Resolving Conflict through Explicit Bargaining

This article analyzes the impact of conciliatory initiatives on conflict resolution in two-party bargaining. It specifically develops and tests a theory of unilateral initiatives derived from Osgood\u27s (1962) notion of Graduated and Reciprocated Initiatives in Tension Reduction (GRIT). The major propositions of the theory indicate that, given a pattern of mutual resistance or hostility, unilateral initiatives and tit-for-tat retaliation in response to punitive action will produce more conciliation and less hostility by an opponent. To test the theory, a bargaining setting was created in a laboratory experiment in which parties exchanged offers and counteroffers on an issue across a number of rounds while also having the option to engage in punitive action against one another. The results indicated that (1) unilateral initiatives produced more concession making and less hostility than a reciprocity strategy, and (2) tit-for-tat retaliation heightened hostility initially but reduced it over time. The article suggests some general, abstract conditions under which two parties in conflict can produce conciliation and reach agreements without the intervention of third parties

On optimal control in a nonlinear interface problem described by hemivariational inequalities

The purpose of this paper is three-fold. Firstly we attack a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions. The investigated problem involves a nonlinear monotone partial differential equation in the interior domain and the Laplacian in the exterior domain. Such a scalar interface problem models nonmonotone frictional contact of elastic infinite media. The variational formulation of the interface problem leads to a hemivariational inequality (HVI), which however lives on the unbounded domain, and thus cannot analyzed in a reflexive Banach space setting. By boundary integral methods we obtain another HVI that is amenable to functional analytic methods using standard Sobolev spaces on the interior domain and Sobolev spaces of fractional order on the coupling boundary. Secondly broadening the scope of the paper, we consider extended real-valued HVIs augmented by convex extended real-valued functions. Under a smallness hypothesis, we provide existence and uniqueness results, also establish a stability result with respect to the extended real-valued function as parameter. Thirdly based on the latter stability result, we prove the existence of optimal controls for four kinds of optimal control problems: distributed control on the bounded domain, boundary control, simultaneous distributed-boundary control governed by the interface problem, as well as control of the obstacle driven by a related bilateral obstacle interface problem.Comment: 26 pages, no figures. arXiv admin note: text overlap with arXiv:2112.1217

Preconditioning for Allen-Cahn variational inequalities with non-local constraints

The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach

Preconditioning for Allen-Cahn variational inequalities with non-local constraints

The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach

An upwind least square formulation for free surfaces calculation of viscoplastic steady-state metal forming problems

International audienceDespite using very large parallel computers, numerical simulation of some forming processes such as multi-pass rolling, extrusion or wire drawing, need long computation time due to the very large number of time steps required to model the steady regime of the process. The direct calculation of the steady-state, whenever possible, allows reducing by 10–20 the computational effort. However, removing time from the equations introduces another unknown, the steady final shape of the domain. Among possible ways to solve this coupled multi-fields problem, this paper selects a staggered fixed-point algorithm that alternates computation of mechanical fields on a prescribed domain shape with corrections of the domain shape derived from the velocity field and the stationary condition v.n = 0. It focuses on the resolution of the second step in the frame of unstructured 3D meshes, parallel computing with domain partitioning, and complex shapes with strong contact restraints. To insure these constraints a global finite elements formulation is used. The weak formulation based on a Galerkin method of the v.n = 0 equation is found to diverge in severe tests cases. The least squares formulation experiences problems in the presence of contact restraints, upwinding being shown necessary. A new upwind least squares formulation is proposed and evaluated first on analytical solutions. Contact being a key issue in forming processes, and even more with steady formulations, a special emphasis is given to the coupling of contact equations between the two problems of the staggered algorithm, the thermo-mechanical and free surface problems. The new formulation and algorithm is finally applied to two complex actual metal forming problems of rolling. Its accuracy and robustness with respect to the shape initialization of the staggered algorithm is discussed, and its efficiency is compared to non-steady simulations