NIRA-3: An improved MATLAB package for finding Nash equilibria in infinite games

A powerful method for computing Nash equilibria in constrained, multi-player games is created when the relaxation algorithm and the Nikaido-Isoda function are used together in a suite of MATLAB routines. This paper updates the MATLAB suite described in \cite{Berridge97} by adapting them to MATLAB 7. The suite is now capable of solving both static and open-loop dynamic games. An example solving a coupled constraints game using the suite is provided.Nikaido-Isoda function; Coupled constraints

Using a finite horizon numerical optimisation method for a periodic optimal control problem

Computing a numerical solution to a periodic optimal control problem is difficult. A method of approximating a solution to a given (stochastic) optimal control problem using Markov chains was developed in [3]. This paper describes an attempt at applying this method to a periodic optimal control problem introduced in [2].Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains

Dendritic structure analysis of CMSX-4 cored turbine blades roots

The microstructure of as-cast cored turbine blades roots, made of the single-crystal CMSX-4 nickel-based superalloy was investigated. Analysed blades were obtained by directional solidification technique in the industrial ALD Bridgman induction furnace. The investigations of the microstructure of blades roots were performed using SEM and X-ray techniques including diffraction topography with the use of Auleytner method. Characteristic shapes of dendrites with various arrangement were observed on the SEM images taken from the cross-sections, made transversely to the main blades axis. The differences in quality of the structure in particular areas of blades roots were revealed. Based on the results, the influence of cooling bores on blades root structure was analysed and the changes in the distribution and geometry of cooling bores were proposed

InfSOCSol2: an updated MATLAB package for approximating the solution to a continuous-time infinite horizon stochastic optimal control problem

This paper describes a suite of MATLAB routines devised to provide an approximately optimal solution to an infinite-horizon stochastic optimal control problem. The suite is an updated version of that described in [Kra01b]. Its routines implement a policy improvement algorithm to optimise a Markov decision chain approximating the original control problem, as described in [Kra01c].Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains

How to use Rosen's normalised equilibrium to enforce a socially desirable Pareto efficient solution

We consider a situation, in which a regulator believes that constraining a complex good created jointly by competitive agents, is socially desirable. Individual levels of outputs that generate the constrained amount of the externality can be computed as a Pareto efficient solution of the agents' joint utility maximisation problem. However, generically, a Pareto efficient solution is not an equilibrium. We suggest the regulator calculates a Nash-Rosen coupled-constraint equilibrium (or a “generalised” Nash equilibrium) and uses the coupled-constraint Lagrange multiplier to formulate a threat, under which the agents will play a decoupled Nash game. An equilibrium of this game will possibly coincide with the Pareto efficient solution. We focus on situations when the constraints are saturated and examine, under which conditions a match between an equilibrium and a Pareto solution is possible. We illustrate our findings using a model for a coordination problem, in which firms' outputs depend on each other and where the output levels are important for the regulator.

Development of Composites with Icosahedral Phase in Al-Cu-Fe Quasicrystalline Alloys Obtained by the Bridgman Method

The composites were obtained by the Bridgman method through solidi cation of Al61Cu27Fe12 alloy (numbers indicate at.%). The microstructure of composites with crystal matrix and quasicrystal reinforcement was studied. The crystalline -phase was the matrix and the quasicrystaline i-phase was the reinforcement of obtained composites. The shape and spatial distribution of reinforcement bres were speci ed. Some geometrical relations of the bres arrangement were de ned. Obtained composite samples were subjected to X-ray phase analysis, optical, and scanning electron microscopy observations, chemical microanalysis and the Laue di raction

A viability theory approach to a two-stage optimal control problem of technology adoption

A new technology adoption problem can be modelled as a two-stage control problem, in which model parameters ("technology") might be altered at some time. An optimal solution to utility maximisation for this class of problems needs to contain information on the time, at which the change will take place (0, finite or never), along with the optimal control strategies before and after the change. For the change, or switch, to occur the "new technology" value function needs to dominate the "old technology" value function, after the switch. We charaterise the value function using the fact that its hypograph is a viability kernel of an auxiliary problem and we study when the graphs can intersect. If they do not, the switch cannot occur at a positive time. Using this characterisation we analyse a technology adoption problem and showmodels, for which the switch will occur at time zero or never.technology adoption, value function, viability kernel, viscosity solutions

InfSOCSol2 An updated MATLAB Package for Approximating the Solution to a Continuous-Time Infinite Horizon Stochastic Optimal Control Problem with Control and State Constraints

This paper is a successor of [AK08]. Both papers describe the same suite of MATLAB R° routines devised to provide an approximately optimal solution to an infinite horizon stochastic optimal control problem. The difference is that this paper explains how to allow for state and control constraints. The suite routines implement a policy improvement algorithm to optimise a Markov decision chain approximating the original control problem, as described in [Kra01c] and [Kra01b].Computational economics, Financial engineering, Approximating Markov decision chains

A report on using parallel MATLAB for solutions to stochastic optimal control problems

Parallel MATLAB is a recent MathWorks product enabling the use of parallel computing methods on multicore personal computers. SOCSol is the generic name of a suite of MATLAB routines that can be used to obtain optimal solutions to continuous-time stochastic optimal control problems. In this report, we compare the performance of a new version of SOCSol utilising parallel MATLAB with that of another version not using parallel computing methods.Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains

Can planners control competitive generators?

Consider an electricity market populated by competitive agents using thermal generating units. Generation often emits pollution which a planner may wish to constrain through regulation. Furthermore, generators’ ability to transmit energy may be naturally restricted by the grid’s facilities. The existence of both pollution standards and transmission constraints can impose several restrictions upon the joint strategy space of the agents. We propose a dynamic, game-theoretic model capable of analysing coupled constraints equilibria (also known as generalised Nash equilibria). Our equilibria arise as solutions to the planner’s problem of avoiding both network congestion and excessive pollution. The planner can use the coupled constraints’ Lagrange multipliers to compute the charges the players would pay if the constraints were violated. Once the players allow for the charges in their objective functions they will feel compelled to obey the constraints in equilibrium. However, a coupled constraints equilibrium needs to exist and be unique for this modification of the players’ objective functions ..[there was a “to” here, incorrect?].. induce the required behaviour. We extend the three-node dc model with transmission line constraints described in [10] and [2] to utilise a two-period load duration curve, and impose multi-period pollution constraints. We discuss the economic and environmental implications of the game’s solutions as we vary the planner’s preferences.