstractThis paper deals with the derivation of the Gibbs equation for a nonviscous gas in the presence of heat flux. The analysis aims to shed some light on the physical interpretation of thermodynamic potentials far from equilibrium. Two different definitions for the chemical potential and thermodynamic pressure far from equilibrium are introduced: nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant heat flux q and nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant J = Vq, where V is the specific volume.
Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases
2022
We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.