An evolutionary algorithmic approach to determine the Nash equilibrium in a duopoly with nonlinearities and constraints

This paper presents an algorithmic approach to obtain the Nash Equilibrium in a duopoly. Analytical solutions to duopolistic competition draw on principles of game theory and require simplifying assumptions such as symmetrical payoff functions, linear demand and linear cost. Such assumptions can reduce the practical use of duopolistic models. In contrast, we use an evolutionary algorithmic approach (EAA) to determine the Nash equilibrium values. This approach has the advantage that it can deal with and find optimum values for duopolistic competition modelled using non-linear functions. In the paper we gradually build up the competitive situation by considering non-linear demand functions, non-linear cost functions, production and environmental constraints, and production in discrete bands. We employ particle swarm optimization with composite particles (PSOCP), a variant of particle swarm optimization, as the evolutionary algorithm. Through the paper we explicitly demonstrate how EAA can solve games with constrained payoff functions that cannot be dealt with by traditional analytical methods. We solve several benchmark problems from the literature and compare the results obtained from EAA with those obtained analytically, demonstrating the resilience and rigor of our EAA solution approach

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGMp/q) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGMp/q and the NDGMp/q can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGMp/q was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGMp/q and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGMp/q was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model

A prediction method for plasma concentration by using a nonlinear grey Bernoulli combined model based on a self-memory algorithm

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The goal of this work is to present and explore the application of a novel nonlinear grey Bernoulli combined model based on a self-memory algorithm, abbreviated as SA-NGBM, for modeling single-peaked sequences of time samples of acetylsalicylate plasma concentration following oral dosing. The self-memorization SA-NGBM routine reduces the dependence on a solitary initial value, as the initial state of the model utilizes multiple time samples. To test its forecasting performance, the SA-NGBM was used to extrapolate the plasma concentration predicted data, in comparison with the later time samples. The results were contrasted with those of the traditional optimized NGBM (ONGBM), exponential smoothing (ES) and simple moving average (SMA) using four popular accuracy and significance tests. That comparison showed that the SA-NGBM was much more accurate and efficient for matching the individual, nonlinear-system stochastic fluctuations than the existing ONGBM, ES and SMA models. The findings have potential applications for signal matching to similar small sample size, single-peaked, plasma concentration series